Datasets:

Mohamed-BC

/

papers-data

like 0

['Peter Wittek', 'Sándor Darányi', 'Efstratios Kontopoulos', 'Theodoros Moysiadis', 'Ioannis Kompatsiaris']

1502.01753v1

Based on the Aristotelian concept of potentiality vs. actuality allowing for the study of energy and dynamics in language, we propose a field approach to lexical analysis. Falling back on the distributional hypothesis to statistically model word meaning, we used evolving fields as a metaphor to express time-dependent changes in a vector space model by a combination of random indexing and evolving self-organizing maps (ESOM). To monitor semantic drifts within the observation period, an experiment was carried out on the term space of a collection of 12.8 million Amazon book reviews. For evaluation, the semantic consistency of ESOM term clusters was compared with their respective neighbourhoods in WordNet, and contrasted with distances among term vectors by random indexing. We found that at 0.05 level of significance, the terms in the clusters showed a high level of semantic consistency. Tracking the drift of distributional patterns in the term space across time periods, we found that consistency decreased, but not at a statistically significant level. Our method is highly scalable, with interpretations in philosophy.

Monitoring Term Drift Based on Semantic Consistency in an Evolving Vector Field

http://arxiv.org/pdf/1502.01753v1

Title Monitoring Term Drift Based Semantic Consistency Evolving Vector Field Summary Based Aristotelian concept potentiality v actuality allowing study energy dynamic language propose field approach lexical analysis Falling back distributional hypothesis statistically model word meaning used evolving field metaphor express timedependent change vector space model combination random indexing evolving selforganizing map ESOM monitor semantic drift within observation period experiment carried term space collection 128 million Amazon book review evaluation semantic consistency ESOM term cluster compared respective neighbourhood WordNet contrasted distance among term vector random indexing found 005 level significance term cluster showed high level semantic consistency Tracking drift distributional pattern term space across time period found consistency decreased statistically significant level method highly scalable interpretation philosophy Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.030528267845511436, 0.04965444281697273, -0.031217029318213463, 0.022996678948402405, -0.03168976306915283, -0.0291778314858675, -0.01496312115341425, 0.028549542650580406, -0.07261703163385391, -0.051482826471328735, 0.042648691684007645, -0.005036256276071072, 0.02993091568350792, 0.008601434528827667, -0.0091627212241292, -0.04660870134830475, 0.07180064171552658, 0.02498958259820938, -0.035348519682884216, 0.04201918840408325, 0.016351107507944107, -0.013373502530157566, -0.00603986531496048, 0.027236413210630417, -0.0029455965850502253, -0.0036968758795410395, -0.012511743232607841, -0.06405196338891983, 0.027976080775260925, -0.0325157530605793, -0.002379929181188345, 0.03751840814948082, 0.010421236976981163, 0.08666123449802399, 2.435229362163227e-06, -0.07799794524908066, -0.040837567299604416, -0.01628657802939415, 0.026286592707037926, 0.006855989806354046, 0.09621009230613708, 0.030329842120409012, -0.011494185775518417, -0.05080016329884529, -0.03251912072300911, 0.024486586451530457, 0.03400389105081558, -0.037506554275751114, 0.017615042626857758, 0.0037620870862156153, -0.009574532508850098, -0.03767981752753258, 0.009884708561003208, -0.014006652869284153, 0.009004911407828331, -0.027552373707294464, 0.03851635754108429, -0.004017136991024017, -0.025639746338129044, 0.012285460717976093, -0.07826646417379379, 0.022332720458507538, -0.02317408099770546, -0.0030178932938724756, 0.03889143094420433, 0.011528088711202145, -0.036133356392383575, 0.008424589410424232, 0.02231060527265072, -0.002762443386018276, 0.060178954154253006, 0.009143763221800327, -0.015625057741999626, -0.007684940937906504, -0.049494609236717224, 0.04145980253815651, -0.02940892055630684, -0.0003096777945756912, -0.006467531900852919, -0.03041757084429264, 0.07934892922639847, 0.030350729823112488, -0.02438884787261486, 0.031569935381412506, -0.03740786015987396, 0.0843549370765686, 0.03708804398775101, -0.05413594841957092, -0.018528824672102928, -0.029153887182474136, -0.004274412523955107, -0.07313578575849533, 0.00549773033708334, 0.005776381120085716, 0.01442581694573164, 0.0557975247502327, 0.0316469669342041, -0.06434188783168793, 0.028075311332941055, -0.11362796276807785, -0.0018542652251198888, 0.02057897299528122, -0.014608935452997684, 0.017317067831754684, 0.07065465301275253, 0.036178115755319595, 0.028267305344343185, -0.018354471772909164, -0.039994098246097565, 0.036319855600595474, -0.0591994933784008, -0.013341897167265415, -0.033797841519117355, 0.01594356819987297, 0.01136952918022871, -0.036993905901908875, -0.08550301939249039, -0.006791239138692617, 0.02230427786707878, -0.022767798975110054, -0.08187884092330933, -0.00869271345436573, -0.013196875341236591, 0.006894140504300594, -0.029867222532629967, 0.03280753642320633, -0.042852453887462616, 0.015148871578276157, -0.034958984702825546, -0.028537161648273468, 0.013022411614656448, -0.018814539536833763, -0.033959727734327316, -0.026533884927630424, -0.014785287901759148, 0.01025187037885189, 0.038798797875642776, -0.04304559528827667, -0.05180862918496132, -0.040287140756845474, -0.0756520926952362, 0.00910461787134409, -0.05099796503782272, -0.05075548589229584, -0.003575294278562069, -0.0017064495477825403, -0.0013982763048261404, -0.023280765861272812, -0.009732801467180252, 0.028031345456838608, -0.05113733932375908, 0.04658546298742294, -0.07408364862203598, -0.0004025830130558461, 0.022736186161637306, 0.009416152723133564, 0.08127669245004654, 0.03334110602736473, 0.03864459693431854, -0.01632879674434662, 0.04861358925700188, 0.016452286392450333, -0.037413228303194046, -0.015022223815321922, -0.007946688681840897, 0.023882735520601273, -0.06507191061973572, 0.00024725202820263803, 0.010377815924584866, 0.047662630677223206, -0.024272168055176735, 0.007964568212628365, 0.0011654284317046404, 0.015211516991257668, 0.023569054901599884, 0.08009088039398193, -0.023963475599884987, 0.047158267349004745, -0.016845790669322014, -0.03530552238225937, -0.007757723797112703, 0.03811866044998169, 0.03440795838832855, -0.022234490141272545, 0.009607446379959583, -0.011135616339743137, -0.013415937311947346, -0.03966134414076805, 0.01489944290369749, -0.052065007388591766, -0.025262439623475075, 0.03605566918849945, -0.0017203715397045016, -0.07097975164651871, 0.03813299164175987, 0.004075843840837479, 0.031406715512275696, 0.04671287164092064, 0.055871736258268356, -0.033672042191028595, -0.013173280283808708, -0.024245617911219597, 0.037962403148412704, 0.056791387498378754, 0.03203180059790611, -0.022782443091273308, -0.04336758702993393, 0.024516310542821884, 0.04069874435663223, 0.020523332059383392, -0.009371560998260975, 0.02827763929963112, -0.03573456034064293, -0.028944358229637146, 0.0053889695554971695, -0.026081262156367302, -0.009918068535625935, -0.006387264933437109, -0.08621476590633392, 0.08403237164020538, -0.0009765623835846782, 0.007373705506324768, -0.029006071388721466, 0.04588699713349342, -0.011350001208484173, -0.003806296968832612, -0.03945736587047577, -0.02397853508591652, 0.006651199888437986, -0.002114949282258749, -0.03482118993997574, 0.012432497926056385, 1.7481566828791983e-05, -0.032264336943626404, -0.002245955402031541, 0.06042783707380295, -0.0020975086372345686, 0.09554348140954971, 0.05157652497291565, 0.00581338070333004, 0.029686234891414642, -0.02415178343653679, 0.0027596899308264256, -0.019352566450834274, 0.04072515666484833, -0.04749959707260132, 0.09426026791334152, -0.03682559356093407, 0.0362575501203537, -0.047849010676145554, 0.06578712165355682, -0.013407280668616295, 0.046744707971811295, -0.014254995621740818, 0.047959890216588974, -0.045973315834999084, 0.04664018005132675, 0.041334979236125946, 0.05027402192354202, -0.0020603309385478497, 0.032497987151145935, 0.024125836789608, -0.020482081919908524, 0.07105942815542221, -0.026596279814839363, -0.057643089443445206, 0.01725868321955204, -0.015314729884266853, -0.004601437598466873, -0.003506438108161092, 0.005719411186873913, 0.02231254056096077, 0.00694252410903573, -0.020658884197473526, 0.050085246562957764, 0.06328994035720825, 0.018454905599355698, -0.013112828135490417, 0.021109547466039658, 0.03969613462686539, -0.03487101569771767, -0.02853141352534294, -0.04226413741707802, 0.0077535370364785194, -0.012796364724636078, 0.047555264085531235, 0.05837314575910568, -0.0325080044567585, -0.01090957596898079, 0.014216842129826546, -0.07467250525951385, -0.050784334540367126, -0.014344236813485622, -0.011490429751574993, 0.004620051477104425, 0.011771229095757008, 0.03239910304546356, -0.017873447388410568, 0.08114936202764511, 0.07195402681827545, 0.045594945549964905, -0.06977923959493637, -0.005676243919879198, -0.05315841734409332, -0.017732372507452965, -0.024475017562508583, -0.0016488711116835475, 0.007543657906353474, 0.058884214609861374, 0.07473654299974442, 0.020958872511982918, -0.010897261090576649, -0.0017041023820638657, 0.03836570307612419, -0.08889231830835342, 0.023170534521341324, -0.023497339338064194, -0.000277585320873186, -0.06305152922868729, 0.02737600915133953, -0.010218972340226173, -0.013387903571128845, 0.02319279871881008, 0.020809752866625786, 0.02171662263572216, -0.06363490968942642, -0.01847470924258232, -0.010825609788298607, 0.048469655215740204, -0.0387364998459816, 0.03773892670869827, 0.03489498794078827, -0.017882097512483597, -0.022994520142674446, -0.05895106494426727, 0.02177542634308338, -0.029823865741491318, 0.05331101641058922, -0.047465622425079346, 0.019707536324858665, 0.014769208617508411, 0.0383763313293457, -0.006593338213860989, 0.022199342027306557, -0.00651034340262413, 0.02249074913561344, 0.062268346548080444, -0.011346728540956974, 0.017255043610930443, 0.025769570842385292, -0.02469775266945362, 0.01449087355285883, 0.021329278126358986, -0.03282740339636803, -0.006330403033643961, -0.009258370846509933, 0.03648842126131058, 0.001853122259490192, -0.027305161580443382, 0.011159808374941349, -0.009201106615364552, 0.06783144921064377, -0.060432299971580505, -0.02168397419154644, -0.07539047300815582, 0.0015413512010127306, 0.009372965432703495, -0.06995466351509094, -0.011423182673752308, -0.020190604031085968, -0.04708268493413925, -0.07385957986116409, -0.015454346314072609, 0.08742494881153107, 0.049379199743270874, -0.013108539395034313, 0.04479410499334335, -0.06180237978696823, -0.04434666410088539, 0.01155906356871128, -0.009515888057649136, -0.04893392696976662, 0.0236885417252779, -0.021716739982366562, 0.0033753870520740747, -0.00569252111017704, -0.04882293567061424, -0.03860308229923248, -0.03047371096909046, 0.0004721403820440173, -0.007449972443282604, -0.046057917177677155, 0.0580594576895237, -0.011216267943382263, 0.024428274482488632, 0.0006044682231731713, -0.02100307308137417, 0.008631561882793903, 0.021775128319859505, 0.018217647448182106, 0.017742879688739777, -0.05753190815448761, -0.004498541355133057, 0.00487259728834033, -0.04679155349731445, 0.029566770419478416, 0.06208290159702301, 0.09340991824865341, -0.06264029443264008, -0.07880240678787231, 0.008333109319210052, -0.02009294554591179, -0.01190182939171791, -0.06394393742084503, 0.004296998027712107, -0.005370371043682098, 0.025297019630670547, 0.008692465722560883, -0.033354539424180984, 0.026633823290467262, -0.022128112614154816, 0.04468756541609764, 0.0446416400372982, -0.024915605783462524, -0.031153477728366852, -0.08668579161167145, 0.014517204836010933, -0.019492948427796364, 0.0024227637331932783, -0.01577536202967167, 0.012436111457645893, 0.022876163944602013, 0.011585875414311886, 0.033046968281269073, 0.056640397757291794, -0.03432735055685043, -0.049868348985910416, -0.03465964272618294, -0.05192890390753746, -0.07380247116088867, -0.005494172219187021, -0.03951520100235939, 0.026279304176568985, 0.029602892696857452, 0.041713450103998184, -0.013791128993034363, -0.01502805482596159, -0.0658353790640831, -0.025424716994166374, 0.05475937947630882, 0.01281353272497654, 0.014479194767773151, -0.016378670930862427, 0.052089713513851166, 0.030641794204711914, -0.030921541154384613, 0.01259568054229021, -0.020253071561455727, -0.05817028135061264, 0.060559455305337906, -0.0193793848156929, 0.022598644718527794, 0.0050334022380411625, 0.013526245020329952, -0.006113425828516483, 0.014185058884322643, 0.006200662814080715, 0.01283483486622572, 0.04709581658244133, -0.026403246447443962, 0.04185491427779198, -0.0008355581085197628, -0.0003856950788758695, 0.006789152976125479, 0.03399491682648659, -0.003977663349360228, 0.02346709370613098, -0.049181051552295685, -0.022775890305638313, 0.02454655058681965, -0.004420117940753698, 0.030767517164349556, -0.0276830792427063, -0.02561579830944538, 0.009640256874263287, -0.0399460643529892, 0.022184589877724648, -0.0375286228954792, -0.0029227312188595533, -0.0005543328006751835, -0.002252019476145506, -0.02408462017774582, -0.046344805508852005, 0.06453169137239456, -0.042662862688302994, -0.019548216834664345, 0.03271887078881264, -0.01636926643550396, -0.018879665061831474, 0.050136491656303406, -0.004921321291476488, 0.051185399293899536, 0.028008921071887016, -0.04475827142596245, -0.035949576646089554, 0.04320945218205452, -0.017114048823714256, 0.017491471022367477, 0.03911227732896805, -0.026236047968268394, -0.02358892746269703, 0.014268469996750355, -0.026441289111971855, -0.01740858517587185, -0.0050679403357207775, 0.04186674579977989, 0.011781961657106876, -0.001033823937177658, 0.02733495831489563, -0.05655290558934212, 0.0063178990967571735, -0.015893779695034027, -0.00548079889267683, -0.00644152844324708, -0.006254780571907759, 0.03184502571821213, 0.008461455814540386, -0.010688531212508678, 0.004609188064932823, -0.0013999183429405093, -0.03689606115221977, -0.00653916597366333, 0.0007940185605548322, -0.040323853492736816, 0.006361843552440405, 0.019144387915730476, -0.009504923596978188, -0.02805313654243946, -0.004570056684315205, 0.013290860690176487, -0.08017803728580475, -0.011934265494346619, 0.04710300639271736, 0.0021791497711092234, 0.027444420382380486, -0.006376005243510008, 0.027382684871554375, 0.07490118592977524, 0.03184368833899498, -0.026104798540472984, -0.02107074111700058, 0.014966798946261406, -0.07008986920118332, 0.0044264765456318855, -0.026689598336815834, -6.307812889107784e-33, -0.030881408601999283, -0.03082484006881714, 0.025345103815197945, -0.01705194264650345, -0.09703590720891953, 0.013576415367424488, -0.0314263291656971, -0.006030462682247162, 0.02399502322077751, 0.02361932583153248, 0.03450324386358261, 0.026553697884082794, -0.01183738000690937, -0.038159411400556564, 0.06806635856628418, 0.0009137901361100376, -0.0012512888060882688, 0.014272303320467472, -0.0011478544911369681, -0.013584436848759651, 0.10351604968309402, 0.01622818037867546, 0.07980117946863174, -0.022596795111894608, 0.07535356283187866, 0.0309537835419178, 0.023762889206409454, -0.01897539757192135, 0.0348581038415432, -0.021076977252960205, -0.005696214735507965, 0.02748124487698078, 0.028617864474654198, -0.025397034361958504, 0.007249000482261181, -0.03329620882868767, 0.02846386283636093, -0.09257390350103378, 0.021630628034472466, 0.01510652806609869, 5.689425233867951e-05, 0.005734355188906193, 0.024846602231264114, 0.04032693803310394, -0.07329981029033661, 0.046194516122341156, 0.057326845824718475, -0.02286243624985218, -0.05529521778225899, -0.022150058299303055, -0.04879409447312355, 0.0402308888733387, -0.017024599015712738, 0.0262044258415699, -0.009642507880926132, -0.06905727088451385, 0.027395496144890785, 0.020470261573791504, -0.05944141000509262, 0.01591506227850914, -0.00849156640470028, 0.03266509622335434, 0.024216599762439728, 0.026435034349560738, 0.01368865929543972, 0.03907128795981407, -0.0028514377772808075, -0.0016091844299808145, 0.008331202901899815, 0.03021450899541378, 0.029121091589331627, 0.0413169302046299, 0.017328646034002304, 0.003489740425720811, 0.06045214459300041, -0.049543753266334534, -0.005755518563091755, 0.00458972854539752, 0.022184517234563828, 0.06810364872217178, -0.004720281343907118, -0.014184569008648396, -0.021354850381612778, -0.0006069856463000178, 0.01592060923576355, 0.011531692929565907, -0.01180227566510439, -0.027119064703583717, -0.009445341303944588, -0.040970489382743835, 0.022385941818356514, -0.01159621775150299, -0.03610138222575188, -0.042681943625211716, -0.005650235339999199, -0.025749990716576576, -0.04848917946219444, -0.01022428274154663, 0.013565911911427975, 0.023976223543286324, -0.01943308673799038, 0.006678590085357428, -0.04868059977889061, 0.048827581107616425, 0.0022249051835387945, -0.02218407206237316, -0.02990094944834709, -0.0013930569402873516, 0.011500193737447262, -0.021375300362706184, 0.04449789971113205, -0.08307119458913803, -0.004468155093491077, -0.05824360251426697, -0.005114505533128977, 0.00865913461893797, -0.005672820843756199, 0.06953263282775879, 0.10872131586074829, 0.03287414088845253, -0.010546915233135223, 0.029536426067352295, 0.02746909111738205, 0.04807286709547043, -0.02494613453745842, 0.009298904798924923, -0.02307184971868992, 0.0330539345741272, 0.06887192279100418, -0.05696449428796768, -0.02020157314836979, -0.013827196322381496, 3.13787410277655e-07, 0.05353768542408943, 0.050486527383327484, -0.009387720376253128, -0.012162198312580585, 0.002922635991126299, -0.009715205989778042, -0.04448993131518364, 0.041595589369535446, -0.03967950865626335, -0.004917786456644535, -0.003822960192337632, -0.027768170461058617, 0.0036373031325638294, 0.04625863581895828, -0.013318398036062717, -0.025496572256088257, -0.0974341332912445, 0.0008356138714589179, -0.08936008810997009, 0.05710857734084129, 0.04528630152344704, 0.007081767078489065, 0.042772576212882996, -0.026558317244052887, -0.02368193306028843, -0.02079751528799534, 0.02169938012957573, 0.004788399673998356, 0.011267893947660923, 0.054883748292922974, 0.004116470459848642, -0.004463981371372938, 0.005503050051629543, -0.03232884407043457, -0.0034634254407137632, 0.029995722696185112, -0.0035698730498552322, -0.025732656940817833, -0.026977067813277245, 0.041245121508836746, -0.006410366389900446, -0.02646382711827755, 0.018299512565135956, -0.04109475761651993, 0.03294161334633827, 0.0017112178029492497, -0.013417842797935009, -0.07695949077606201, -0.019021108746528625, 0.04517583176493645, 0.07037413865327835, 0.017652004957199097, -0.03828941658139229, 0.004602956119924784, 0.014821657910943031, 0.020846787840127945, -0.05056627467274666, -0.07764995843172073, 0.02002333104610443, 0.031026987358927727, -0.012659643776714802, -0.04816918820142746, -0.0029706917703151703, 0.013108395971357822, 0.0025575091131031513, -0.010986854322254658, 0.001998988911509514, 2.770578195928225e-34, 0.033421944826841354, -0.010044768452644348, -0.00783015787601471, 0.006939553190022707, -0.02511899173259735, 0.01848035864531994, 0.04050484672188759, 0.040675513446331024, 0.0053232633508741856, -0.02193061262369156, -0.00955582782626152]

['Jan Chorowski', 'Navdeep Jaitly']

1612.02695v1

The recently proposed Sequence-to-Sequence (seq2seq) framework advocates replacing complex data processing pipelines, such as an entire automatic speech recognition system, with a single neural network trained in an end-to-end fashion. In this contribution, we analyse an attention-based seq2seq speech recognition system that directly transcribes recordings into characters. We observe two shortcomings: overconfidence in its predictions and a tendency to produce incomplete transcriptions when language models are used. We propose practical solutions to both problems achieving competitive speaker independent word error rates on the Wall Street Journal dataset: without separate language models we reach 10.6% WER, while together with a trigram language model, we reach 6.7% WER.

Towards better decoding and language model integration in sequence to sequence models

http://arxiv.org/pdf/1612.02695v1

Title Towards better decoding language model integration sequence sequence model Summary recently proposed SequencetoSequence seq2seq framework advocate replacing complex data processing pipeline entire automatic speech recognition system single neural network trained endtoend fashion contribution analyse attentionbased seq2seq speech recognition system directly transcribes recording character observe two shortcoming overconfidence prediction tendency produce incomplete transcription language model used propose practical solution problem achieving competitive speaker independent word error rate Wall Street Journal dataset without separate language model reach 106 WER together trigram language model reach 67 WER Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.02097560651600361, 0.07567127794027328, 0.01599881425499916, 0.03510940074920654, -0.020172972232103348, 0.010558419860899448, -0.004460576921701431, -0.018668076023459435, -0.033789921551942825, -0.0422428734600544, -0.02375395968556404, -0.04202241078019142, 0.060631562024354935, 0.06385961920022964, 0.028060397133231163, -0.039579831063747406, 0.04060348495841026, -0.012209617532789707, 0.0344073586165905, 0.02504158951342106, 0.017609354108572006, 0.004111291375011206, 0.006500408053398132, 0.06688769161701202, 0.032120753079652786, 0.0044698272831737995, -0.022372541949152946, -0.010449827648699284, -0.02675403282046318, -0.03192843124270439, -0.00757574150338769, 0.09024613350629807, 0.017829125747084618, 0.061050526797771454, 2.2921249183127657e-06, -0.029924266040325165, -0.015870612114667892, -0.026062166318297386, -0.02994951419532299, 0.024116482585668564, 0.01482919231057167, -0.018244806677103043, -0.025815853849053383, 0.0527682788670063, -0.012651178985834122, -0.0016564643010497093, 0.05397673323750496, 0.02930067479610443, 0.02749190665781498, 0.039189841598272324, -0.017718534916639328, -0.0527728870511055, 0.05039612576365471, -0.0029894595500081778, 0.0031788842752575874, -0.0193362794816494, 0.02051263488829136, -0.012057104147970676, 0.023654254153370857, 0.0019985903054475784, -0.014929145574569702, 0.040818434208631516, -0.021364906802773476, -0.03219066932797432, 0.0037895827554166317, 0.004973142873495817, -0.025283431634306908, -0.04943776875734329, -0.019483208656311035, 0.057851824909448624, -0.01342079322785139, -0.008140859194099903, 0.016980227082967758, 0.024678872898221016, -0.0007788331131450832, -0.03765607252717018, -0.03229999169707298, -0.007897170260548592, -0.013875787146389484, -0.01645299792289734, 0.032278209924697876, 0.028318224474787712, -0.004555308260023594, -0.0318402461707592, -0.013307576067745686, 0.0001841284683905542, 0.009048251435160637, -0.015339873731136322, -0.021619481965899467, -0.033244840800762177, 0.008639366365969181, -0.036904022097587585, 0.052962180227041245, 0.024463769048452377, -0.0007445060182362795, 0.018205299973487854, -0.030011383816599846, -0.08864792436361313, 0.0020263127516955137, -0.061078090220689774, 0.03768830746412277, 0.04448571056127548, 0.0012025239411741495, 0.014210516586899757, -0.0016411775723099709, 0.07337087392807007, 0.019215799868106842, -0.024495985358953476, -0.03470104932785034, 0.02722257189452648, 0.0030884507577866316, -0.018628083169460297, -0.03295895829796791, 0.01811468042433262, -0.005974314175546169, -0.046482838690280914, -0.0650450810790062, -0.011868655681610107, 0.026743071153759956, -0.006074727512896061, 0.020799292251467705, -0.0013770991936326027, -0.03476253151893616, -0.025128960609436035, 0.013163595460355282, 0.029070476070046425, 0.030302416533231735, 0.027783716097474098, -0.021247172728180885, -0.05922272056341171, 0.01068487111479044, 0.010091399773955345, -0.0025645194109529257, 0.017734570428729057, -0.01987830363214016, 0.07564353942871094, 0.022287016734480858, -0.034920960664749146, -0.013805489987134933, 0.005596152972429991, -0.041755013167858124, -0.0240129753947258, -0.05344938114285469, -0.10257254540920258, 0.034719932824373245, 0.006807108875364065, -0.040810663253068924, -0.021381638944149017, 0.03302175551652908, 0.005883719306439161, -0.024692369624972343, 0.06356197595596313, -0.036518096923828125, 0.009842462837696075, 0.05426834151148796, 0.013168161734938622, 0.07059279829263687, 0.04145057871937752, 0.077054463326931, -0.04040208458900452, 0.012874494306743145, -0.05681212246417999, 0.004333576653152704, 0.06947354227304459, -0.009206549264490604, -0.01807338371872902, -0.04919153451919556, -0.02718479000031948, 0.03022814728319645, -0.008508032187819481, 0.03205104544758797, 0.08079670369625092, 0.005611268803477287, 0.001151544158346951, 0.044270459562540054, 0.10314585268497467, 0.01841237209737301, 0.012287243269383907, -0.02116256020963192, 0.016434362158179283, 0.029999352991580963, 0.010078713297843933, 0.0074335066601634026, 0.01655680686235428, 0.02819584682583809, 0.021525511518120766, 0.04680124297738075, 0.04284261167049408, 0.003328952006995678, -0.04575447365641594, -0.026209047064185143, -0.03529033437371254, 0.01023299340158701, -0.007796078454703093, 0.04978814348578453, -0.02414451539516449, -0.0613928958773613, 0.02144128642976284, 0.0038753701373934746, -0.05152818560600281, 0.0024514892138540745, -0.020312830805778503, 0.003496347926557064, 0.0357782207429409, 0.025192007422447205, 0.009080859832465649, 0.018072206526994705, -0.053216658532619476, -0.04039574787020683, 0.016669899225234985, 0.010361449792981148, -0.006683418992906809, -0.014391216449439526, -0.06724324077367783, 0.008057682774960995, 0.07427369058132172, 0.020040780305862427, 0.020427575334906578, -0.03897050768136978, 0.03779216855764389, 0.03890688717365265, 0.06976694613695145, -0.04590022936463356, 0.002325596986338496, -0.06758813560009003, -0.05490743741393089, -0.04775126650929451, -0.006301036570221186, 0.03576098382472992, 0.04761786386370659, 0.011134685017168522, 0.02945946715772152, 0.045484770089387894, -0.02564222551882267, 0.023326264694333076, 0.06050670146942139, -0.05464479699730873, -0.0497344508767128, 0.054100800305604935, -0.011700032278895378, 0.030689241364598274, 0.04250248149037361, 0.03155726194381714, -0.0742022693157196, 0.0032364921644330025, -0.055900394916534424, 0.042714450508356094, -0.051792800426483154, 0.049918875098228455, -0.0020452647004276514, 0.03983740136027336, -0.01615891605615616, 0.012637676671147346, -0.02329244464635849, 0.01570982299745083, 0.014889903366565704, -0.006716798525303602, 0.006950037088245153, -0.056817613542079926, -0.016312645748257637, 0.04740229621529579, -0.0120273781940341, 0.014441406354308128, 0.015831420198082924, -0.023629141971468925, -0.03986692801117897, -0.014127473346889019, -0.057407595217227936, -0.024844296276569366, -0.006120466161519289, 0.03622416779398918, 0.012033219449222088, 0.030554326251149178, -0.0016523214289918542, -0.013262099586427212, -0.030134763568639755, -0.02488200180232525, 0.037255629897117615, -0.036516640335321426, 0.02463349886238575, -0.02912798337638378, -0.0348660908639431, -0.04533197358250618, -0.013252281583845615, -0.02550610527396202, 0.040972042828798294, 0.00163755111861974, -0.08068437874317169, -0.04596053436398506, 0.036940183490514755, 0.014235918410122395, 0.014011763036251068, 0.010205009020864964, -0.061287201941013336, -0.014123045839369297, -0.0357174314558506, 0.023163747042417526, 0.05727798491716385, 0.01747835800051689, -0.020608771592378616, -0.0030889713671058416, -0.024432068690657616, -0.017816077917814255, -0.0241230558604002, 0.011146984063088894, 0.04267840459942818, -0.0020076697692275047, -0.05365271121263504, -0.011449716985225677, 0.10311004519462585, 0.009946634992957115, 0.03236895054578781, -0.053788937628269196, -0.006565702613443136, -0.038257256150245667, 0.016725564375519753, -0.01493269857019186, -0.015384649857878685, -0.07475272566080093, 0.028180569410324097, -0.0034804027527570724, -0.04779655858874321, 0.02627832256257534, -0.06504945456981659, -0.02582623064517975, -0.04898138344287872, -0.03265547752380371, -0.02002679370343685, 0.031019190326333046, -0.010171978734433651, 0.021343082189559937, -0.002663638675585389, -0.09053359925746918, -0.0172803346067667, -0.0021165621001273394, -0.031924352049827576, -0.07666350901126862, 0.04415948688983917, 0.012260857038199902, -0.018528403714299202, -0.057882171124219894, 0.00485291937366128, -0.020028013736009598, 0.02835800126194954, -0.043743256479501724, 0.006474332418292761, 0.04790574312210083, -0.03042079322040081, -0.003101299051195383, 0.07157489657402039, 0.0062519870698452, 0.04143733158707619, -0.037360601127147675, 0.028768319636583328, -0.015625953674316406, 0.045748256146907806, 0.06087493896484375, 0.0018997648730874062, 0.010484535247087479, -0.024706684052944183, 0.06463654339313507, 0.020487485453486443, -0.0026596279349178076, 0.0545031912624836, -0.004737741779536009, -0.00323464791290462, 0.038236696273088455, 0.0011938739335164428, -0.028091661632061005, 0.04358096420764923, 0.039109762758016586, -0.05256704241037369, 0.008956343866884708, 0.12087737768888474, 0.005858779419213533, -0.03750339522957802, -0.01778269186615944, -0.03949223458766937, -0.0018749985611066222, 0.010092292912304401, 0.014720368199050426, -0.04018034040927887, -0.01899019628763199, 0.041451361030340195, 0.03890575096011162, 0.023792719468474388, 0.014606039971113205, -0.03228893503546715, -0.06001836061477661, 0.028386691585183144, 0.04452511668205261, -0.055544912815093994, -0.06402146816253662, 0.006878760177642107, -0.009420331567525864, 0.003295535920187831, -0.005323218647390604, 0.06943100690841675, -0.014988468959927559, 0.00440642237663269, 0.045410312712192535, -0.0811748281121254, -0.04458673670887947, -0.011642700992524624, -0.01634431816637516, 0.06832082569599152, 0.06847578287124634, 0.0423833392560482, -0.0336056612432003, -0.01265354547649622, -0.0007859852630645037, -0.008034543134272099, -0.024972328916192055, 0.013363182544708252, 0.009377078153192997, -0.004418292548507452, -0.020600268617272377, -0.020012766122817993, 0.05256364122033119, -0.04926098883152008, 0.03294947370886803, -0.008246669545769691, 0.048555824905633926, 0.018809743225574493, 0.0131757240742445, -0.030539538711309433, 0.02392924390733242, 0.008892479352653027, 0.029222289100289345, 0.03458784893155098, -0.04106198623776436, -0.01894313655793667, -0.04646090790629387, 0.025452446192502975, -0.045010630041360855, -0.02841859497129917, 0.0412454716861248, 0.031885646283626556, -0.07193933427333832, -0.0625133067369461, -0.08151143044233322, -0.017386125400662422, 0.011835846118628979, 0.03198081627488136, 0.0578249953687191, 0.018585413694381714, 0.012883556075394154, -0.04579182341694832, -0.032018885016441345, 0.04423971101641655, 0.03029624931514263, -0.10500777512788773, 0.023185843601822853, -0.003379327245056629, -0.01441523153334856, -0.017873989418148994, -0.027645768597722054, -0.06603176891803741, -0.0647047683596611, 0.03509668633341789, 0.01458042487502098, 0.020937982946634293, -0.010535180568695068, -0.024334752932190895, -0.03373993560671806, -0.01143814716488123, 0.003451375523582101, -0.04903743788599968, -0.002272099955007434, 0.0460004098713398, 0.0024357049260288477, -0.017804449424147606, 0.013793598860502243, 0.004074805416166782, 0.02653266303241253, -0.05500717833638191, 0.0272221602499485, -0.03921517729759216, -0.0895489826798439, 0.0007710743229836226, 0.004944130312651396, 0.046534180641174316, 0.009599404409527779, 0.023375609889626503, -0.005467554088681936, 0.010756371542811394, -0.0017745823133736849, 0.02564862184226513, -0.05160476639866829, -0.016011342406272888, 0.017946217209100723, 0.012355613522231579, -0.0024305805563926697, -0.03809349238872528, -0.04640161618590355, -0.0601126030087471, 0.00942128524184227, 0.10254820436239243, 0.010572478175163269, 0.02685479447245598, 0.015487881377339363, -0.048387181013822556, -0.014642755500972271, 0.0318184532225132, -0.019859498366713524, 0.031900644302368164, -0.04026069864630699, 0.0016078246990218759, -0.022844983264803886, 0.015569834969937801, 0.04166411608457565, 0.03163144737482071, -0.00021133225527592003, -0.018349118530750275, -0.024248916655778885, -0.01577216573059559, 0.07821346819400787, -0.013626165688037872, 0.016047710552811623, 0.011560505256056786, 0.02949540689587593, -0.04589046537876129, 0.05418863147497177, -0.034142546355724335, 0.027261586859822273, 0.02193473093211651, 0.004599325358867645, -0.03005121275782585, -0.02152920700609684, 0.0421772375702858, 0.05234923213720322, -0.02107161283493042, 0.019977502524852753, -0.030099622905254364, -0.0008792735170572996, -0.00837501510977745, 0.009253456257283688, -0.009236692450940609, -0.07791541516780853, -0.01680220663547516, -0.037225063890218735, -0.09562775492668152, 0.03153876215219498, -0.0034916403237730265, 0.03420376405119896, -0.010211855173110962, -0.002861735410988331, -0.009741226211190224, -0.022139491513371468, -0.009553425014019012, -0.045788031071424484, 0.020093465223908424, -0.017073391005396843, -0.042032886296510696, 0.0045786951668560505, -6.386486521956412e-33, -0.02449466846883297, -0.0339115709066391, -0.011392058804631233, -0.01251089945435524, -0.025370566174387932, 0.00249790633097291, -0.0258401557803154, 0.0064093731343746185, 0.0071642594411969185, -0.02583971619606018, -0.03055112063884735, 0.027687953785061836, 0.01386080589145422, 0.002063955646008253, 0.03040490299463272, 0.03199048340320587, 0.029217015951871872, -0.016973882913589478, 0.004958081990480423, -0.013161893002688885, 0.05039047449827194, 0.0770248994231224, 0.08302898705005646, -0.03734305873513222, 0.012387026101350784, -0.029639875516295433, 0.04202256724238396, -0.045147188007831573, 0.05819899961352348, 0.04391612485051155, 0.002762572141364217, -0.01645393669605255, -0.013826758600771427, -0.05090987682342529, -0.040487971156835556, 0.052395302802324295, -0.08473246544599533, 0.004670135676860809, -0.004366058390587568, 0.053141262382268906, 0.019402721896767616, -0.017295051366090775, 0.04083145409822464, -0.03879861533641815, -0.04393165931105614, 0.00218495586887002, 0.009742897003889084, -0.023584626615047455, -0.04197428748011589, -0.012058557011187077, -0.037966061383485794, 0.038469184190034866, -0.001861142460256815, 0.025621457025408745, 0.05996668338775635, 0.06629316508769989, -0.01353918295353651, -0.015582011081278324, -0.06245112791657448, 0.0330083854496479, 0.01573164016008377, 0.08153580129146576, 0.04631233960390091, 0.05248085409402847, 0.00455791549757123, -0.01005825586616993, 0.029726795852184296, -0.06681560724973679, 0.009157182648777962, 0.009626436047255993, 0.038727279752492905, 0.003462128574028611, 0.03952881693840027, -0.03592555224895477, 0.051275577396154404, -0.06945085525512695, -0.054991744458675385, 0.03845733776688576, 0.014211759902536869, 0.02701696567237377, 0.045411616563797, -0.004790576174855232, -0.06278439611196518, -0.023126473650336266, -0.019560717046260834, -0.012900703586637974, -0.01438938733190298, -0.024936046451330185, 0.02915535867214203, -0.028158916160464287, 0.028544891625642776, -0.02135908417403698, 0.059162016957998276, -0.033601414412260056, -0.0042991735972464085, 0.0073942807503044605, -0.01617877371609211, -0.003214640310034156, -0.029157614335417747, 0.04475376754999161, -0.07384315878152847, -0.002746036509051919, 0.019484566524624825, 0.03212222456932068, 0.014877407811582088, 0.005925614386796951, -0.00933885294944048, -0.0023733845446258783, -0.04900190606713295, -0.00731201097369194, 0.002733685076236725, -0.003905919846147299, 0.02757817879319191, 0.05772024020552635, 0.03366381302475929, -0.054038409143686295, 0.006229001097381115, 0.04926571622490883, 0.014203764498233795, -0.00447205500677228, -0.04782450199127197, 0.0019635804928839207, 0.014139869250357151, 0.05432543903589249, -0.05670832097530365, 0.00553604681044817, -0.06056750565767288, 0.05756561830639839, 0.029719242826104164, -0.00879516452550888, -0.00768444174900651, 0.04019968584179878, 2.7944471980845265e-07, 0.003079427173361182, 0.04963900148868561, -0.0019402895122766495, -0.0020662834867835045, 0.01608084887266159, 0.004676348064094782, -0.039166029542684555, 0.044275738298892975, 0.01584349013864994, 0.038674045354127884, -0.007058143150061369, -0.023026280105113983, 0.0685950219631195, -0.0026636759284883738, -0.09788591414690018, -0.06505590677261353, -0.06953412294387817, 0.07044669985771179, -0.045863013714551926, 0.03949975594878197, 0.027949396520853043, 0.10103071480989456, -0.02381167933344841, -0.009315401315689087, 0.018997328355908394, -0.02126821130514145, 0.026189740747213364, 0.022338267415761948, 0.01753835752606392, 0.0012502456083893776, 0.0345584899187088, -0.007128257304430008, -0.035167593508958817, -0.015561632812023163, -0.03374270722270012, 0.045418355613946915, 0.030987448990345, 0.06672991812229156, -0.025597764179110527, -0.001557034789584577, 0.028833797201514244, 0.011337866075336933, -0.028279535472393036, -0.03136736527085304, 0.037476468831300735, 0.009924134239554405, -0.04209234192967415, -0.03674959018826485, -0.018959209322929382, 0.00626586377620697, 0.0015509286895394325, 0.012763633392751217, 0.01489100232720375, 0.0008539329865016043, 0.038430217653512955, -0.049285806715488434, -0.006537796463817358, -0.04072021692991257, -0.022793063893914223, -0.004994404036551714, 0.009810399264097214, -0.047176532447338104, -0.029861463233828545, -0.0010955281322821975, -0.003793876152485609, -0.0031888759694993496, 0.0037910856772214174, 3.0715336779200204e-34, 0.0003120740584563464, -0.01741142012178898, 0.022519681602716446, 0.04381922632455826, 0.01282669696956873, -0.05078722909092903, 0.03877192363142967, 0.056978221982717514, 0.037270769476890564, -0.08045539259910583, -0.05425562337040901]

['Dzmitry Bahdanau', 'Kyunghyun Cho', 'Yoshua Bengio']

1409.0473v7

Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural machine translation often belong to a family of encoder-decoders and consists of an encoder that encodes a source sentence into a fixed-length vector from which a decoder generates a translation. In this paper, we conjecture that the use of a fixed-length vector is a bottleneck in improving the performance of this basic encoder-decoder architecture, and propose to extend this by allowing a model to automatically (soft-)search for parts of a source sentence that are relevant to predicting a target word, without having to form these parts as a hard segment explicitly. With this new approach, we achieve a translation performance comparable to the existing state-of-the-art phrase-based system on the task of English-to-French translation. Furthermore, qualitative analysis reveals that the (soft-)alignments found by the model agree well with our intuition.

Neural Machine Translation by Jointly Learning to Align and Translate

http://arxiv.org/pdf/1409.0473v7

Title Neural Machine Translation Jointly Learning Align Translate Summary Neural machine translation recently proposed approach machine translation Unlike traditional statistical machine translation neural machine translation aim building single neural network jointly tuned maximize translation performance model proposed recently neural machine translation often belong family encoderdecoders consists encoder encodes source sentence fixedlength vector decoder generates translation paper conjecture use fixedlength vector bottleneck improving performance basic encoderdecoder architecture propose extend allowing model automatically softsearch part source sentence relevant predicting target word without form part hard segment explicitly new approach achieve translation performance comparable existing stateoftheart phrasebased system task EnglishtoFrench translation Furthermore qualitative analysis reveals softalignments found model agree well intuition Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.016232138499617577, 0.019071346148848534, -0.006837559398263693, 0.06399498879909515, -0.04284335672855377, 0.006947672460228205, 0.02146477811038494, -0.015255913138389587, -0.04788481444120407, -0.0093612689524889, -0.029340293258428574, -0.021650521084666252, 0.03916667401790619, 0.009066462516784668, 0.03122551552951336, -0.026467308402061462, 0.019305609166622162, 0.04065674543380737, -0.0273881945759058, 0.005449487362056971, 0.03363252431154251, 0.015710942447185516, 0.009436668828129768, 0.03362618014216423, -0.0015946970088407397, -0.007531666196882725, -0.014310155995190144, 0.017490016296505928, 0.01678391918540001, 0.0066125355660915375, 0.03946578502655029, 0.027099760249257088, 0.004897012375295162, 0.05497244745492935, 2.2321660253510345e-06, -0.007113906089216471, -0.03756663203239441, -0.021078243851661682, 0.031363874673843384, -0.018713656812906265, 0.006229161750525236, -0.08776481449604034, -0.010954775847494602, 0.021193111315369606, -0.03677869588136673, 0.017762018367648125, 0.07720991224050522, 0.018153635784983635, 0.06006661430001259, 0.09203577041625977, -0.00517529109492898, -0.07431136816740036, 0.004640186671167612, -0.02600318193435669, -0.03573726490139961, -0.06757912784814835, -0.018887734040617943, -0.009249080903828144, -0.07784552872180939, 0.004013588652014732, -0.026899056509137154, 0.06620510667562485, 0.008159046992659569, -0.024787018075585365, 0.0008279155590571463, 0.011773101054131985, -0.028955958783626556, -0.05457170680165291, -0.002304120920598507, 0.06913456320762634, -0.02425362356007099, 0.009333671070635319, -0.011557080782949924, -0.012661627493798733, -0.014258995652198792, -0.00362096494063735, -0.023298177868127823, 0.015756022185087204, -0.006029646843671799, 0.025818394497036934, 0.028355251997709274, 0.03240177407860756, 0.015464515425264835, -0.008018149994313717, -0.02996544912457466, 0.009043003432452679, 0.010929331183433533, -0.030394326895475388, -0.039716776460409164, -0.008530300110578537, -0.004849015269428492, 0.00899185985326767, 0.06299621611833572, 0.017750820145010948, -0.02484545111656189, 0.02516867220401764, -0.04909568279981613, -0.1283995658159256, 0.030390484258532524, -0.10584068298339844, 0.037836603820323944, 0.021296171471476555, 0.016220547258853912, 0.022130729630589485, -0.019626399502158165, 0.08783164620399475, -0.024253811687231064, 0.027790240943431854, -0.08998691290616989, 0.012646094895899296, -0.023556601256132126, -0.007729745004326105, -0.04534612223505974, 0.013008739799261093, -0.027623461559414864, -0.044147342443466187, -0.06461527198553085, -0.01240547839552164, 0.020499389618635178, 0.02402454800903797, 0.04075781628489494, 0.03535453975200653, -0.07179468125104904, -0.028874939307570457, -0.00272969133220613, 0.0807107612490654, -0.025445660576224327, -0.004593974445015192, -0.010957617312669754, -0.01025050412863493, 0.007964072749018669, 0.02912120148539543, -0.024458743631839752, -0.024476589635014534, -0.024521024897694588, 0.06660891324281693, -0.012200512923300266, 0.009650932624936104, 0.00287186773493886, -0.01570853218436241, -0.019037744030356407, -0.015930218622088432, -0.01100119762122631, -0.04635072499513626, 0.089967280626297, -0.006687501911073923, -0.018982039764523506, -0.046002574265003204, 0.006655223201960325, 0.021271711215376854, -0.010012409649789333, 0.08784403651952744, -0.001218317192979157, -0.005733953323215246, 0.03258587419986725, -0.001422623172402382, 0.05275766924023628, 0.03822825103998184, 0.05375172942876816, 0.036033716052770615, 0.016314057633280754, 0.00022868979431223124, -0.03968105837702751, 0.05767784267663956, 0.019418731331825256, -0.04080063849687576, -0.020931094884872437, -0.012521516531705856, 0.045797280967235565, 0.049008000642061234, -0.019338130950927734, 0.05805441364645958, 0.015547244809567928, -0.0031386937480419874, 0.056553103029727936, 0.05118727684020996, 0.06505243480205536, 0.06863436847925186, 0.008682150393724442, 0.015186656266450882, -0.04229569062590599, 0.018648209050297737, -0.007979880087077618, 0.05171052739024162, -0.02979769930243492, -0.010833597742021084, 0.018751133233308792, 0.03066927194595337, -0.019600994884967804, -0.031112225726246834, 0.007551182527095079, -0.029084688052535057, -0.0004821384500246495, -0.038079820573329926, 0.029566077515482903, -0.012178417295217514, -0.053455743938684464, 0.03551262617111206, -0.021482478827238083, -0.011603170074522495, 0.006630285177379847, 0.0050331843085587025, -0.04829232767224312, 0.0017318790778517723, 0.011904984712600708, 0.010303238406777382, -0.07242149859666824, -0.009276814758777618, -0.06330602616071701, 0.029780007898807526, 0.030863307416439056, 0.014026455581188202, -0.017247764393687248, -0.07529090344905853, 0.0030547690112143755, 0.031593404710292816, -0.012197744101285934, 0.019728591665625572, -0.05249204486608505, 0.040185410529375076, 0.06339479982852936, 0.06357331573963165, -0.05877349525690079, 0.04072574898600578, -0.018373604863882065, -0.02079503983259201, -0.002686283551156521, 0.04329710453748703, 0.02707149274647236, 0.02778259478509426, 0.0038395326118916273, 0.022206461057066917, 0.02979113720357418, -0.032819218933582306, -0.03171008452773094, 0.03957681357860565, -0.03321871533989906, -0.05661572515964508, 0.02513636089861393, -0.038947220891714096, 0.010226579383015633, 0.00481787882745266, -0.034935738891363144, -0.0512007512152195, -0.015492466278374195, -0.02352253347635269, -0.04300396516919136, -0.0067835417576134205, 0.06046371906995773, 0.00565992621704936, 0.028980515897274017, -0.04670979827642441, 0.032227035611867905, 0.023820267990231514, 0.010741032660007477, -0.044033899903297424, -0.026102550327777863, 0.039854053407907486, -0.037748582661151886, -0.010917768813669682, 0.04056653380393982, 0.011523401364684105, 0.014525245875120163, 0.0247897207736969, 0.024041878059506416, -0.03171995282173157, -0.054177433252334595, -0.04296610876917839, 0.02051025815308094, -0.004354469478130341, 0.018736984580755234, 0.045712895691394806, 0.020736094564199448, 0.035060204565525055, 0.007293805945664644, -0.056041549891233444, 0.04782047122716904, 0.028191106393933296, -0.019483592361211777, 0.030867990106344223, 0.02548806555569172, 0.007404983043670654, -0.03820829465985298, -0.01350130420178175, -0.008855936117470264, 0.025479333475232124, 0.06653961539268494, -0.07708229869604111, -0.09339602291584015, 0.021787021309137344, -0.026316987350583076, 0.0019571345765143633, 0.019856654107570648, -0.08676440268754959, -0.009986324235796928, -0.012948418036103249, 0.00792437419295311, 0.06750981509685516, 0.03279166296124458, -0.012698246166110039, 0.004913490265607834, 0.006578054744750261, -0.034676987677812576, 0.00866980105638504, -0.027544235810637474, -0.008788730949163437, -0.02849230356514454, -0.018311865627765656, 0.0034018869046121836, 0.02853894792497158, 0.03016139566898346, 0.0031630955636501312, -0.050769541412591934, 0.024952108040452003, -0.019693173468112946, 0.006776990834623575, -0.03847271203994751, -0.006391407921910286, -0.02371879294514656, 0.014080471359193325, -0.012082858011126518, -0.03295990079641342, 0.06307977437973022, -0.006769199855625629, -0.003801665734499693, -0.0719626247882843, -0.03456784412264824, -0.030642887577414513, 0.05009905993938446, -0.045542504638433456, 0.03537154942750931, -0.01856904849410057, -0.045763418078422546, -0.03304988518357277, -0.01337683666497469, -0.003916063345968723, -0.030303437262773514, 0.039255283772945404, -0.015701504424214363, -0.0037649073638021946, -0.060092732310295105, -0.026887238025665283, -0.01591145247220993, -0.027244238182902336, -0.009532460011541843, 0.0032349582761526108, 0.05127493292093277, -0.02438361942768097, -0.03147950768470764, 0.02170889638364315, -0.014868097379803658, 0.01709042862057686, -0.047740787267684937, 0.03556830435991287, -0.044216543436050415, 0.007026349194347858, 0.0275395680218935, -0.02697603404521942, -0.04451819509267807, -0.05228572338819504, 0.009485953487455845, 0.00857336912304163, -0.04051036387681961, 0.01784992218017578, -0.06953881680965424, -0.040716905146837234, 0.03176318481564522, -0.003056520828977227, -0.025976749137043953, -0.02085687965154648, 0.041019536554813385, -0.041679009795188904, 0.02108027972280979, 0.12335904687643051, 0.010382832027971745, -0.06651655584573746, -0.023722371086478233, -0.02386227436363697, -0.0128095718100667, 0.01322432141751051, 0.037781327962875366, -0.01819932647049427, -0.0050752353854477406, -0.011819153092801571, 0.013454988598823547, 0.06106355041265488, -0.005746390204876661, -0.03261246159672737, -0.064795583486557, -0.023748790845274925, 0.05271404981613159, -0.017856579273939133, -0.06220191344618797, 0.015432055108249187, -0.043173618614673615, -0.0339529775083065, 0.01600358821451664, 0.01588224060833454, 0.04308377951383591, -0.0034475112333893776, 0.0017755940789356828, -0.0014236788265407085, -0.0005548957851715386, -0.02416807785630226, -0.11189921200275421, 0.05086416378617287, 0.08363766223192215, 0.08482913672924042, -0.019855722784996033, -0.04065576195716858, 0.02706219255924225, -0.0009143807110376656, 0.022795990109443665, 0.011999664828181267, 0.02094687893986702, -0.013654330745339394, -0.013414707034826279, 0.0005503894062712789, 0.011332659982144833, -0.025301622226834297, 0.05375007539987564, 0.046391237527132034, 0.04875311255455017, -0.0058202664367854595, 0.04429485276341438, -0.018293878063559532, 0.033368539065122604, -0.005374939646571875, 0.0273787472397089, -0.00516425259411335, -0.03188559040427208, 0.007612123619765043, -0.010644732043147087, 0.006013768259435892, -0.05279204994440079, -0.0074613383039832115, 0.021166445687413216, -0.055361367762088776, -0.010785873979330063, -0.09961585700511932, -0.05057472735643387, 0.0037569717969745398, 0.06497747451066971, 0.07170787453651428, 0.022543184459209442, 0.05548509955406189, -0.01662832871079445, 0.0011294366559013724, -0.02017212100327015, 0.034028563648462296, 0.03776165843009949, -0.04055791720747948, 0.04144134372472763, 0.029905375093221664, -0.004853652324527502, 0.026616016402840614, -0.0055288998410105705, -0.056346483528614044, -0.06813424080610275, -0.024320174008607864, 0.031039563938975334, 0.009548146277666092, 0.025364577770233154, -0.031178532168269157, -0.03926154226064682, -0.023638879880309105, 0.02821345627307892, -0.021935533732175827, -0.02056206949055195, 0.016184747219085693, -0.002495993860065937, -0.014563058502972126, 0.025546105578541756, -0.0010306107578799129, -0.012900986708700657, -0.019059082493185997, 0.03364410623908043, -0.0027323332615196705, -0.07860361784696579, 0.03637572377920151, 0.02554992027580738, 0.039374496787786484, -0.014580076560378075, 0.006817580200731754, -0.03087303601205349, 0.016935205087065697, -0.004867116920650005, -0.029878992587327957, -0.03172175586223602, -0.010995771735906601, 0.05557696148753166, -0.0330183170735836, 0.013588991016149521, -0.0009067690698429942, 0.011764252558350563, -0.038724660873413086, -0.00266328826546669, 0.03435250371694565, -0.04076170176267624, 0.045781541615724564, -0.017194081097841263, 0.022872507572174072, -0.011163229122757912, -0.001885761390440166, 0.0017961139092221856, 0.037090301513671875, -0.04018152132630348, 0.04068674519658089, 0.024030884727835655, 0.0381067618727684, -0.03115162067115307, 0.03432226926088333, 0.03466840460896492, -0.011626561172306538, -0.05598009377717972, -0.013816488906741142, 0.0793377161026001, -0.041105277836322784, 0.05739516392350197, 0.018036648631095886, 0.000736422196496278, 0.008519846946001053, 0.0819026455283165, -0.034377504140138626, -0.0034318279940634966, 0.03204101696610451, -0.027412721887230873, 0.0025352512020617723, -0.05178613215684891, 0.040349069982767105, -0.051493287086486816, -0.047046128660440445, 0.001963638002052903, -0.046926919370889664, -0.017788367345929146, 0.011297287419438362, 0.020418155938386917, -0.03273318335413933, -0.04517989233136177, 0.008051017299294472, 0.02399591915309429, -0.0357438288629055, 0.012176179327070713, 0.041298381984233856, 0.03954713046550751, 0.018374856561422348, 0.010940580628812313, 0.07194256782531738, -0.033934738487005234, -0.0024077605921775103, -0.048936594277620316, 0.0281691774725914, -0.0016388989752158523, -0.014955567196011543, -0.055552851408720016, -6.57512250853668e-33, -0.044061705470085144, -0.0176483616232872, 0.0111584747210145, -0.0472826212644577, -0.0527493953704834, -0.006197000853717327, -0.012478161603212357, -0.013079389929771423, -0.01911548152565956, -0.0066096168011426926, -0.008718876168131828, 0.014962403103709221, 0.01742541231215, 0.015073325484991074, 0.05433404818177223, 0.00801296066492796, 0.014914088882505894, -0.033367156982421875, 0.012254391796886921, -0.016752686351537704, 0.019082071259617805, 0.06530705839395523, 0.09535915404558182, -0.06395189464092255, 0.02588695101439953, -0.020579230040311813, -0.002034996170550585, 0.03200525417923927, 0.0002967417240142822, -0.0037369211204349995, 0.02774566225707531, -0.03303849324584007, 0.016388101503252983, -0.032199688255786896, -0.030564311891794205, 0.021325107663869858, -0.04980017617344856, -0.019711200147867203, 0.0034357772674411535, 0.042315129190683365, -0.03368491306900978, -0.020951759070158005, 0.06866712868213654, -0.03656146302819252, -0.02865590713918209, 0.009252122603356838, 0.04175277054309845, -0.04705985262989998, 0.0008052822086028755, -0.013811984099447727, -0.0583767294883728, -0.010852054692804813, -0.017781279981136322, 0.0011262388434261084, 0.052015721797943115, 0.03869523108005524, -0.006562991067767143, -0.007129542529582977, -0.10855448246002197, 0.015496406704187393, -0.021439779549837112, 0.09314391762018204, 0.0723523274064064, 0.04072456434369087, -0.018066009506583214, 0.025455916300415993, 0.008358345367014408, -0.03224271163344383, -0.0053367395885288715, 0.021657707169651985, 0.013410571031272411, 0.0318126454949379, 0.07959134876728058, 0.012989562936127186, 0.03954780474305153, -0.024460922926664352, -0.06327423453330994, 0.05473162978887558, 0.0051977261900901794, 0.015615267679095268, 0.042126066982746124, 0.02654481865465641, -0.04190203174948692, -0.017284583300352097, -0.007558888290077448, -0.006943166255950928, -0.02551439218223095, -0.052795179188251495, -0.020736539736390114, 0.01205162238329649, -0.003962482791393995, 0.016865544021129608, 0.045949649065732956, -0.03906926512718201, 0.05098900571465492, -0.009254376403987408, -0.006237106863409281, -0.011539936996996403, -0.02814880944788456, 0.03305093199014664, -0.015859348699450493, -0.05591964349150658, -0.023892296478152275, 0.042584966868162155, 0.03176140785217285, 0.0033816739451140165, 0.05935291573405266, 0.006481541786342859, -0.016888059675693512, -6.099727033870295e-05, -0.03339196369051933, -0.05800017714500427, 0.015580341219902039, -0.01175312977284193, 0.0054403916001319885, -0.015456654131412506, -0.018069196492433548, 0.07097887247800827, 0.0583902932703495, 0.00449378089979291, -0.03293300420045853, -0.011672088876366615, 0.040539294481277466, 0.03568590432405472, -0.07251006364822388, 0.04017708823084831, -0.03647662326693535, 0.012081021443009377, 0.044210199266672134, -0.04263252019882202, -0.030419694259762764, 0.01402355171740055, 2.9939945989099215e-07, 0.05248010531067848, 0.04575757682323456, 0.03293022885918617, -0.0007095018518157303, 0.012273546308279037, 0.026308365166187286, -0.029672592878341675, 0.07170701026916504, -0.01355729065835476, 0.03428887948393822, 0.06110624969005585, -0.03087722696363926, 0.03544749692082405, 0.0020403568632900715, -0.0868396908044815, -0.0024020024575293064, -0.08345629274845123, 0.021424967795610428, -0.061087217181921005, 0.026037173345685005, 0.06742902100086212, 0.10369593650102615, 0.033818237483501434, 0.014797655865550041, -0.019206762313842773, -0.01914135180413723, 0.00784964207559824, 0.019267316907644272, -0.005093108396977186, 0.02767661027610302, 0.010404196567833424, -0.019940584897994995, -0.047586433589458466, -0.0014285451034083962, -0.0350959487259388, 0.0357024148106575, 0.056196074932813644, 0.04460792988538742, -0.011301075108349323, 0.005882736295461655, 0.02285187318921089, -0.00824082363396883, -0.007389053702354431, -0.049000803381204605, 0.04071616753935814, -0.06849219650030136, -0.06455879658460617, 0.012675411999225616, 0.020698267966508865, 0.031098296865820885, 0.04337448626756668, 0.009303540922701359, 0.022765500470995903, 0.00432449858635664, 0.03818874433636665, -0.026233049109578133, -0.013091648928821087, -0.03912300243973732, -0.04639647156000137, 0.011391209438443184, -0.02172846533358097, 0.013130789622664452, -0.014057139866054058, -0.011875408701598644, 0.02441047690808773, -0.041002966463565826, -0.009225335903465748, 2.6461537260148686e-34, 0.009837628342211246, -0.017131157219409943, 0.007169498596340418, 0.025126449763774872, 0.01856454834342003, -0.023823386058211327, -0.049270302057266235, 0.03041723184287548, -0.0008565096068195999, -0.03496326133608818, -0.0657862052321434]

['Jean Pouget-Abadie', 'Dzmitry Bahdanau', 'Bart van Merrienboer', 'Kyunghyun Cho', 'Yoshua Bengio']

1409.1257v2

The authors of (Cho et al., 2014a) have shown that the recently introduced neural network translation systems suffer from a significant drop in translation quality when translating long sentences, unlike existing phrase-based translation systems. In this paper, we propose a way to address this issue by automatically segmenting an input sentence into phrases that can be easily translated by the neural network translation model. Once each segment has been independently translated by the neural machine translation model, the translated clauses are concatenated to form a final translation. Empirical results show a significant improvement in translation quality for long sentences.

Overcoming the Curse of Sentence Length for Neural Machine Translation using Automatic Segmentation

http://arxiv.org/pdf/1409.1257v2

Title Overcoming Curse Sentence Length Neural Machine Translation using Automatic Segmentation Summary author Cho et al 2014a shown recently introduced neural network translation system suffer significant drop translation quality translating long sentence unlike existing phrasebased translation system paper propose way address issue automatically segmenting input sentence phrase easily translated neural network translation model segment independently translated neural machine translation model translated clause concatenated form final translation Empirical result show significant improvement translation quality long sentence Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.020197276026010513, 0.029057249426841736, -0.0055040884763002396, 0.05541546642780304, -0.04097885265946388, 0.0034373069647699594, 0.04737241938710213, 0.004094036296010017, -0.045474689453840256, -0.0030410634353756905, 0.008909204974770546, 0.008727390319108963, 0.03498250991106033, 0.0009199061314575374, 0.037287477403879166, -0.08106303960084915, 0.012066361494362354, 0.004808159079402685, 0.004047675058245659, 0.03862627595663071, 0.04202299937605858, -0.01306547038257122, 0.016559600830078125, 0.010794686153531075, -0.02373804897069931, -0.0041292281821370125, -0.016153067350387573, 0.024108359590172768, 0.0024322771932929754, -0.018942449241876602, 0.006848673336207867, -0.0010973593452945352, -0.00963264238089323, 0.04709110036492348, 2.3174793568614405e-06, -0.030357062816619873, -0.05940539017319679, -0.011441396549344063, 0.016807815060019493, 0.0014372237492352724, 0.03994716331362724, -0.06154273822903633, -0.0065672677010297775, 0.027120178565382957, -0.0007631000480614603, 0.0474117174744606, 0.027185600250959396, 0.10980281978845596, 0.051988810300827026, 0.08902961015701294, -0.023712653666734695, -0.07159817218780518, 0.020820066332817078, -0.04023980349302292, -0.027247993275523186, -0.029224438592791557, -0.02056233584880829, -0.01696416549384594, -0.04060020297765732, -0.0034144395031034946, -0.008221196942031384, 0.06232035532593727, 0.022448495030403137, -0.03247513994574547, -0.005633961874991655, 0.010939616709947586, -0.05061697959899902, -0.036834705621004105, 0.02130580134689808, 0.060887400060892105, -0.05374820530414581, 0.02870531938970089, -0.0008389315917156637, 0.0054185157641768456, 0.01551024243235588, -0.08240686357021332, -0.058830853551626205, 0.0408332422375679, 0.007045741192996502, 0.0123493866994977, -0.006227042060345411, 0.061032555997371674, 0.006968912202864885, -0.0012235749745741487, -0.04858223348855972, 0.009738512337207794, 0.004598773084580898, -0.0475279800593853, -0.009415187872946262, -0.013863809406757355, 0.0033286819234490395, -4.526157499640249e-05, 0.08192270994186401, 0.00885095540434122, 0.007658650167286396, 0.029184255748987198, -0.04789644107222557, -0.0840989351272583, 0.007317679934203625, -0.08781089633703232, -0.01346893236041069, 0.029210584238171577, 0.002996724098920822, 0.01174013689160347, -0.04420777037739754, 0.04822689667344093, -0.01893465220928192, 0.033507175743579865, -0.06818453222513199, 0.0075772893615067005, -0.019206907600164413, 0.005944163538515568, -0.07785054296255112, 0.035284385085105896, -0.032051365822553635, -0.037757694721221924, -0.03926997259259224, -0.002469862112775445, 0.034723520278930664, -0.012596998363733292, 0.025148026645183563, 0.024102533236145973, -0.02584240958094597, -0.026868458837270737, 0.00014316321176011115, 0.03145677596330643, -0.024399492889642715, -0.01401561964303255, 0.0007938349153846502, 0.012012729421257973, 0.0033644039649516344, 0.0167242344468832, 0.005094969179481268, -0.022457104176282883, -0.017567409202456474, 0.03551153466105461, -0.02797165885567665, -0.019052039831876755, -0.039064958691596985, -0.025698544457554817, -0.05619722977280617, -0.008775625377893448, -0.0225684754550457, -0.05773964524269104, 0.046987250447273254, -0.026950901374220848, 0.0009031877852976322, 0.027125373482704163, 0.01274883933365345, 0.02712855488061905, -0.025356221944093704, 0.049363743513822556, -0.03162621334195137, -0.013730970211327076, 0.017702458426356316, 0.0012532667024061084, 0.10981246083974838, 0.02125830203294754, 0.07086566090583801, 0.04011167958378792, 0.053722988814115524, 0.0276480745524168, -0.024480925872921944, 0.04345443844795227, -0.014910717494785786, -0.016009384766221046, -0.049391865730285645, -0.019495666027069092, 0.006665117107331753, 0.034313615411520004, -0.005681447219103575, 0.07775276154279709, 0.007197825238108635, 0.010538788512349129, 0.04159823805093765, 0.05697670951485634, 0.042056404054164886, 0.07056205719709396, 0.0002626613131724298, 0.013776039704680443, -0.01756182312965393, 0.04850195348262787, -0.016917694360017776, 0.005145064555108547, 0.02972974255681038, 0.030483458191156387, 0.024054240435361862, 0.026365244761109352, 0.0003381816786713898, -0.06199539452791214, 0.013644756749272346, -0.02941054478287697, 0.03756605088710785, -0.038225576281547546, 0.017023198306560516, 0.023846298456192017, -0.04786327853798866, 0.03818456083536148, -0.04330722242593765, -0.0755511000752449, -0.005391326732933521, -0.02856774628162384, -0.04218043386936188, 0.05036801099777222, 0.021136175841093063, -0.007545776665210724, -0.027029821649193764, -0.014497908763587475, 0.013168180361390114, 0.04828609153628349, 0.004846065770834684, 0.0036281938664615154, 0.009591919369995594, -0.06253864616155624, 0.025082116946578026, 0.04084661602973938, -0.0018996578874066472, -0.01452477928251028, -0.04101157188415527, 0.040828555822372437, 0.0705660954117775, -0.0023121361155062914, -0.06282205879688263, 0.04190310835838318, 0.02956630289554596, -0.013256787322461605, 0.015117709524929523, 0.03205234929919243, 0.005784200504422188, 0.042043574154376984, -0.0028690770268440247, -0.0014428975991904736, 0.022238340228796005, -0.03691639006137848, -0.04167061299085617, 0.022366639226675034, -0.08203738182783127, -0.07711426913738251, -0.011022428050637245, -0.04871312901377678, 0.0038769314996898174, -0.01923375017940998, -0.03851231187582016, -0.06056778132915497, -0.02247018739581108, -0.022870158776640892, -0.009880431927740574, -0.002202605130150914, 0.07457815110683441, -0.011830157600343227, 0.033227041363716125, -0.044135965406894684, 0.025555724278092384, 0.021193532273173332, -0.022290121763944626, -0.032658472657203674, -0.03669639304280281, 0.04710373282432556, -0.03973754867911339, -0.021050142124295235, 0.022866228595376015, -0.0075525506399571896, 0.004172924906015396, 0.03396061807870865, 0.022182852029800415, -0.0501495897769928, -0.03735452890396118, -0.06155978888273239, 0.012033043429255486, -0.014719224534928799, 0.007402549963444471, 0.03250563144683838, 0.0384284071624279, -0.0021703823003917933, -0.009357110597193241, -0.01885722018778324, 0.023550989106297493, 0.0021474468521773815, -0.021602224558591843, 0.043858930468559265, 0.015403135679662228, 0.00929507240653038, -0.018810704350471497, -0.005979148205369711, -0.009087611921131611, 0.015100997872650623, 0.05028246343135834, -0.09138476848602295, -0.0845755934715271, 0.02977815456688404, 0.00488737178966403, -0.0013421369949355721, 0.02396482042968273, -0.08845190703868866, -0.028908759355545044, -0.03176555782556534, 0.021107923239469528, 0.07025773078203201, 0.023298300802707672, -0.043448664247989655, 0.025454943999648094, 0.005873925052583218, 0.014228611253201962, 0.0028998092748224735, -0.022067511454224586, 0.03727326542139053, -0.015085316263139248, -0.03465389832854271, 0.03741677105426788, 0.01931294985115528, 0.03387928381562233, 0.010611706413328648, -0.01872451789677143, -0.006859866436570883, -0.0604214146733284, 0.002919806633144617, 0.0037873322144150734, -0.0010507378028705716, -0.03252683952450752, 0.002724668476730585, 0.003148467745631933, -0.0049245343543589115, 0.02330065704882145, -0.032877545803785324, -0.012379913590848446, -0.07354315370321274, -0.04183448106050491, -0.041716068983078, 0.055099956691265106, 0.007620788179337978, 0.011916990391910076, 0.03734087571501732, -0.03684491664171219, -0.03840358927845955, 0.023339373990893364, -0.03865663707256317, 0.01907108537852764, 0.05745062232017517, -0.016731493175029755, -0.024521641433238983, -0.04694356024265289, -0.009651669301092625, -0.02145186997950077, 0.0014981069834902883, -0.001149327028542757, -0.007060183212161064, 0.06897855550050735, -0.010282689705491066, 0.015608157962560654, 0.045177605003118515, 0.019512124359607697, 0.058082617819309235, -0.08195453137159348, 0.014661732129752636, -0.020822513848543167, 0.017421796917915344, 0.003839427139610052, -0.03431859612464905, -0.0032863409724086523, -0.023099759593605995, 0.04541179537773132, 0.027946630492806435, -0.016830258071422577, -0.013996908441185951, -0.05756596475839615, -0.0250394344329834, -0.0017765017691999674, -0.04713236540555954, -0.020078890025615692, -0.01484986487776041, 0.048933371901512146, -0.1034693717956543, 0.012757010757923126, 0.12662944197654724, 0.02344680391252041, -0.054560694843530655, -0.015415762551128864, -0.025980789214372635, 0.0036841765977442265, 0.001789747504517436, 0.025882454589009285, -0.023118063807487488, -0.020021583884954453, 0.007744045928120613, 0.029461689293384552, 0.01772891916334629, -0.005758709739893675, -0.03666618466377258, -0.05336553230881691, 0.009456584230065346, 0.03405587002635002, -0.050974465906620026, -0.005606799386441708, 0.03243989869952202, -0.04251908138394356, -0.013059718534350395, 0.012566043063998222, 0.002206383040174842, 0.0003428664058446884, -0.018996616825461388, -0.012402386404573917, -0.04597913846373558, 0.011621017009019852, -0.05071035027503967, -0.057399529963731766, -0.0053979200311005116, 0.06050874665379524, 0.0700540766119957, -0.033332884311676025, 0.005513121373951435, 0.09834440797567368, -0.007542699109762907, 0.036710359156131744, 0.008309252560138702, 0.04921938478946686, 0.016594503074884415, 0.0029194941744208336, -0.0054946946911513805, -0.0005032359040342271, 0.011652623303234577, 0.049980565905570984, 0.0691622719168663, 0.033839140087366104, 0.02311716042459011, 0.022966520860791206, -0.035990018397569656, -0.007660923060029745, -0.034831807017326355, 0.022020751610398293, 0.0028503146022558212, -0.01841486245393753, -0.038335565477609634, -0.02878825180232525, -0.01934794895350933, -0.08127127587795258, 0.02158326283097267, 0.023067446425557137, -0.08758284151554108, -0.02084549330174923, -0.1007445901632309, -0.07668087631464005, 0.009741588495671749, 0.062330279499292374, 0.05282251909375191, 0.014043590053915977, 0.03724907711148262, 0.006226605270057917, -0.00936463288962841, -0.033577654510736465, 0.021737506613135338, 0.0028338241390883923, -0.061588652431964874, 0.058429621160030365, -0.003476737765595317, -0.0005446429713629186, 0.03742970526218414, -0.025739770382642746, -0.06098580360412598, -0.05097022280097008, -0.001965672243386507, 0.013917314819991589, 0.010095854289829731, 0.05929124355316162, -0.054975077509880066, -0.04231947287917137, 0.008256113156676292, 0.014348184689879417, 0.00531832966953516, -0.025921382009983063, 0.023882390931248665, 0.03746713325381279, 0.007901462726294994, 0.022931283339858055, -0.0037680137902498245, -0.008980026468634605, -0.02321964129805565, 0.026531333103775978, -0.03813875466585159, -0.06703106313943863, -0.0014824311947450042, 0.023935699835419655, 0.034818384796381, 0.002477104775607586, 0.027852237224578857, -0.02876865677535534, 0.02798055112361908, -0.03400462120771408, -0.012567880563437939, -0.03872380033135414, 0.023188617080450058, 0.0597725436091423, 0.0018193575087934732, 0.02249811217188835, 0.005102434195578098, -0.02020374871790409, -0.05043676868081093, 0.012717167846858501, 0.02589501067996025, -0.03956373780965805, -0.0030932496301829815, 0.003267570398747921, 0.00305874808691442, -0.01298616174608469, -0.0065457564778625965, 0.011897440068423748, 0.02518060989677906, -0.04107902944087982, 0.05018150806427002, 0.01923011615872383, -0.004463260993361473, -0.05087966471910477, 0.05602138489484787, 0.013536889106035233, 0.016519978642463684, -0.04706792160868645, 0.03375750035047531, 0.05180174484848976, -0.0343436636030674, 0.06821022927761078, 0.021845128387212753, -0.007761784829199314, -0.001925041084177792, 0.0691547840833664, -0.01059674471616745, -0.009088262915611267, -0.01816059648990631, -0.0010570548474788666, -0.0208293329924345, -0.04209187999367714, 0.007363833487033844, -0.023370737209916115, -0.05972746014595032, 0.04172534495592117, -0.05038468912243843, -0.024684105068445206, 0.013637656345963478, -0.006662874016910791, -0.016880275681614876, -0.025702878832817078, -0.006256032269448042, 0.03217444196343422, -0.010433741845190525, -0.005138945300132036, 0.0027709375135600567, 0.06798895448446274, -0.006781937088817358, 0.005146660842001438, 0.06778306514024734, -0.005368153564631939, -0.0200662724673748, -0.028108960017561913, -0.0040427702479064465, 0.020514877513051033, -0.02505715936422348, -0.03332257270812988, -6.250010893141975e-33, 0.000642816536128521, -0.025496402755379677, -0.0011299330508336425, -0.04796391353011131, -0.08428391069173813, -0.00478763272985816, -0.02565905638039112, -0.0034477002918720245, 0.01148795336484909, 0.008329920470714569, -0.02800649031996727, 0.01618557795882225, 0.032794855535030365, 0.01467218715697527, 0.021138807758688927, 0.02005859836935997, 0.06631091982126236, -0.014306974597275257, 0.01296233106404543, -0.0024527290370315313, 0.014560172334313393, 0.058407142758369446, 0.05285385623574257, -0.004560197703540325, 0.03644166141748428, -0.013965347781777382, -0.012610292993485928, 0.02052110806107521, 0.04078132286667824, 0.006464841775596142, 0.02333720773458481, -0.026255324482917786, 0.04691384360194206, -0.04333197697997093, -0.04198720306158066, 0.034698743373155594, -0.07760398089885712, -0.0008000238449312747, -0.003186596557497978, 0.05569591000676155, -0.02035336196422577, -0.024935191497206688, 0.08844053000211716, -0.041952043771743774, 0.02259831316769123, 0.02500412054359913, 0.05460158735513687, -0.06660410761833191, -0.005753659643232822, -0.016143212094902992, -0.07716472446918488, 0.00711936317384243, -0.003995876293629408, -0.0035678583662956953, 0.04035460203886032, 0.04262685775756836, -0.02239876054227352, -0.012647181749343872, -0.08168861269950867, 0.006268698256462812, 0.01113663986325264, 0.052305903285741806, 0.01759887859225273, 0.024563707411289215, -0.041893988847732544, -0.04215167462825775, 0.03012775629758835, -0.024748938158154488, -0.002720441436395049, 0.05240919440984726, 0.015158035792410374, -0.0004261127323843539, 0.08967649191617966, -0.0028343412559479475, 0.037956319749355316, -0.037061240524053574, -0.05427872762084007, 0.03438703715801239, -0.012314327992498875, 0.0188330989331007, 0.014839230105280876, 0.028688617050647736, -0.05115602910518646, -0.03615235909819603, 0.02240452542901039, -0.020054802298545837, -0.0017384100938215852, -0.01545009296387434, -0.002891405951231718, 0.019284972921013832, -0.006005102768540382, -0.025973794981837273, 0.05029613524675369, -0.03241903707385063, 0.02394813299179077, -0.021033432334661484, -0.03279458358883858, 0.019138038158416748, -0.013192457146942616, 0.0015431095380336046, -0.029164312407374382, -0.016796376556158066, -0.027053462341427803, 0.04313711076974869, 0.019424637779593468, -0.018275277689099312, 0.08287166804075241, -0.025393063202500343, -0.012441554106771946, 0.014373430982232094, 0.0017371551366522908, -0.03916937857866287, 0.01874580793082714, 0.07100145518779755, -0.01742807775735855, -0.021059509366750717, -0.014177165925502777, 0.08164069056510925, 0.03311382606625557, -0.005569512955844402, -0.04489520937204361, 0.0183195061981678, 0.03429802134633064, 0.04638422653079033, -0.0888921394944191, 0.035482008010149, -0.0225591491907835, 0.051499154418706894, 0.041674986481666565, -0.07180067151784897, -0.03951742500066757, 0.003153938101604581, 2.8655912842623366e-07, 0.016362981870770454, 0.05512755736708641, 0.03670983761548996, -0.0077989366836845875, 0.005404382478445768, 0.03006652742624283, -0.007473121862858534, 0.04149201884865761, -0.03142932802438736, 0.06809855252504349, 0.03708922490477562, -0.03182501718401909, 0.02987147681415081, -0.007404359057545662, -0.1319909393787384, -0.019410407170653343, -0.019245699048042297, 0.0021446712780743837, -0.05655750632286072, 0.026243411004543304, 0.06420408934354782, 0.08599625527858734, 0.018810581415891647, 0.022671891376376152, 0.008146336302161217, -0.0523374043405056, -0.0362260639667511, 0.040906116366386414, -0.023158159106969833, 0.02749646082520485, 0.03278251364827156, 0.0418720543384552, -0.06950584053993225, -0.027714530006051064, -0.024821244180202484, 0.008903119713068008, 0.05004075914621353, 0.05751257762312889, 0.005219017155468464, 0.020824432373046875, 0.06700428575277328, -0.021557239815592766, 0.003554800758138299, -0.040797311812639236, 0.06050833687186241, -0.04073575139045715, -0.019956883043050766, 0.019684694707393646, 0.05836694687604904, 0.018296902999281883, 0.011837974190711975, 0.002142176264896989, -0.004112684167921543, -0.0033406727015972137, 0.03529902175068855, -0.05225475877523422, -0.010655093938112259, -0.06046086922287941, -0.03210888057947159, 0.008172914385795593, -0.0011473122285678983, 0.002644857158884406, -0.01808546669781208, 0.020753059536218643, 0.0009953394765034318, -0.03577139601111412, -0.01345048937946558, 2.7574656941980466e-34, 0.017544690519571304, -0.01777716539800167, 0.018287286162376404, -0.004347031470388174, 0.022097645327448845, -0.044344279915094376, -0.028936250135302544, 0.0016230720793828368, -0.01843719743192196, -0.026922421529889107, -0.05984582006931305]

['William Chan', 'Nan Rosemary Ke', 'Ian Lane']

1504.01483v1

Deep Neural Network (DNN) acoustic models have yielded many state-of-the-art results in Automatic Speech Recognition (ASR) tasks. More recently, Recurrent Neural Network (RNN) models have been shown to outperform DNNs counterparts. However, state-of-the-art DNN and RNN models tend to be impractical to deploy on embedded systems with limited computational capacity. Traditionally, the approach for embedded platforms is to either train a small DNN directly, or to train a small DNN that learns the output distribution of a large DNN. In this paper, we utilize a state-of-the-art RNN to transfer knowledge to small DNN. We use the RNN model to generate soft alignments and minimize the Kullback-Leibler divergence against the small DNN. The small DNN trained on the soft RNN alignments achieved a 3.93 WER on the Wall Street Journal (WSJ) eval92 task compared to a baseline 4.54 WER or more than 13% relative improvement.

Transferring Knowledge from a RNN to a DNN

http://arxiv.org/pdf/1504.01483v1

Title Transferring Knowledge RNN DNN Summary Deep Neural Network DNN acoustic model yielded many stateoftheart result Automatic Speech Recognition ASR task recently Recurrent Neural Network RNN model shown outperform DNNs counterpart However stateoftheart DNN RNN model tend impractical deploy embedded system limited computational capacity Traditionally approach embedded platform either train small DNN directly train small DNN learns output distribution large DNN paper utilize stateoftheart RNN transfer knowledge small DNN use RNN model generate soft alignment minimize KullbackLeibler divergence small DNN small DNN trained soft RNN alignment achieved 393 WER Wall Street Journal WSJ eval92 task compared baseline 454 WER 13 relative improvement Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.015455097891390324, 0.028654413297772408, 0.007837031036615372, 0.03152240067720413, -0.02903357334434986, -0.03145992010831833, 0.044474970549345016, -0.016366124153137207, -0.04448847472667694, 0.003005929524078965, -0.03364250808954239, 0.010486699640750885, 0.061562370508909225, 0.026221472769975662, 0.01799595169723034, -0.04036860540509224, 0.028314147144556046, 0.004599221516400576, -0.012163334526121616, -0.02496170811355114, 0.015868118032813072, -0.013192901387810707, -0.05808360129594803, 0.015541592612862587, 0.005602146033197641, 0.008730264380574226, -0.026432115584611893, 0.012943392619490623, 0.039289530366659164, -0.03602448105812073, -0.010585315525531769, 0.010119280777871609, 0.04200464114546776, 0.05972922220826149, 2.284019956277916e-06, -0.02518177218735218, -0.023910921066999435, 0.008836152032017708, -0.03713630512356758, -0.013312284834682941, -0.006492714863270521, 0.011428073048591614, -0.016720805317163467, 0.03127870708703995, -0.02279554307460785, -0.03422076255083084, 0.04937973618507385, 0.05722787231206894, 0.008443447761237621, 0.05707576498389244, -0.01626727543771267, -0.0006632014992646873, 0.04735967889428139, -0.034348782151937485, -0.021488826721906662, -0.029712164774537086, 0.03965349867939949, -0.01925177313387394, -0.020952366292476654, -0.013204631395637989, -0.02276340313255787, 0.06526083499193192, -0.0024889176711440086, 0.017327243462204933, 0.039021093398332596, 0.004059665836393833, -0.031352490186691284, -0.01189033966511488, -0.015805836766958237, 0.08458849042654037, -0.018421286717057228, 0.0020188353955745697, 0.041101351380348206, 0.00988758634775877, -0.04539744183421135, -0.015688562765717506, -0.044845446944236755, -0.023931778967380524, 0.007723440881818533, 0.022157523781061172, -0.019759560003876686, -0.001982754096388817, 0.035617683082818985, -0.02436685562133789, -0.004581974353641272, -0.017968948930501938, -0.001608342514373362, -0.016988519579172134, 0.01609683781862259, -0.03727620467543602, 0.04592416062951088, -0.06873118877410889, 0.02484411932528019, 0.012304004281759262, 0.02837591990828514, -0.0014849029248580337, -0.05137578025460243, -0.06573015451431274, 0.010148233734071255, -0.027960307896137238, 0.0036383746191859245, -0.009662652388215065, -0.05150795355439186, -0.008488746359944344, -0.033183056861162186, 0.042642269283533096, -0.025784624740481377, -0.010532376356422901, -0.010705490596592426, 0.015250872820615768, -0.045427288860082626, 0.011503388173878193, -0.0010896712774410844, 0.04858855903148651, 0.011889235116541386, -0.06178174912929535, -0.07333774119615555, -0.03138876333832741, -0.0017067576991394162, -0.0009665114339441061, 0.01909380406141281, 0.04071536660194397, -0.0505087673664093, 0.003472886746749282, 0.0044425432570278645, 0.06874959915876389, 0.025642547756433487, 0.06166992336511612, 0.024850280955433846, -0.058566685765981674, 0.01671735569834709, 0.028585372492671013, 0.03936534747481346, -0.0052275522612035275, -0.011978584341704845, 0.04752320423722267, 0.008598577231168747, 0.029999949038028717, -0.02310589700937271, 0.04400857910513878, -0.030976301059126854, -0.014712249860167503, 0.002509237267076969, -0.07544092833995819, 0.04214552417397499, -0.01968378759920597, -0.02480343170464039, -0.023153912276029587, 0.040965694934129715, -0.014742404222488403, 0.004196450114250183, 0.04471571743488312, -0.056970708072185516, 0.01700751855969429, 0.03896239772439003, -0.0062406170181930065, 0.057033609598875046, -0.005046299658715725, 0.06340627372264862, -0.003911563660949469, -0.020927000790834427, -0.0513288713991642, -0.040431562811136246, 0.028033509850502014, -0.0020617067348212004, -0.030415672808885574, -0.017835522070527077, -0.04105808958411217, -0.024045225232839584, 0.0946197584271431, 0.02749171480536461, 0.041594333946704865, 0.02809729054570198, 0.014549423940479755, 0.08701577037572861, 0.028854627162218094, 0.08322261273860931, 0.06309686601161957, -0.034572865813970566, -0.001489349058829248, -0.0037134247832000256, -0.028371207416057587, -0.008146659471094608, 0.04111466556787491, 0.005805263761430979, 0.011071747168898582, 0.0029828331898897886, 0.008704403415322304, -0.014012525789439678, -0.03112112544476986, 0.014920705929398537, -0.015785181894898415, -0.03375784307718277, 0.032291099429130554, 0.07278895378112793, 0.010400048457086086, -0.028901243582367897, 0.026228198781609535, 0.015208620578050613, 0.004956468939781189, -0.0038721561431884766, -0.034489892423152924, -0.009395251050591469, -0.004767723381519318, -0.016760531812906265, -0.06605935841798782, -0.058276861906051636, -0.03507255017757416, -0.03620728477835655, 0.013217244297266006, -0.019143225625157356, 0.04435170814394951, 0.03680558130145073, -0.0768066868185997, -0.01748770847916603, 0.02797122858464718, -0.031768884509801865, 0.08273450285196304, -0.033058617264032364, 0.06794190406799316, -0.0011075726943090558, 0.01922621764242649, 0.014898779802024364, 0.0038330662064254284, -0.017653902992606163, -0.028051618486642838, -0.005803030915558338, 0.05537997558712959, 0.03655153885483742, 0.04242340475320816, -0.009323752485215664, -0.02280881442129612, 0.05193936452269554, -0.05369022861123085, -0.016147950664162636, 0.006859481334686279, -0.10249608755111694, -0.03563074395060539, -0.002812544349581003, -0.023873120546340942, 0.03825648874044418, 0.04459172487258911, -0.0022366123739629984, -0.07642154395580292, 0.029498955234885216, 0.003713379381224513, 0.03798476979136467, 0.0011695852736011147, 0.008111676201224327, 0.04677020385861397, 0.01762801595032215, 0.02754000946879387, -0.000973341113422066, 0.030479013919830322, -0.015544136054813862, -0.021273480728268623, -0.05136962980031967, 0.006080008111894131, -0.10130974650382996, -0.03700112923979759, 0.04009682685136795, -0.0495024137198925, -0.01590929925441742, -0.02054235152900219, 0.011870737187564373, -0.025727365165948868, 0.012132219970226288, -0.032987628132104874, 0.006344595458358526, -0.005871105007827282, 0.017778435721993446, -5.8766916481545195e-05, 0.05811844393610954, 0.028711572289466858, -0.003415839048102498, -0.09109007567167282, 0.012217654846608639, 0.016184460371732712, -0.038731519132852554, 0.027930470183491707, 0.03560810536146164, -0.027515167370438576, -0.048870302736759186, -0.01235928200185299, 0.0031905383802950382, -0.01760018989443779, -0.0010350256925448775, -0.05711297690868378, -0.003555968636646867, 0.023699481040239334, 0.0014465617714449763, 0.032341547310352325, -0.016636407002806664, -0.037207406014204025, -0.023447643965482712, -0.014970995485782623, -0.019675428047776222, 0.03906196728348732, -0.007756513077765703, -0.016011197119951248, -0.023047005757689476, 0.0053097945638000965, -0.0256096962839365, 0.022645944729447365, 0.013852355070412159, 0.04388207942247391, -0.010707426816225052, 0.03669075295329094, -0.05072209611535072, 0.042242806404829025, 0.04720399156212807, 0.025144057348370552, 0.009792681783437729, -0.03315982222557068, -0.011945771053433418, -0.022419530898332596, -0.04321535676717758, -0.036586061120033264, -0.004215268883854151, 0.029958553612232208, -0.005811833776533604, -0.0033340645022690296, 0.006510143633931875, -0.04551481828093529, -0.025678077712655067, -0.02666534297168255, -0.09156849980354309, -0.027867456898093224, -0.0019433164270594716, -0.0299316868185997, 0.023989448323845863, -0.012311136350035667, -0.04094499722123146, -0.010918468236923218, -0.030173517763614655, -0.022324034944176674, -0.037805452942848206, 0.057889457792043686, -0.022676510736346245, -0.0008441607933491468, -0.040200214833021164, -0.04414769262075424, -0.04836006462574005, 0.04998723044991493, -0.0170757994055748, 0.018621018156409264, -0.0010842144256457686, -0.029037663713097572, 0.009447626769542694, 0.019846569746732712, 0.0298477616161108, 0.07242102175951004, 0.01151695754379034, 0.021411286666989326, -0.036345720291137695, 0.06449621170759201, 0.0644923523068428, 0.012769099324941635, -0.017469698563218117, 0.05439465865492821, 0.03160560876131058, 0.004260912537574768, 0.06451865285634995, 0.00792111549526453, -0.12289228290319443, -0.0066681113094091415, 0.028448564931750298, -0.00342951319180429, -0.01320001482963562, 0.016432953998446465, 0.033228497952222824, -0.059240251779556274, 0.019909488037228584, 0.04048469290137291, -0.03637038171291351, -0.02300296537578106, -0.011368063278496265, 0.007486793212592602, -0.019622741267085075, -0.013143718242645264, -0.010573879815638065, -0.03287791833281517, -0.014689150266349316, 0.05605247616767883, 0.009425784461200237, 0.04708201810717583, -0.017368115484714508, -0.012214228510856628, -0.06083034723997116, 0.014310643076896667, 0.0028136265464127064, -0.057778846472501755, -0.064752958714962, -0.023217668756842613, -0.016975976526737213, -0.00837039016187191, 0.03697134926915169, -0.019324438646435738, 0.01927020773291588, -0.03736965358257294, 0.065275639295578, -0.10255137830972672, -0.006262629758566618, 0.03151308745145798, -0.058877840638160706, 0.07423239201307297, 0.09739254415035248, 0.046734560281038284, -0.05004670470952988, -0.022800056263804436, -0.009096646681427956, 0.03564678877592087, 0.046594295650720596, 0.007242327090352774, 0.024526331573724747, 0.004002486355602741, -0.015267915092408657, 0.022269655019044876, 0.07447658479213715, -0.06384429335594177, 0.030701933428645134, 0.028800930827856064, 0.054358936846256256, 0.022158898413181305, 0.008661998435854912, -0.023254118859767914, 0.022164279595017433, 0.04376406967639923, 0.030698712915182114, -0.0011889588786289096, 0.0061808121390640736, -0.004912617150694132, 0.02700772136449814, 0.0527690164744854, 0.0033742741215974092, -0.0038088972214609385, -0.02867897041141987, -0.008814734406769276, -0.057707902044057846, -0.08086656033992767, -0.00027725950349122286, -0.016204489395022392, 0.053316857665777206, 0.07552570849657059, 0.02951161563396454, 0.06266148388385773, 0.012818302027881145, -0.016401229426264763, -0.001661887625232339, 0.010709419846534729, 0.060368992388248444, -0.023791003972291946, -0.024678101763129234, 0.01768925040960312, -0.0510493703186512, -0.010032898746430874, -0.027037154883146286, -0.02183650992810726, -0.02302371710538864, 0.04592026770114899, -0.0034560144413262606, 0.021845506504178047, 0.03788146749138832, -0.04962977021932602, -0.014811951667070389, 0.04601972550153732, 0.02235976792871952, -0.021730411797761917, 0.0064629316329956055, 0.04145052656531334, 0.025101572275161743, 0.0006871434743516147, 0.0017784701194614172, -0.04642322659492493, 0.04963226616382599, 0.0024078558199107647, -0.012197878211736679, 0.021426362916827202, -0.07094347476959229, 0.0005935307708568871, 0.01299812737852335, 0.08257945626974106, 0.032793305814266205, -0.0006662147352471948, -0.049192775040864944, 0.05523378774523735, 0.013190850615501404, 0.06699632108211517, -0.08015378564596176, -0.002773429499939084, 0.03839416429400444, 0.07655882835388184, 0.0025067399255931377, -0.016405560076236725, 0.03515206649899483, -0.09530927985906601, -0.005701411981135607, 0.08075808733701706, 0.0390687920153141, 0.02870316617190838, -0.0031113270670175552, 0.03200773894786835, -0.023607484996318817, 0.018546056002378464, 0.028823109343647957, 0.03715090453624725, -0.022842833772301674, 0.025373170152306557, 0.006012177560478449, -0.004283620044589043, 0.01859189011156559, 0.01762653887271881, -0.02007165364921093, -0.02835542894899845, -0.012126087211072445, 0.035276614129543304, 0.03161180764436722, -0.014110212214291096, -0.006654323078691959, 0.04045811668038368, 0.03463556990027428, -0.02243456430733204, 0.0470777228474617, -0.06569155305624008, 0.04734739661216736, 0.05186617374420166, 0.006857900880277157, 0.01045499462634325, 0.04177234694361687, 0.01691545732319355, 0.029334083199501038, 0.04174590855836868, -0.013941090553998947, 0.02231411263346672, -0.017512017861008644, -5.5917200370458886e-05, 0.03450700268149376, 0.007716236636042595, -0.01924767531454563, -0.01586182229220867, 0.024189719930291176, -0.08278922736644745, 0.05140165612101555, -0.01307305321097374, 0.03741716593503952, -0.04845118150115013, 0.025944214314222336, -0.020673351362347603, 0.0014844014076516032, -0.0037582945078611374, 0.010204808786511421, -0.008913888595998287, -0.023451736196875572, -0.03554505854845047, -0.007703046314418316, -6.563806906042077e-33, -0.016341328620910645, 0.03677637502551079, -0.007484480272978544, -0.031288325786590576, -0.0605466365814209, 0.025873037055134773, -0.03353020176291466, -0.015743060037493706, -0.012787998653948307, 0.008448245003819466, -0.0481097586452961, -0.00855750497430563, 0.024833377450704575, 0.04813098534941673, 0.01146099716424942, -0.0314008928835392, 0.06445339322090149, 0.007648324593901634, 0.059643637388944626, -0.010246999561786652, 0.019016360864043236, 0.06041274592280388, 0.04780404642224312, -0.04963750019669533, -0.0587923564016819, 0.029597928747534752, 0.033797699958086014, -0.046187158674001694, 0.0004265912575647235, -0.02314024418592453, 0.0006253673927858472, 0.026269251480698586, -0.01725202426314354, -0.032639577984809875, -0.014190686866641045, 0.039056845009326935, -0.09572074562311172, 0.011852823197841644, -0.027162330225110054, 0.02668575383722782, -0.014322550036013126, 0.00576885836198926, 0.07324652373790741, -0.00694842915982008, -0.00845924112945795, -0.0007018574397079647, 0.03980450704693794, -0.022255955263972282, -0.03760787099599838, -0.08229979872703552, -0.02306777983903885, 0.008678887039422989, -0.02852007932960987, -0.024084890261292458, 0.0331139899790287, 0.005342009011656046, -0.031588081270456314, -0.012752437964081764, -0.10959536582231522, 0.007163817994296551, -0.001667661126703024, 0.07238397747278214, 0.04560960456728935, 0.019415171816945076, 0.005785376764833927, 0.010328714735805988, 0.04777497425675392, -0.06261657178401947, 0.0007981426897458732, 0.02197522483766079, -0.00802360288798809, 0.08879943937063217, 0.021958261728286743, 0.011867194436490536, 0.04878707230091095, -0.03386624529957771, -0.06633438169956207, 0.0032460044603794813, 0.006508955731987953, 0.018530510365962982, -0.006787506863474846, 0.05594988912343979, -0.051373012363910675, -0.0007552366005256772, -0.01527765765786171, 0.012236280366778374, -0.026389451697468758, -0.016015833243727684, 0.049222562462091446, -0.014903047122061253, 0.03675589710474014, 0.01240044180303812, 0.004044944420456886, -0.0712309330701828, 0.05491619557142258, -0.028017623350024223, 0.047041211277246475, -0.011004237458109856, -0.009923312813043594, -0.024891577661037445, -0.09504634886980057, -0.013178800232708454, 0.05169735476374626, 0.07216160744428635, 0.04108341038227081, -0.022104401141405106, 0.020542720332741737, 0.038503505289554596, -0.04298781603574753, -0.0322328582406044, -0.013791377656161785, 0.013636365532875061, 0.007938744500279427, 0.012865938246250153, 0.00023161302669905126, -0.05704480782151222, 0.011634498834609985, 0.011277241632342339, -0.018320174887776375, 0.005089128389954567, -0.027169739827513695, 0.002226285869255662, 0.013086248189210892, 0.005150181241333485, -0.10084358602762222, -0.009117710404098034, -0.03453324735164642, -0.03198300674557686, 0.02788553573191166, -0.022570502012968063, -0.015736989676952362, 0.022022794932127, 3.0505324843943527e-07, -0.07871505618095398, 0.0013850254472345114, 0.04044486582279205, -0.07114627212285995, 0.02526513859629631, 0.0054619633592665195, -0.013099661096930504, 0.02741917409002781, 0.01260232925415039, 0.001363765331916511, 0.02915877103805542, 0.006628409028053284, 0.07275418937206268, -0.02950303815305233, -0.09097710251808167, -0.04425355792045593, -0.07055547833442688, 0.02408135123550892, 0.006148636341094971, 0.015178014524281025, 0.006077286787331104, 0.07016312330961227, 0.0112198106944561, -0.0486309789121151, 0.04148692637681961, 0.00681014358997345, -0.010702281259000301, -0.0013101211516186595, 0.040482062846422195, -0.025087907910346985, 0.025283433496952057, -0.01618921384215355, -0.05178233981132507, -0.014086442068219185, -0.009518575854599476, 0.018437424674630165, 0.02073073573410511, 0.04781213030219078, -0.044338710606098175, -0.04869721457362175, -0.0051276590675115585, 0.05712612718343735, 0.015466362237930298, -0.007644582074135542, 0.04103092849254608, -0.03542647510766983, -0.05568838119506836, -0.06440135836601257, -0.027230938896536827, -0.0052526299841701984, -0.004341075196862221, 0.03339662775397301, 0.03842754289507866, -0.033896688371896744, -0.002611233154311776, -0.02422477863729, -0.05815983936190605, -0.04628517106175423, 0.027270762249827385, 0.02513730339705944, -0.056308552622795105, -0.017606278881430626, -0.033069491386413574, 0.008189131505787373, 0.018099069595336914, -0.029703855514526367, -0.024845294654369354, 2.4009577726365804e-34, -0.04487959295511246, -0.012305778451263905, -0.014155220240354538, 0.004529247526079416, -0.003433228237554431, -0.04440087452530861, -0.0017749473918229342, 0.03614737465977669, -0.02369157038629055, -0.05975586548447609, -0.05958068370819092]

['Sarath Chandar', 'Mitesh M. Khapra', 'Hugo Larochelle', 'Balaraman Ravindran']

1504.07225v3

Common Representation Learning (CRL), wherein different descriptions (or views) of the data are embedded in a common subspace, is receiving a lot of attention recently. Two popular paradigms here are Canonical Correlation Analysis (CCA) based approaches and Autoencoder (AE) based approaches. CCA based approaches learn a joint representation by maximizing correlation of the views when projected to the common subspace. AE based methods learn a common representation by minimizing the error of reconstructing the two views. Each of these approaches has its own advantages and disadvantages. For example, while CCA based approaches outperform AE based approaches for the task of transfer learning, they are not as scalable as the latter. In this work we propose an AE based approach called Correlational Neural Network (CorrNet), that explicitly maximizes correlation among the views when projected to the common subspace. Through a series of experiments, we demonstrate that the proposed CorrNet is better than the above mentioned approaches with respect to its ability to learn correlated common representations. Further, we employ CorrNet for several cross language tasks and show that the representations learned using CorrNet perform better than the ones learned using other state of the art approaches.

Correlational Neural Networks

http://arxiv.org/pdf/1504.07225v3

Title Correlational Neural Networks Summary Common Representation Learning CRL wherein different description view data embedded common subspace receiving lot attention recently Two popular paradigm Canonical Correlation Analysis CCA based approach Autoencoder AE based approach CCA based approach learn joint representation maximizing correlation view projected common subspace AE based method learn common representation minimizing error reconstructing two view approach advantage disadvantage example CCA based approach outperform AE based approach task transfer learning scalable latter work propose AE based approach called Correlational Neural Network CorrNet explicitly maximizes correlation among view projected common subspace series experiment demonstrate proposed CorrNet better mentioned approach respect ability learn correlated common representation employ CorrNet several cross language task show representation learned using CorrNet perform better one learned using state art approach Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.012877211906015873, 0.0465271919965744, -0.013225826434791088, 0.03985082358121872, -0.031307924538850784, 0.03361591696739197, 0.038085710257291794, -0.0033907159231603146, 0.014290286228060722, 0.005074954591691494, -0.06664880365133286, -0.001258045551367104, 0.051832761615514755, 0.008261256851255894, 0.009200862608850002, -0.055637817829847336, 0.019240424036979675, 0.043437644839286804, -0.04262537881731987, -0.048932187259197235, -0.004228933714330196, -0.05393192917108536, 0.02188131771981716, 0.013165095821022987, -0.04264106601476669, -0.024949833750724792, -0.015067319385707378, -0.03839066997170448, 0.022722482681274414, 0.017305217683315277, 0.00242210878059268, 0.021110808476805687, 0.05724968761205673, 0.011383111588656902, 2.168533455915167e-06, -0.00552557734772563, -0.023792795836925507, -0.012226027436554432, 0.060905564576387405, -0.04349870979785919, -0.019682761281728745, -0.0008808413986116648, 0.0365653894841671, 0.0002194270637119189, -0.043883729726076126, 9.493177640251815e-05, 0.053339727222919464, 0.09351514279842377, 0.035133060067892075, 0.03445195406675339, -0.02505231276154518, -0.0735660046339035, 0.009240963496267796, -0.052051737904548645, -0.004950893111526966, -0.027123643085360527, 0.034408263862133026, 0.05444527044892311, -0.007079466246068478, -0.006415585987269878, -0.05612801015377045, 0.024858947843313217, 0.03321238234639168, 0.0002164338220609352, -0.01999475061893463, 0.011333689093589783, -0.05447135493159294, -0.013158496469259262, 0.0006936073768883944, 0.0798504501581192, -0.024554764851927757, 0.006319308187812567, -0.00041316315764561296, 0.018570253625512123, -0.03256547823548317, -0.011229893192648888, -0.039180416613817215, 0.005745869595557451, -0.002413068898022175, 0.03997187316417694, -0.03474948927760124, 0.060827095061540604, -0.007346423342823982, -0.02805732749402523, -0.0324237123131752, -0.02107536792755127, 0.00028070007101632655, 0.022511979565024376, -0.04129071161150932, -0.010911828838288784, 0.020549966022372246, 0.015092100016772747, 0.007438380271196365, 0.003082477953284979, -0.0051082042045891285, -0.03358003497123718, -0.004307333845645189, -0.08852645009756088, 0.02178940363228321, -0.05248899385333061, 0.025245659053325653, 0.008068890310823917, -0.03273732215166092, 0.023303180932998657, -0.06139335781335831, 0.09743084013462067, -0.038830868899822235, 0.02761596068739891, -0.02580246515572071, -0.028189074248075485, -0.0645693764090538, -0.021822204813361168, -0.014933062717318535, 0.07248915731906891, 0.035686057060956955, -0.04820651933550835, -0.09104023873806, -0.012645972892642021, -0.05925283953547478, 0.047069329768419266, 0.02993881329894066, 0.0787004828453064, 0.010419604368507862, 0.022963520139455795, 0.03527338057756424, 0.009951511397957802, -0.010466231033205986, 0.022363444790244102, -0.04822381213307381, 0.007507234811782837, 0.03348737210035324, 0.05763127654790878, 0.020559657365083694, -0.0005461283726617694, -0.014012403786182404, 0.04995570331811905, 0.021884189918637276, 0.01385029498487711, 0.03161007538437843, -0.015026169829070568, -0.018701164051890373, -0.0170455202460289, -0.0032728281803429127, -0.0772206112742424, 0.03893527016043663, -0.003512871917337179, -0.0047553530894219875, -0.04037486016750336, -0.03676915913820267, -0.022140875458717346, -0.058423034846782684, 0.059734929352998734, 0.026258258149027824, -0.014754120260477066, 0.03930012136697769, 0.00935453176498413, 0.02625005692243576, 0.023222103714942932, 0.01921118050813675, 0.030442746356129646, -0.013828870840370655, -0.005612314213067293, 0.00856612715870142, -0.005873571615666151, -0.020601382479071617, -0.08230684697628021, -0.052850183099508286, -0.03522650897502899, 0.06459777802228928, 0.004273606929928064, 0.022161215543746948, 0.02992064505815506, -0.01589040271937847, -0.03588152304291725, 0.013422290794551373, 0.022869916632771492, 0.08186906576156616, 0.013587112538516521, 0.024827681481838226, -0.009075148962438107, 0.02771851420402527, 0.033223956823349, 0.036589354276657104, 0.059270624071359634, -0.004164310172200203, -0.042215894907712936, -0.019302811473608017, -0.006463716272264719, -0.069792740046978, -0.018602361902594566, 0.045538727194070816, -0.03308061510324478, -0.025175191462039948, -0.025837808847427368, 0.05069117993116379, -0.025916125625371933, 0.0029323443304747343, -0.03828095644712448, 0.026657946407794952, 0.018373237922787666, -0.017918258905410767, 0.0012970608659088612, -0.005591967608779669, -0.03106577880680561, 0.004466677084565163, -0.004679890349507332, -0.03984064608812332, 0.014530097134411335, -0.023617776110768318, -0.027396084740757942, 0.023890890181064606, -0.022215327247977257, -0.01589125767350197, -0.029467536136507988, -0.0612192265689373, -0.013721240684390068, 0.014995663426816463, 0.06306546181440353, -0.08684470504522324, 0.0403217189013958, 0.0564807653427124, 0.032057806849479675, -0.005510143935680389, -0.011600242927670479, -0.005894200876355171, 0.06252092123031616, 0.04420172795653343, 0.07015622407197952, -0.012000530026853085, 0.01987878605723381, 0.016219988465309143, 0.0142303965985775, 0.003679528832435608, -0.06586934626102448, -0.020029503852128983, 0.05586955323815346, -0.07104828208684921, -0.03936557471752167, -0.0004358010774012655, -0.056128449738025665, 0.0062318965792655945, 0.03700822964310646, -0.003534801071509719, -0.053051795810461044, 0.06303583085536957, 0.0193367600440979, 0.02267574332654476, 0.007868570275604725, -0.0036015205550938845, -0.002309964969754219, 0.03642173483967781, -0.007334703579545021, 0.07077660411596298, 0.025382619351148605, 0.005806859582662582, 0.06605308502912521, -0.02297675609588623, 0.07123153656721115, -0.011574669741094112, -0.03528975322842598, 0.00038746470818296075, 0.009413428604602814, -0.00030145898927003145, 0.024922199547290802, -0.015007054433226585, 0.014743530191481113, -0.021929142996668816, -0.017349496483802795, -0.02857508882880211, 0.0043383375741541386, -0.027136273682117462, 0.009217921644449234, -0.014125164598226547, 0.04940813034772873, -0.018501244485378265, -0.06161140650510788, 0.09374935179948807, 0.011146978475153446, -0.0008023171103559434, 0.017588863149285316, 0.023063795641064644, 0.01132996566593647, -0.017398929223418236, -0.020752618089318275, -0.02178838849067688, 0.06107300892472267, 0.03787360340356827, -0.0915876254439354, -0.01071842573583126, 0.06738990545272827, -0.017923900857567787, 0.02583233267068863, -0.011404654942452908, 0.0003794076037593186, -0.013722953386604786, -0.033039823174476624, -0.025011250749230385, 0.01742006465792656, -0.0038600172847509384, -0.02762635052204132, 0.03147298842668533, 0.003326677018776536, -0.05678481236100197, 0.008413254283368587, -0.03544527292251587, 0.013644559308886528, 0.018390335142612457, 0.015472490340471268, -0.012853454798460007, 0.0022842090111225843, 0.03164071962237358, -0.005984497722238302, -0.033008042722940445, -0.012432881630957127, 0.012855680659413338, -0.0021228280384093523, -0.08035634458065033, -0.051376454532146454, 0.005535861011594534, -0.0023091244511306286, -0.029565338045358658, 0.006822019349783659, -0.002820681780576706, 0.00010651969932951033, 0.05116758123040199, -0.0003465240588411689, 0.016199873760342598, -0.05774928629398346, 0.019788794219493866, 0.03290140628814697, 0.03319567069411278, -0.01730426959693432, -0.059327382594347, -0.04810689017176628, 0.01989009976387024, 0.03556705266237259, -0.005174210295081139, -0.005414305720478296, 0.029192959889769554, -0.028741057962179184, -0.01181896310299635, -0.035943567752838135, -0.0776674896478653, 0.02968030422925949, 0.005251698661595583, 0.04038320481777191, -0.03102831169962883, 0.013632187619805336, -0.03127593919634819, 0.003936488181352615, -0.0024116775020956993, 0.01294553279876709, 0.008752272464334965, 0.0050776950083673, -0.005716440733522177, 0.04952576756477356, 0.03864763304591179, 0.041102781891822815, -0.027368225157260895, 0.0065160952508449554, 0.004934594500809908, 0.03225255012512207, -0.033025410026311874, 0.023586565628647804, -0.06167170777916908, 0.035689447075128555, 0.005094445310533047, 0.030898738652467728, -0.03864264860749245, -0.012983785010874271, -0.032431215047836304, -0.0013874437427148223, 0.02062775008380413, 0.05486122518777847, -0.005030801985412836, -0.1423313021659851, -0.03867223858833313, -0.04119893163442612, -0.05000980198383331, 0.03125263750553131, 0.04208294674754143, -0.0034617509227246046, -0.00413576839491725, -0.028641531243920326, -0.0480116531252861, 0.03112298995256424, -0.04269978031516075, 0.0037530690897256136, -0.03241034597158432, -0.0251312218606472, -0.01235960517078638, 0.011756434105336666, -0.07675899565219879, -0.029634827747941017, 0.02409554086625576, -0.008541210554540157, -0.008860494941473007, -0.026538090780377388, 0.01732390932738781, -0.04524793103337288, 0.037731464952230453, -0.057038694620132446, -0.02694755606353283, -0.007696037646383047, -0.052178915590047836, 0.015624907799065113, 0.06068994104862213, 0.05868981033563614, -0.046656783670186996, -0.030298011377453804, -0.03689683973789215, -0.03572852537035942, 0.04572796821594238, -0.01594073325395584, 0.043950196355581284, 0.006752020679414272, -0.04549046978354454, 0.031433962285518646, 0.032433319836854935, -0.0215908195823431, 0.022545386105775833, -0.00485087838023901, 0.05856935307383537, -0.015200791880488396, -0.023626770824193954, -0.037132132798433304, -0.00675659254193306, 0.0033912144135683775, 0.02066962793469429, 0.036759860813617706, 0.0028410840313881636, -0.001090066391043365, 0.04340531677007675, 0.010677877813577652, -0.010713777504861355, 0.01913599669933319, 0.0009639293421059847, 0.019122973084449768, -0.05361722409725189, -0.06656630337238312, -0.004984232131391764, 0.017064737156033516, 0.04425470903515816, 0.02590128406882286, 0.010440632700920105, 0.02076135016977787, -0.0343111976981163, -0.04802148789167404, -0.025008399039506912, 0.0375489816069603, -0.001983864465728402, -0.046773847192525864, 0.04603610932826996, 0.023152325302362442, -0.04829460009932518, -0.01621090993285179, -0.054643698036670685, -0.040952038019895554, -0.03312840312719345, -0.025280006229877472, 0.04295191913843155, -0.001445594010874629, 0.03244710713624954, -0.03062533773481846, -0.03458638861775398, 0.007526215631514788, 0.052355967462062836, 0.0005942240240983665, -0.007776224985718727, 0.011459900997579098, -0.035971883684396744, -0.02704237774014473, 0.012939206324517727, -0.03415830433368683, 0.03607684373855591, 0.016996070742607117, 0.009965253062546253, -0.015000667423009872, -0.006891313474625349, 0.025522639974951744, -0.0196421816945076, 0.043023861944675446, 0.02537061832845211, 0.04182807356119156, -0.049439117312431335, -0.008867932483553886, -0.022997839376330376, -0.018953753635287285, -0.006079729646444321, 0.03349142521619797, -0.0030982724856585264, 0.024952545762062073, -0.007633389439433813, 0.02496849000453949, 0.043048590421676636, -0.047151751816272736, -0.030745618045330048, 0.020173516124486923, -0.024264847859740257, 0.020505638793110847, -0.047244906425476074, 0.02967376820743084, -0.003276941366493702, -0.008074715733528137, 0.045847345143556595, 0.015074225142598152, -0.022868867963552475, 0.018753020092844963, 0.01029013842344284, 0.04730444401502609, -0.06462270766496658, 0.03774108365178108, 0.004090351052582264, 0.0008657281869091094, -0.011430934071540833, 0.02627405896782875, 0.0496707521378994, -0.019913366064429283, 0.005096632055938244, -0.02470768429338932, 0.024575838819146156, -0.03849704563617706, 0.030306583270430565, -0.012472960166633129, -0.02246757037937641, 0.04852979630231857, -0.04072890803217888, 0.014170367270708084, -0.03691326081752777, 0.10075320303440094, -0.08929406851530075, -0.027751374989748, -0.04455668106675148, -0.02928822487592697, -0.0142897330224514, 0.038761917501688004, 0.09977768361568451, -0.01290479488670826, -0.046170271933078766, -0.0015824821311980486, -0.005589078646153212, -0.04215718060731888, 0.06956201791763306, -0.014091100543737411, 0.005413925275206566, 0.06351086497306824, 0.029856296256184578, 0.015713611617684364, 0.046651605516672134, 0.030921459197998047, 0.0002473431813996285, 0.010130955837666988, 0.024789100512862206, -0.01100084651261568, 0.006428917404264212, -5.920105832189808e-33, 0.0298154354095459, -0.003776020370423794, -0.024834290146827698, -0.01369741652160883, 0.008225704543292522, 0.025054283440113068, -0.02912677824497223, 0.017223158851265907, -0.022981425747275352, -0.019076235592365265, -0.0045053656212985516, -0.016629181802272797, 0.00460055610165, 0.019967300817370415, 0.07284494489431381, 0.002509874990209937, -0.0002867814910132438, 0.019845159724354744, 0.04110073298215866, 0.012882948853075504, 0.050766050815582275, 0.04490760341286659, 0.03534430265426636, -0.11822263896465302, -0.037895455956459045, 0.039852581918239594, 0.04594830423593521, -0.01018348429352045, 0.033695220947265625, 0.011565335094928741, -0.0433436818420887, 0.022177264094352722, 0.03430155664682388, 0.0075548687018454075, -0.022367751225829124, -0.006011637859046459, -0.06525174528360367, -0.09534917026758194, -0.05705204978585243, 0.028630400076508522, -0.05766863375902176, 0.013380110263824463, 0.04364151135087013, -0.019090956076979637, 0.031640131026506424, 0.02146146260201931, 0.06561553478240967, -0.012712026946246624, 0.0028118574991822243, -0.010670579969882965, -0.02992427907884121, 0.007994722574949265, -0.012333442457020283, 0.022046612575650215, 0.056125473231077194, 0.0584685318171978, -0.006464844103902578, 0.034115083515644073, -0.07180680334568024, 0.03304911032319069, -0.0684180036187172, 0.021682102233171463, 0.035668209195137024, -0.007666986435651779, 0.039061933755874634, 0.06134055554866791, -0.012209136039018631, -0.02961517684161663, -0.0389799028635025, 0.009343478828668594, 0.008619796484708786, 0.046718042343854904, 0.01437515951693058, 0.07925883680582047, 0.022404566407203674, -0.062451764941215515, -0.07675530761480331, 0.06853001564741135, 0.008034024387598038, 0.046296026557683945, 0.00317883281968534, -0.025582438334822655, -0.046131256967782974, -0.03993787616491318, 0.011268260888755322, 0.026083750650286674, -0.06594528257846832, -0.03485214710235596, 0.019544510170817375, -0.012714620679616928, -0.0093195466324687, 0.0009494326077401638, 0.00013546097034122795, -0.07952826470136642, -0.015622662380337715, 0.053050678223371506, -0.010259300470352173, 0.023350117728114128, 0.02872297912836075, 0.002295232377946377, -0.043151501566171646, -0.05421353504061699, -0.016261884942650795, 0.008454681374132633, 0.02654767595231533, 0.0009488495998084545, 0.09218602627515793, 0.009459963999688625, 0.022065885365009308, -0.023206286132335663, 0.004391556605696678, -0.08505957573652267, 0.02811095304787159, -0.009851092472672462, -3.0630730179836974e-05, 0.023016804829239845, -0.008758747950196266, -0.004057306796312332, 0.0035456973128020763, 0.009557593613862991, -0.002667240099981427, -0.057423800230026245, 0.06993641704320908, 0.046751718968153, -0.0059041171334683895, -0.036006052047014236, -0.05375607684254646, 0.014190267771482468, 0.0553271621465683, -0.04238874837756157, -0.020080646499991417, -0.00032918929355219007, 2.855287561942532e-07, 0.007484168279916048, -0.03163799270987511, 0.022228065878152847, -0.05554137006402016, 0.0197532307356596, 0.01779739372432232, -0.021036257967352867, 0.09379585087299347, -0.010586859658360481, -0.005981510505080223, 0.03278718516230583, -0.014620775356888771, -0.01579206809401512, -0.012239523231983185, -0.022115221247076988, 0.028618093580007553, 4.4261218135943636e-05, -0.015188774093985558, 0.0008005875861272216, -0.014984049834311008, 0.07965478301048279, 0.0503825768828392, 0.011162807233631611, -0.005383064039051533, 0.01836167462170124, 0.04478849470615387, 0.04909275844693184, 0.0014296069275587797, 0.03764033690094948, -0.007902052253484726, -0.004178105387836695, -0.0039078365080058575, -0.009291992522776127, 0.019847018644213676, 0.011335259303450584, 0.04250418022274971, 0.08063966780900955, -0.06927218288183212, -0.0033684661611914635, -0.035124264657497406, 0.0018961261957883835, 0.026168229058384895, -0.0058278352953493595, -0.015961283817887306, 0.07021354138851166, -0.07986035943031311, -0.05251453071832657, -0.03120535798370838, 0.0045732236467301846, 0.061646655201911926, 0.0481080636382103, 0.026766296476125717, 0.00017276588187087327, -0.02033841423690319, 0.006215975154191256, -0.020268632099032402, 0.004440947901457548, -0.05786038190126419, 0.044900983572006226, -0.0027879311237484217, -0.05249442905187607, 0.046772826462984085, -0.015852533280849457, -0.037154726684093475, 0.07282575964927673, 0.017273971810936928, 0.024200018495321274, 1.9705266388539988e-34, -0.037505850195884705, 0.023851893842220306, 0.008768288418650627, -0.05439142882823944, -0.052527304738759995, -0.03466898947954178, -0.09137266874313354, 0.011122629046440125, 0.015840332955121994, -0.039338331669569016, -0.06759653985500336]

['Jan Chorowski', 'Dzmitry Bahdanau', 'Dmitriy Serdyuk', 'Kyunghyun Cho', 'Yoshua Bengio']

1506.07503v1

Recurrent sequence generators conditioned on input data through an attention mechanism have recently shown very good performance on a range of tasks in- cluding machine translation, handwriting synthesis and image caption gen- eration. We extend the attention-mechanism with features needed for speech recognition. We show that while an adaptation of the model used for machine translation in reaches a competitive 18.7% phoneme error rate (PER) on the TIMIT phoneme recognition task, it can only be applied to utterances which are roughly as long as the ones it was trained on. We offer a qualitative explanation of this failure and propose a novel and generic method of adding location-awareness to the attention mechanism to alleviate this issue. The new method yields a model that is robust to long inputs and achieves 18% PER in single utterances and 20% in 10-times longer (repeated) utterances. Finally, we propose a change to the at- tention mechanism that prevents it from concentrating too much on single frames, which further reduces PER to 17.6% level.

Attention-Based Models for Speech Recognition

http://arxiv.org/pdf/1506.07503v1

Title AttentionBased Models Speech Recognition Summary Recurrent sequence generator conditioned input data attention mechanism recently shown good performance range task cluding machine translation handwriting synthesis image caption gen eration extend attentionmechanism feature needed speech recognition show adaptation model used machine translation reach competitive 187 phoneme error rate PER TIMIT phoneme recognition task applied utterance roughly long one trained offer qualitative explanation failure propose novel generic method adding locationawareness attention mechanism alleviate issue new method yield model robust long input achieves 18 PER single utterance 20 10times longer repeated utterance Finally propose change tention mechanism prevents concentrating much single frame reduces PER 176 level Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.019523048773407936, 0.0204450786113739, 0.008692066185176373, 0.04665157571434975, 0.0042520323768258095, -0.046689894050359726, 0.04492989555001259, -0.01992475427687168, -0.030953174456954002, -0.037043068557977676, -0.05595624819397926, -0.045688990503549576, 0.053314339369535446, 0.027763931080698967, 0.05054059252142906, -0.07282478362321854, -0.010233495384454727, 0.002408494707196951, 0.003717900952324271, 0.03548959270119667, 0.02941533736884594, -0.0021077371202409267, -0.01845041662454605, 0.06267230212688446, 0.006113787647336721, 0.01457064226269722, -0.018543776124715805, -0.006540514994412661, -0.005166841670870781, -0.017630353569984436, 0.0035605260636657476, 0.07733456790447235, 0.01868715137243271, 0.033350348472595215, 2.456105448800372e-06, -0.01263565756380558, -0.015105504542589188, -0.012667174451053143, 0.0371665321290493, -0.012073268182575703, 0.054084330797195435, -0.010797534137964249, -0.00944295059889555, 0.06409472227096558, 0.005634389817714691, -0.006546809803694487, 0.0697324126958847, 0.06402835994958878, 0.028870152309536934, 0.061469666659832, -0.0037034121342003345, -0.050375550985336304, 0.030149178579449654, -0.033479150384664536, 0.019641336053609848, -0.013260927982628345, -0.0030382222030311823, -0.05809525027871132, -0.0013284174492582679, -0.012569257989525795, -0.01470824796706438, 0.046862322837114334, -0.005217752419412136, -0.0037017858121544123, 0.030026564374566078, 0.03221360966563225, -0.017080921679735184, -0.024060672149062157, -0.01277151145040989, 0.08150885254144669, -0.04450085759162903, -0.016086667776107788, 0.01835942082107067, 0.022042864933609962, -0.021470969542860985, -0.05275730788707733, -0.03529172018170357, 0.0260054599493742, -0.02479657530784607, -0.020549645647406578, -0.008221066556870937, 0.024460745975375175, -0.002897802274674177, -0.026996202766895294, -0.0019921225029975176, -0.05454625189304352, 0.00699278200045228, -0.03376105800271034, -0.04941282793879509, -0.042719971388578415, -0.017399609088897705, -0.045707788318395615, 0.06858209520578384, 0.047715313732624054, 0.04333923012018204, 0.005965331569314003, -0.03963756933808327, -0.11320449411869049, 0.024674871936440468, -0.06189202889800072, 0.048772312700748444, 0.029606716707348824, -0.05551481619477272, 0.00218715681694448, -0.0053295656107366085, 0.07153059542179108, -0.026271779090166092, -0.024174140766263008, -0.01793541945517063, 0.0232826117426157, -0.013702752068638802, 0.021754691377282143, -0.0408325158059597, 0.01951010525226593, -0.031539831310510635, -0.027059899643063545, -0.048657506704330444, -0.017938600853085518, 0.02544676885008812, -0.028965456411242485, 0.04414726793766022, 0.017738599330186844, -0.05352373421192169, -0.023530153557658195, 0.0011870644520968199, 0.01473207212984562, 0.017936917021870613, 0.03590850532054901, -0.0122101791203022, -0.026824038475751877, -0.014218582771718502, 0.04472009092569351, 0.02504303678870201, 0.020285101607441902, -0.023769481107592583, 0.08061374723911285, 0.01570582017302513, -0.014707962982356548, -0.03142084926366806, 0.005773032549768686, -0.0417177751660347, -0.044571440666913986, -0.009267810732126236, -0.07488391548395157, 0.02979814074933529, -0.018282223492860794, -0.027664080262184143, 0.01076857466250658, 0.016835743561387062, 0.012449009343981743, 0.010032882913947105, 0.06720104813575745, 0.015837328508496284, 0.009571473114192486, 0.05573030561208725, -0.011441746726632118, 0.029536154121160507, -0.009191073477268219, 0.07895068824291229, 0.01474341843277216, -0.006704510655254126, -0.054855942726135254, 0.011976099573075771, 0.030832821503281593, -0.002658306621015072, -0.01300059724599123, 0.010366798378527164, -0.023897195234894753, 0.010790875181555748, 0.028453396633267403, 0.04280495271086693, 0.061890143901109695, 0.009693562984466553, -0.010932810604572296, 0.08140382915735245, 0.07231732457876205, 0.026992902159690857, 0.033542245626449585, 0.0053693149238824844, -0.0020634003449231386, -0.029910942539572716, -0.00672128377482295, -0.022386301308870316, 0.02687189355492592, -0.0075492896139621735, 0.022919313982129097, 0.05540157109498978, -0.013830657117068768, -0.01341424323618412, -0.025134354829788208, -0.012197097763419151, -0.017030686140060425, -0.033666543662548065, 0.0011946590384468436, 0.05120457336306572, 0.020238427445292473, -0.07400678098201752, 0.006262144539505243, -0.0021891428623348475, -0.058335136622190475, -0.023747636005282402, -0.002920199651271105, 0.011472727172076702, 0.052451033145189285, 0.011937682516872883, -0.01623339205980301, 0.0018517699791118503, -0.055045101791620255, -0.014578436501324177, 0.048753269016742706, -0.0039246948435902596, 0.030813971534371376, 0.006933911237865686, -0.08991679549217224, 0.015532506629824638, 0.05495137348771095, -0.008478477597236633, 0.02740553766489029, -0.029670197516679764, 0.02554258704185486, 0.02443469874560833, 0.06391609460115433, -0.05186450853943825, 0.029366420581936836, -0.003015114227309823, -0.04786079004406929, 0.020945271477103233, 0.01810850016772747, 0.06971582025289536, 0.04096940904855728, -0.00701063871383667, 0.02115631476044655, 0.05994614586234093, -0.05094731226563454, 0.03529392555356026, 0.036541156470775604, -0.06183406338095665, -0.028749756515026093, 0.019890232011675835, -0.011242739856243134, 0.035955771803855896, 0.005664801225066185, 0.023288477212190628, -0.07757828384637833, 0.04853691905736923, -0.05940756946802139, 0.05622272938489914, -0.01644556224346161, 0.06769581884145737, 0.019840694963932037, 0.021647581830620766, -0.012797833420336246, 0.009272999130189419, -0.02007914148271084, -0.0037189554423093796, 0.004821585025638342, 0.030588800087571144, 0.0018755900673568249, -0.07830614596605301, -0.02091626264154911, -0.009211071766912937, -0.01721750572323799, 0.03839682787656784, -0.022533943876624107, 0.01696433126926422, -0.017360756173729897, -0.0399659089744091, -0.06533382087945938, -0.0016793716931715608, -0.002550367498770356, -0.003129104617983103, 0.02597769908607006, 0.022930042818188667, 0.017268940806388855, -0.007103771436959505, -0.020355205982923508, -0.017192509025335312, -0.0032372467685490847, -0.023460401222109795, -0.009071802720427513, -0.0365767627954483, 0.0010654113721102476, -0.07168101519346237, 0.001444885740056634, 0.006912580691277981, 0.008227110840380192, 0.017318882048130035, -0.07022639364004135, -0.02103937603533268, 0.015142313204705715, 0.02061137557029724, 0.0473308265209198, 0.0007270195055752993, -0.04407733678817749, -0.0030177158769220114, -0.032568562775850296, 0.042437274008989334, 0.06146848201751709, 0.0009387749014422297, -0.03660466521978378, -0.023363443091511726, -0.020164044573903084, -0.0072048259899020195, 0.014417647384107113, -0.0146273048594594, 0.054745107889175415, 0.0331663154065609, -0.01016413327306509, -0.027473755180835724, 0.05267929658293724, 0.050136465579271317, 0.04019254818558693, -0.04885300621390343, -0.012091116048395634, -0.010387557558715343, -0.0035304806660860777, -0.0006288696895353496, -0.004357145167887211, -0.041941143572330475, -0.01015211921185255, -0.033569544553756714, -0.046884845942258835, 0.017876483500003815, -0.05543035641312599, -0.021440869197249413, -0.025625240057706833, -0.006552246864885092, -0.025265149772167206, 0.03314677253365517, -0.0024768540170043707, 0.009895064868032932, 0.018543163314461708, -0.05607476830482483, 0.017648542299866676, 0.00022873423586133868, -0.00851635355502367, -0.06154249608516693, 0.042969271540641785, 0.023175589740276337, -0.028910135850310326, -0.03953300043940544, -0.021676834672689438, -0.04938891530036926, 0.03270614519715309, -0.02864154987037182, -0.02421792596578598, 0.004094660747796297, -0.04131945222616196, -0.020382758229970932, 0.07046319544315338, 0.03717484325170517, 0.07484825700521469, -0.01839602366089821, 0.0369880348443985, -0.018197985365986824, 0.04529344663023949, 0.02811061218380928, 0.0018705615075305104, -0.037016816437244415, 0.012422101572155952, 0.008673381060361862, 0.004254771862179041, 0.012267561629414558, -0.005058336071670055, -0.07663826644420624, -0.012991131283342838, 0.016343753784894943, -0.007344452198594809, -0.015378073789179325, 0.011605797335505486, 0.043542489409446716, -0.09324904531240463, -0.005681880749762058, 0.08700288087129593, -0.0005702835624106228, -0.03555484488606453, -0.021195871755480766, 0.025508571416139603, -0.007688577752560377, 0.007499569095671177, 0.008405810222029686, -0.0027217883616685867, -0.030122078955173492, 0.009399693459272385, 0.03958436846733093, 0.024887846782803535, 0.011513235978782177, -0.019577540457248688, -0.07885905355215073, 0.06501699984073639, 0.015898261219263077, -0.09243384748697281, -0.07700550556182861, -0.025460708886384964, -0.011807520873844624, -0.004383824300020933, -0.012098136357963085, 0.04415364935994148, -0.0026152951177209616, -0.014639521948993206, 0.02965979464352131, -0.050237126648426056, -0.011097382754087448, -0.01010613702237606, -0.0538659393787384, 0.05221185088157654, 0.08517833799123764, 0.015713896602392197, -0.0006625461974181235, -0.06159384548664093, -0.004326922819018364, 0.021426301449537277, -0.0004837645683437586, 0.008049432188272476, 0.010472760535776615, -0.0011804859386757016, -0.005760690197348595, -0.016978556290268898, 0.06688351929187775, -0.03698095679283142, 0.04354646056890488, 0.04085857421159744, 0.041439905762672424, 0.005640358664095402, 0.02959885261952877, -0.04338172450661659, 0.05740901827812195, 0.02335469238460064, 0.01499383058398962, 0.02924470044672489, -0.04746211692690849, -0.021621931344270706, -0.017954012379050255, 0.01645643450319767, -0.09290467947721481, -0.017295710742473602, 6.62403108435683e-05, -0.0017514450009912252, -0.08108486235141754, -0.09416636824607849, -0.038258299231529236, -0.005092825274914503, 0.02034885622560978, 0.04371487349271774, -0.005232429131865501, 0.04310514032840729, 0.01595877856016159, -0.038205090910196304, 0.041160572320222855, 0.04974409565329552, 0.031884465366601944, -0.09382397681474686, -0.006407556124031544, 0.025544723495841026, -0.05484773591160774, 0.01596832275390625, 0.032312531024217606, -0.06979365646839142, -0.05487832799553871, 0.010119214653968811, 0.035240430384874344, 0.011104660108685493, 0.02801002748310566, -0.06287968903779984, -0.027736764401197433, 0.015453391708433628, -0.06926944851875305, -0.024907168000936508, 0.01347252819687128, 0.06194194406270981, -0.011993223801255226, -0.001263663754798472, -0.014020049944519997, -0.028944851830601692, 0.0579167939722538, 0.009218545630574226, -0.005986247211694717, -0.020716438069939613, -0.06257432699203491, -0.013226518407464027, -0.003013000590726733, 0.04640205204486847, 0.02143132872879505, 0.029253236949443817, -0.05934157222509384, 0.03278685733675957, 0.04020058363676071, 0.031629983335733414, -0.03825506195425987, 0.004852575249969959, 0.03134631738066673, 0.010019185021519661, 0.014548206701874733, -0.04907332733273506, -0.027332637459039688, -0.04032953828573227, 0.04329480975866318, 0.08860266208648682, -0.04111303761601448, 0.06482886523008347, -0.02134324423968792, -0.021056052297353745, -0.02460469678044319, 0.030815739184617996, -0.041262682527303696, 0.050573475658893585, 0.01724034547805786, 0.029732994735240936, -0.021219365298748016, 0.022770725190639496, 0.005196688696742058, 0.02282913215458393, 0.01684160903096199, -0.016149183735251427, -0.06812948733568192, 0.0004967980203218758, 0.05581163614988327, -0.026733431965112686, 0.03479796648025513, 0.02381782978773117, 0.016877586022019386, -0.03982795774936676, 0.05315183848142624, -0.03656425327062607, 0.02994898147881031, 0.002507599536329508, 0.007942111231386662, 0.0046258289366960526, -0.015314025804400444, 0.05034380033612251, 0.0004915020545013249, 0.008687576279044151, 0.025783399119973183, -0.00331886182539165, -0.027027321979403496, -0.020862625911831856, -0.00578072527423501, 0.008516419678926468, -0.040107373148202896, 0.018821291625499725, -0.001771792070940137, -0.05391144007444382, 0.06358562409877777, -0.008341561071574688, 0.0330657996237278, -0.020249905064702034, 0.01280568540096283, -0.010646533221006393, -0.013047244399785995, 0.007715682499110699, -0.03330438211560249, 0.004830014426261187, -0.013089651241898537, -0.04754403978586197, -0.04557730630040169, -6.281199697005168e-33, -0.0188473891466856, -0.017177265137434006, 0.017055707052350044, -0.022488446906208992, -0.06390388309955597, 0.006716941948980093, -0.037750955671072006, 0.022302407771348953, -0.005925951059907675, -0.02091287262737751, -0.007842850871384144, -0.009401834569871426, 0.008080776780843735, 0.04143688827753067, 0.029846370220184326, 0.03632337599992752, 0.023809680715203285, -0.00595495430752635, 0.01578555628657341, 0.016373172402381897, 0.04410502314567566, 0.028047064319252968, 0.06525587290525436, -0.04908035323023796, -0.033645689487457275, -0.019306456670165062, 0.01165391132235527, -0.06279119104146957, 0.011267882771790028, 0.05903063714504242, -0.016610128805041313, 0.009695676155388355, -0.01819038949906826, -0.05494527146220207, -0.012804821133613586, 0.06671521812677383, -0.09658403694629669, 0.029540054500102997, -0.0053054229356348515, 0.019065074622631073, -0.0203893780708313, -0.020977016538381577, 0.08365046977996826, -0.004389597102999687, 0.022042933851480484, -0.002601913409307599, 0.035614464432001114, -0.06157583370804787, -0.04456509277224541, -0.0012011658400297165, -0.05694158002734184, 0.029270291328430176, -0.01953541487455368, -0.025691784918308258, 0.012895895168185234, 0.06110672280192375, -0.0333227775990963, 0.014193146489560604, -0.10463575273752213, 0.03401215001940727, 0.03804296255111694, 0.04536617547273636, 0.03336575627326965, 0.06574028730392456, 0.00440142210572958, -0.023028086870908737, 0.009311635978519917, -0.02333403378725052, -0.0006690238951705396, -0.022273490205407143, 0.01633100025355816, 0.03129834681749344, 0.08411157131195068, -0.032126523554325104, 0.009910532273352146, -0.02757815644145012, -0.026567496359348297, 0.0008321872446686029, 0.019144872203469276, 0.026251595467329025, 0.07934015989303589, -0.009770766831934452, -0.07060931622982025, 0.01408423949033022, -0.008117989636957645, -0.011123817414045334, -0.020012736320495605, -0.008691481314599514, 0.02803117409348488, 0.024685518816113472, 0.035764288157224655, -0.020812496542930603, 0.04856126010417938, -0.007614274509251118, 0.06637724488973618, -0.04390070214867592, 0.004515727981925011, 0.0005694995634257793, -0.019947029650211334, 0.024857982993125916, -0.08316178619861603, 0.02742033265531063, 0.03265684098005295, 0.05515669658780098, -0.02004595845937729, 0.007605141960084438, 0.02732851542532444, 0.0007423335337080061, -0.01876504346728325, -0.0013786510098725557, -0.027136052027344704, 0.0278630293905735, 0.005826284643262625, 0.08423076570034027, 0.012462591752409935, -0.053060442209243774, -0.007519584149122238, 0.07870569825172424, -0.008477481082081795, -0.0166325606405735, -0.034710124135017395, -0.015408104285597801, 0.032182879745960236, 0.023508237674832344, -0.08269505202770233, 0.02179514616727829, -0.02820972353219986, 0.04390425607562065, 0.01998157985508442, -0.02553459256887436, -0.023906439542770386, 0.03876645863056183, 3.042903813366138e-07, -0.011955732479691505, -0.008983843959867954, 0.026587218046188354, 0.005093226674944162, 0.01907699555158615, 0.009443790651857853, -0.0280706025660038, 0.044990964233875275, 0.006183465477079153, 0.02568538300693035, 0.02553381770849228, -0.01800352893769741, 0.05891601741313934, -0.032461147755384445, -0.08331798762083054, -0.05984943360090256, -0.08434059470891953, 0.04395120218396187, -0.02000385895371437, 0.032394181936979294, 0.016458842903375626, 0.12130478769540787, -0.00395749369636178, -0.002836375730112195, 0.016552938148379326, 0.0018890860956162214, 0.01438719779253006, 0.01937084086239338, 0.015013482421636581, -0.04441498592495918, 0.04540805518627167, 0.022643238306045532, -0.06950763612985611, -0.031597692519426346, -0.05417332053184509, 0.01385888084769249, 0.012517038732767105, 0.04466070234775543, -0.05314108729362488, -0.04777553305029869, 0.018108656629920006, 0.008730201050639153, -0.016598835587501526, -0.030107732862234116, 0.026334304362535477, -0.009706784039735794, -0.017948439344763756, -0.02498178742825985, 0.0068945749662816525, 0.024131707847118378, -0.01977052539587021, -0.01125948503613472, 0.01414876151829958, -0.021456539630889893, 0.018883520737290382, -0.056711580604314804, -0.006094860844314098, -0.06644652038812637, 0.007313517853617668, -0.0038480765651911497, -0.03275996074080467, -0.008610072545707226, -0.030334046110510826, -0.04741306230425835, 0.01689946837723255, -0.03570912033319473, -0.014725386165082455, 2.923133026258476e-34, 0.015411294996738434, -0.02553517185151577, -0.0028656902723014355, 0.02313890866935253, 0.023811690509319305, -0.03726424276828766, 0.019406363368034363, -0.004618757404386997, 0.04220721870660782, -0.08047361671924591, -0.0731663852930069]

['Haşim Sak', 'Andrew Senior', 'Kanishka Rao', 'Françoise Beaufays']

1507.06947v1

We have recently shown that deep Long Short-Term Memory (LSTM) recurrent neural networks (RNNs) outperform feed forward deep neural networks (DNNs) as acoustic models for speech recognition. More recently, we have shown that the performance of sequence trained context dependent (CD) hidden Markov model (HMM) acoustic models using such LSTM RNNs can be equaled by sequence trained phone models initialized with connectionist temporal classification (CTC). In this paper, we present techniques that further improve performance of LSTM RNN acoustic models for large vocabulary speech recognition. We show that frame stacking and reduced frame rate lead to more accurate models and faster decoding. CD phone modeling leads to further improvements. We also present initial results for LSTM RNN models outputting words directly.

Fast and Accurate Recurrent Neural Network Acoustic Models for Speech Recognition

http://arxiv.org/pdf/1507.06947v1

Title Fast Accurate Recurrent Neural Network Acoustic Models Speech Recognition Summary recently shown deep Long ShortTerm Memory LSTM recurrent neural network RNNs outperform feed forward deep neural network DNNs acoustic model speech recognition recently shown performance sequence trained context dependent CD hidden Markov model HMM acoustic model using LSTM RNNs equaled sequence trained phone model initialized connectionist temporal classification CTC paper present technique improve performance LSTM RNN acoustic model large vocabulary speech recognition show frame stacking reduced frame rate lead accurate model faster decoding CD phone modeling lead improvement also present initial result LSTM RNN model outputting word directly Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.008163961581885815, 0.01952042616903782, 0.02254086546599865, 0.06792142987251282, -0.011170904152095318, -0.03642510622739792, 0.03995650261640549, 0.010094176046550274, -0.057481907308101654, -0.03643953800201416, -0.05215294286608696, -0.04255299270153046, 0.07225282490253448, 0.014487023465335369, -0.03520418331027031, -0.0427321121096611, 0.0034624694380909204, 0.0005632483516819775, -0.008522660471498966, 0.004687953740358353, 0.0014965242007747293, 0.0052717458456754684, -0.04055975377559662, 0.0320378877222538, 0.009128776378929615, 5.84251138207037e-05, -0.0052088480442762375, -0.01172308437526226, -0.026317568495869637, -0.06842688471078873, 0.0022982198279350996, 0.036409392952919006, 0.0502600371837616, 0.046736329793930054, 2.213074822066119e-06, -0.002043791813775897, 0.0076934704557061195, -0.024216055870056152, -0.011403301730751991, 0.006796912755817175, 0.028160303831100464, 0.035893991589546204, -0.004106242675334215, 0.04729863256216049, -0.021640049293637276, -0.04404962435364723, 0.01928986981511116, 0.03934936970472336, 0.005264713428914547, 0.06241333484649658, 0.0015755408676341176, -0.051986537873744965, 0.0701206773519516, -0.021371515467762947, 0.026425177231431007, -0.025124775245785713, 0.010592687875032425, -0.010849537327885628, 0.019963910803198814, -0.014636734500527382, 0.007982996292412281, 0.03832656145095825, -0.0012431455543264747, 0.0133037269115448, 0.008781734853982925, 0.03256512060761452, 0.007064231671392918, 0.008708297275006771, 0.00392856914550066, 0.08447233587503433, 0.004394082352519035, -0.01853903755545616, 0.018779313191771507, 0.02311468869447708, -0.053669050335884094, -0.03641778230667114, -0.027015652507543564, -0.00010826246580109, -0.00906494539231062, -0.005054336041212082, -0.018202727660536766, 0.048705533146858215, 0.04297761619091034, 0.02082938142120838, 0.01080483291298151, -0.021685749292373657, 0.0030085332691669464, -0.039524491876363754, -0.04486022889614105, -0.05862971767783165, 0.04144987091422081, -0.044905535876750946, 0.040828533470630646, 0.03303445875644684, 0.024443993344902992, -0.0021143201738595963, 0.009421247988939285, -0.08370932936668396, 0.014700066298246384, -0.061250727623701096, 0.01490073837339878, 0.019739005714654922, -0.054738838225603104, 0.004241494927555323, -0.03663492575287819, 0.06229030340909958, -0.00443691061809659, -0.007897543720901012, 0.007967120036482811, 0.016864972189068794, -0.05028972402215004, -0.0010751854861155152, -0.005566662177443504, 0.055788759142160416, -0.01535868737846613, -0.031503256410360336, -0.07309894263744354, -0.025197472423315048, 0.030256913974881172, -0.01018355693668127, 0.02596951089799404, 0.04309181496500969, -0.024253513664007187, -0.011362987570464611, -0.00141698878724128, -0.0022889110259711742, 0.001370802172459662, 0.05059487000107765, -0.02258897013962269, -0.051627520471811295, 0.009659720584750175, 0.018253879621624947, 0.049122344702482224, -0.010830730199813843, -0.006154877133667469, 0.061646465212106705, 0.016750609502196312, -0.033951569348573685, -0.039749741554260254, 0.01698472537100315, -0.03561408817768097, -0.016671231016516685, -0.030203117057681084, -0.08096814900636673, 0.02858351171016693, -0.027191154658794403, -0.02386440336704254, -0.003445398062467575, 0.033395782113075256, 0.012402824126183987, 0.00780255114659667, 0.08077535778284073, -0.0008950791088864207, -0.0013012478593736887, 0.08082471787929535, 0.005506599321961403, 0.049926530569791794, -0.009135575965046883, 0.08694487065076828, 0.0009920008014887571, 0.000876686186529696, -0.03888711705803871, 0.015659581869840622, 0.030072640627622604, -0.018732279539108276, -0.01571977511048317, -0.04092476889491081, -0.022458724677562714, 0.008794386871159077, 0.0735478550195694, 0.0057565681636333466, 0.052421048283576965, -0.01611414924263954, 0.010173698887228966, 0.056628819555044174, 0.06452047824859619, 0.04514877870678902, 0.028193946927785873, -0.0022245245054364204, 0.02910107932984829, -0.001920896116644144, -0.03386502340435982, -0.003439053427428007, -0.007660872768610716, -0.004692286252975464, 0.01094719860702753, -0.0018599133472889662, -0.01506446860730648, -0.011311271227896214, -0.012751352973282337, -0.00427250424399972, -0.05873999744653702, -0.002625160152092576, -0.006377123296260834, 0.045869577676057816, 0.007595863193273544, -0.050066184252500534, 0.015622966922819614, -0.010068832896649837, -0.043842799961566925, -0.03170151263475418, -0.030306151136755943, 0.028732215985655785, 0.032369524240493774, 0.04785468801856041, -0.04517345875501633, -0.03531846031546593, -0.05179841071367264, -0.03071836195886135, 0.01990853063762188, -0.017728684470057487, 0.033336102962493896, 0.009313407354056835, -0.08338163048028946, 0.008628208190202713, 0.08204861730337143, -0.016959842294454575, 0.07116805016994476, -0.005640898831188679, 0.06172564998269081, 0.03527175262570381, 0.02596183307468891, -0.005913317669183016, 0.009396850131452084, 0.0028357096016407013, -0.015673397108912468, 0.03866846486926079, 0.02007221430540085, 0.07200931757688522, 0.0410691574215889, 0.01441790722310543, -0.003153315745294094, 0.048278458416461945, -0.05437276139855385, -0.017743857577443123, 0.013260433450341225, -0.11167600750923157, -0.03205343335866928, 0.026248907670378685, -0.0017760710325092077, 0.06621108949184418, 0.03196166455745697, 0.01568484492599964, -0.0878714919090271, 0.05018778145313263, 0.004508881364017725, 0.03557421639561653, -0.04899178817868233, 0.03878442198038101, 0.03449774533510208, 0.029724188148975372, 0.01446293480694294, 0.01902330107986927, -0.011257471516728401, 0.026389602571725845, 0.03439090773463249, 0.05140228942036629, 0.004120437428355217, -0.07704096287488937, -0.02276499569416046, 0.044947460293769836, -0.03998321667313576, 0.0054179830476641655, -0.021385492756962776, 0.009965036995708942, -0.009840166196227074, -0.01742572709918022, -0.06050645560026169, 0.007659409660845995, 0.008874213322997093, -0.018454331904649734, -0.020674996078014374, 0.035708390176296234, 0.0186945628374815, -0.0015703515382483602, -0.023352596908807755, -0.016488628461956978, 0.012696458958089352, -0.03349437192082405, 0.007520084269344807, 0.030711106956005096, -0.029068417847156525, -0.05620281398296356, -0.009066070429980755, -0.0021418402902781963, -0.010154861025512218, -0.0025324432644993067, -0.0786556676030159, 0.011264554224908352, 0.0010045196395367384, 0.03174939751625061, 0.05278759449720383, -0.006309413351118565, -0.06193828210234642, -0.009989981539547443, -0.02858465351164341, 0.008058706298470497, 0.0204728152602911, 0.023165639489889145, -0.03869951143860817, -0.009515419602394104, -0.010292424820363522, -0.022547252476215363, 0.012838222086429596, 0.014635390602052212, 0.04190580174326897, -0.009467771276831627, 0.00483467523008585, -0.02225280925631523, 0.050831202417612076, 0.05583970248699188, 0.06020957604050636, 0.004931940697133541, -0.06225132942199707, -0.038151588290929794, -0.018144797533750534, -0.015145746059715748, -0.04977669194340706, -0.06778337806463242, 0.01679191179573536, 0.01007603295147419, 0.011553815566003323, 0.0011752931168302894, -0.06932063400745392, -0.014286160469055176, -0.05662677064538002, -0.047327958047389984, -0.029469115659594536, 0.03177813068032265, -0.013158133253455162, -0.015507357195019722, -0.022164970636367798, -0.07592356204986572, 0.023358214646577835, -0.008575891144573689, 0.01072302833199501, -0.07090721279382706, 0.01020319014787674, -0.001630727550946176, 0.005902360193431377, -0.04782412573695183, -0.034858159720897675, -0.0506291463971138, -0.029614361003041267, -0.021956000477075577, -0.025281816720962524, -0.0026649152860045433, -0.03251485154032707, -0.015171835198998451, 0.0581824816763401, 0.012820350006222725, 0.05078950151801109, -0.01317085511982441, 0.0522899366915226, -0.030114764347672462, 0.0862002894282341, 0.027368102222681046, 0.005036264657974243, -0.04611926153302193, 0.05059163644909859, 0.048431575298309326, -0.010688667185604572, 0.025048764422535896, 0.019270649179816246, -0.10254107415676117, -0.012716180644929409, 0.006249961908906698, -0.011171904392540455, -0.032496415078639984, 0.04448636621236801, -0.014966321177780628, -0.09521494060754776, 0.012288681231439114, 0.10637519508600235, 0.004275661893188953, -0.064687579870224, -0.06097748875617981, 0.021581759676337242, -0.04512740299105644, -0.015503105707466602, -0.012243736535310745, -0.03984302654862404, -0.03656335547566414, 0.022107191383838654, 0.001414955360814929, 0.017524870112538338, -0.01721370406448841, -0.012258589267730713, -0.07387811690568924, 0.012636027298867702, 0.0022807300556451082, -0.05435926839709282, -0.02629965730011463, -0.030555030331015587, -0.0455913245677948, 0.010745016857981682, 0.02477557770907879, 0.02005322277545929, -0.01233439240604639, -0.040354810655117035, 0.04125180467963219, -0.09460755437612534, -0.018988197669386864, 0.059997379779815674, -0.03169737756252289, 0.04809186980128288, 0.09891960024833679, 0.04745515063405037, -0.07616433501243591, -0.055791452527046204, 0.020366011187434196, -0.002505498006939888, 0.010364264249801636, 0.005232708062976599, 0.0019872579723596573, -0.04146529734134674, 0.012030907906591892, 0.025659428909420967, 0.05280496925115585, -0.030176013708114624, 0.011695722118020058, 0.011393521912395954, 0.0359455831348896, -0.016747303307056427, -0.009921387769281864, -0.02131683938205242, 0.04186117649078369, 0.013537375256419182, 0.04551215097308159, 0.002959894249215722, -0.027299299836158752, -0.020671429112553596, 0.04158915579319, 0.02906166948378086, -0.038999006152153015, 0.02659132331609726, 8.120314305415377e-05, 0.013303572311997414, -0.055866774171590805, -0.06837671995162964, -0.05091845244169235, -0.010666834190487862, 0.005140347871929407, 0.05865193530917168, 0.03935759514570236, 0.02826300822198391, 0.050131745636463165, -0.0557045042514801, -0.006735818926244974, 0.016199782490730286, 0.04815103858709335, -0.08583582192659378, 0.052360597997903824, 0.06710166484117508, -0.056893281638622284, 0.007438987493515015, -0.012252368964254856, -0.05914600193500519, -0.028214601799845695, 0.01780989207327366, -0.029442258179187775, 0.015969449654221535, 0.06264816224575043, -0.06204759329557419, -0.05212615802884102, 0.013867493718862534, -0.009434901177883148, -0.032174959778785706, -0.019675323739647865, 0.04728123918175697, 0.026935862377285957, -0.014560097828507423, -0.013435122556984425, -0.049836769700050354, 0.05521200969815254, -0.03761762008070946, -0.008309511467814445, -0.04408107325434685, -0.048161473125219345, -0.02050231769680977, 0.0014708179514855146, 0.06558097153902054, 0.007822330109775066, 0.02235020138323307, -0.04667045176029205, 0.04219153895974159, 0.03968895226716995, 0.04393917694687843, -0.006033957004547119, 0.02583443745970726, 0.021356556564569473, 0.02066323347389698, -0.01894206739962101, -0.04685463011264801, 0.01621435582637787, -0.06988196074962616, 0.009104412980377674, 0.08488854020833969, 0.029836274683475494, 0.0253467857837677, -0.014995341189205647, -0.013094414956867695, -0.03679652512073517, 0.032111555337905884, 0.007410822436213493, 0.030874164775013924, -0.009903378784656525, 0.020514842122793198, -0.015339785255491734, 0.006899932865053415, -0.013096357695758343, 0.00452087540179491, 0.020001977682113647, 0.013595151714980602, -0.05501755699515343, 0.029469745233654976, 0.061756834387779236, -0.017149079591035843, -0.025469059124588966, 0.008215488865971565, 0.042587634176015854, -0.03640056401491165, 0.028646470978856087, -0.03439239412546158, 0.03569534048438072, 0.04528060182929039, 0.027318181470036507, -0.028835035860538483, 0.009807871654629707, 0.03335772454738617, 0.03991134092211723, 0.01289014145731926, 0.043784357607364655, -0.0015494039980694652, -0.02099599875509739, 0.006201540119946003, -0.0035923966206610203, 0.06469687074422836, -0.02452712692320347, 0.011134165339171886, 0.01954006962478161, -0.04638921096920967, 0.0804448276758194, -0.020582033321261406, 0.05534452572464943, -0.029108678922057152, 0.033643823117017746, -0.016389545053243637, 0.011988344602286816, 0.04352825507521629, 0.014286009594798088, -0.013173103332519531, 0.02165335789322853, -0.058473046869039536, -0.0449349470436573, -6.1144506805532414e-33, -0.00020984238653909415, -0.00621700007468462, 0.003334138775244355, -0.018591199070215225, -0.03842172399163246, 0.014314606785774231, -0.021608607843518257, -0.004354230593889952, -0.006198204588145018, -0.012434420175850391, -0.04696917161345482, 0.017887737601995468, 0.03236733004450798, 0.05281871557235718, 0.027375904843211174, -0.010055115446448326, 0.04120120778679848, -0.015866611152887344, 0.05068397521972656, 0.0014264688361436129, 0.01984819583594799, 0.07582372426986694, 0.059441082179546356, -0.014392438344657421, -0.03808606043457985, -0.014492066577076912, 0.030606430023908615, -0.027051622048020363, 0.0437498614192009, 0.03182322904467583, -0.041269417852163315, 0.0013305096654221416, -0.006227253936231136, -0.0372597835958004, 0.014249111525714397, 0.045682020485401154, -0.12193737179040909, -0.0029497926589101553, -0.0036626767832785845, 0.03287271410226822, -0.009446104057133198, 0.009231164120137691, 0.041529808193445206, 0.03158602863550186, -0.022346580401062965, 0.03312723711133003, 0.029795663431286812, -0.03737471625208855, -0.050262343138456345, -0.057667192071676254, -0.021342124789953232, 0.03699344024062157, 0.001099074142985046, -0.02008664980530739, 0.05340198799967766, -0.037969835102558136, -0.027663713321089745, 0.035451047122478485, -0.13236382603645325, 0.015137999318540096, -0.007082551252096891, 0.03505680710077286, 0.025104044005274773, 0.05114266648888588, -0.024370962753891945, 0.013822670094668865, 0.02513323910534382, -0.053779151290655136, -0.019565848633646965, 0.01657501980662346, 0.008590026758611202, 0.060901883989572525, 0.022201452404260635, -0.003038665745407343, 0.07070057839155197, -0.053756143897771835, -0.04499714449048042, 0.00992579385638237, 0.020871559157967567, 0.022263554856181145, 0.07216931879520416, 0.011098830960690975, -0.07304731756448746, 0.010594451799988747, -0.02817436121404171, 0.020230012014508247, -0.03553062677383423, -0.016455618664622307, 0.05761013180017471, -0.0060691530816257, 0.03245978429913521, -0.025912640616297722, 0.020297912880778313, -0.014245796017348766, 0.006033571902662516, -0.02692044898867607, 0.008034632541239262, -0.01430475153028965, -0.01951381377875805, 0.024471234530210495, -0.04456297308206558, -0.006364887580275536, 0.02962426096200943, 0.047857385128736496, -0.009522221982479095, -0.015286237001419067, -0.004092545714229345, -0.012776384130120277, -0.02730897068977356, -0.01762370392680168, 0.011365645565092564, 0.008367100730538368, 0.00913799088448286, 0.041029490530490875, 0.012654160149395466, -0.019319046288728714, 0.0034687949810177088, 0.07262995839118958, -0.011972284875810146, -0.0008772374130785465, -0.005962852854281664, -0.03660910204052925, 0.017254728823900223, 0.024819612503051758, -0.055325739085674286, -0.001207500696182251, -0.012262968346476555, 0.02507157251238823, 0.05193769186735153, -0.02988113835453987, 0.003451209282502532, 0.03182409331202507, 2.8473203883550013e-07, -0.04109489917755127, -0.008084234781563282, 0.031965773552656174, -0.015594473108649254, 0.01407973188906908, 0.0012406768510118127, -0.006431439891457558, 0.0029269892256706953, -0.002802429022267461, 0.010046012699604034, 0.03527234122157097, -0.00759850163012743, 0.04368333891034126, -0.00853753462433815, -0.11504016071557999, -0.047141123563051224, -0.11296647787094116, 0.032084982842206955, -0.02871466800570488, 0.011742201633751392, 0.009753147140145302, 0.10691659897565842, 0.024362843483686447, -0.04983723908662796, 0.01836753636598587, -0.033297453075647354, 0.009974824264645576, 0.009527876041829586, 0.023829258978366852, -0.013393016532063484, 0.01874961331486702, 0.01460718922317028, -0.01832369714975357, -0.026868237182497978, -0.03208683803677559, 0.036029208451509476, 0.029312757775187492, -0.00041553916526027024, -0.02559099905192852, -0.05451270565390587, 0.00859665684401989, 0.027005085721611977, -0.02177603729069233, 0.023314835503697395, 0.04896501079201698, 0.017565449699759483, -0.022268077358603477, -0.0097503075376153, -0.020896241068840027, -0.013777918182313442, 0.003504118649289012, 0.005072643980383873, 0.014862004667520523, -0.014995910227298737, 0.0009704888216219842, -0.04103400930762291, -0.031133180484175682, -0.09335450828075409, 0.018085746094584465, 0.011719903908669949, -0.04390040785074234, -0.009548591449856758, -0.02380714938044548, -0.0329887717962265, 0.037899620831012726, -0.021610666066408157, -0.006296208128333092, 2.570302886729397e-34, 0.008195532485842705, -0.010030852630734444, -0.01962157152593136, 0.040521472692489624, -0.0008416189812123775, -0.009460962377488613, 0.002893428085371852, 0.020339353010058403, 0.01821795664727688, -0.07958836853504181, -0.048421382904052734]

['William Chan', 'Navdeep Jaitly', 'Quoc V. Le', 'Oriol Vinyals']

1508.01211v2

We present Listen, Attend and Spell (LAS), a neural network that learns to transcribe speech utterances to characters. Unlike traditional DNN-HMM models, this model learns all the components of a speech recognizer jointly. Our system has two components: a listener and a speller. The listener is a pyramidal recurrent network encoder that accepts filter bank spectra as inputs. The speller is an attention-based recurrent network decoder that emits characters as outputs. The network produces character sequences without making any independence assumptions between the characters. This is the key improvement of LAS over previous end-to-end CTC models. On a subset of the Google voice search task, LAS achieves a word error rate (WER) of 14.1% without a dictionary or a language model, and 10.3% with language model rescoring over the top 32 beams. By comparison, the state-of-the-art CLDNN-HMM model achieves a WER of 8.0%.

Listen, Attend and Spell

http://arxiv.org/pdf/1508.01211v2

Title Listen Attend Spell Summary present Listen Attend Spell LAS neural network learns transcribe speech utterance character Unlike traditional DNNHMM model model learns component speech recognizer jointly system two component listener speller listener pyramidal recurrent network encoder accepts filter bank spectrum input speller attentionbased recurrent network decoder emits character output network produce character sequence without making independence assumption character key improvement LAS previous endtoend CTC model subset Google voice search task LAS achieves word error rate WER 141 without dictionary language model 103 language model rescoring top 32 beam comparison stateoftheart CLDNNHMM model achieves WER 80 Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.001111628138460219, 0.024756576865911484, 0.018808944150805473, 0.058023370802402496, -0.025091195479035378, -0.033588431775569916, 0.026153886690735817, -0.021866867318749428, -0.039743371307849884, -0.005591810680925846, -0.0414145402610302, -0.021855205297470093, 0.04940786957740784, 0.05602109432220459, 0.03506952151656151, -0.0466773547232151, 0.033503640443086624, -0.042835939675569534, -0.04022390395402908, 0.00332151772454381, 0.018438056111335754, 0.020454823970794678, -0.051284514367580414, 0.04742072522640228, 0.03114589862525463, 0.014985824935138226, -0.042493924498558044, -0.03688701614737511, 0.004756182432174683, -0.016061516478657722, -0.01697828620672226, -0.0009549399837851524, 0.015273531898856163, 0.06125536933541298, 2.2255705971474526e-06, -0.018084341660141945, -0.03464613854885101, -0.0370941124856472, -0.00040467813960276544, -0.00013784016482532024, -0.022022712975740433, 0.010545304045081139, -0.02911733277142048, 0.03706444054841995, 0.0067380573600530624, -0.02239595726132393, 0.05460476875305176, 0.028015919029712677, 0.017464222386479378, 0.05098990350961685, 0.001329271588474512, -0.0577111542224884, 0.037469323724508286, -0.016764994710683823, 0.05777918919920921, -0.03739716857671738, -0.014024858362972736, -0.019334720447659492, 0.006340492982417345, -0.05001312866806984, -0.02044759877026081, 0.0640338808298111, -0.029319774359464645, -0.022274337708950043, 0.059352800250053406, 0.013081650249660015, -0.013420687057077885, -0.04119609668850899, 0.004419477190822363, 0.09410947561264038, -0.005092183593660593, -0.024402551352977753, 0.02080787718296051, 0.045073240995407104, 0.0008806618861854076, -0.010746651329100132, -0.02622733637690544, -0.006589751224964857, 0.011126275174319744, 0.004156801849603653, 0.016962511464953423, 0.048035942018032074, 0.012077873572707176, -0.01377784088253975, 0.0020886375568807125, 0.012262606993317604, 0.02298647165298462, -0.05061579495668411, -0.012742164544761181, -0.007274586241692305, 0.06736203283071518, -0.015819676220417023, 0.06362687796354294, 0.05926871299743652, -0.016233310103416443, 0.004073224030435085, -0.0066420696675777435, -0.08449159562587738, 9.85021597443847e-06, -0.017376601696014404, 0.0680912509560585, 0.040898993611335754, -0.017589306458830833, -0.013217665255069733, -0.028617840260267258, 0.030156748369336128, 0.01308412291109562, -0.03527460992336273, -0.0076933917589485645, -0.016065578907728195, -0.017761237919330597, 0.004500380717217922, -0.035653553903102875, 0.027045534923672676, -0.0015198871260508895, -0.021003613248467445, -0.046466778963804245, -0.028723379597067833, 0.013717561028897762, 0.01769627258181572, -0.02686363086104393, 0.006249164696782827, -0.041062578558921814, -0.025704478845000267, 0.03677752986550331, 0.07456343621015549, 0.009846195578575134, 0.04666527360677719, 0.006488496903330088, -0.043651070445775986, -0.006369848735630512, 0.03385104238986969, 0.029230374842882156, 0.004174458794295788, -0.004287071526050568, 0.10637447237968445, 0.0031306808814406395, -0.023721300065517426, -0.009151861071586609, 0.005780947860330343, -0.02704411931335926, -0.019554924219846725, -0.009527420625090599, -0.0942281112074852, 0.02178741805255413, -0.02222013846039772, -0.010036042891442776, 0.009833001531660557, 0.03218161314725876, 0.0021891766227781773, 0.03650474548339844, 0.06854356825351715, -0.027357088401913643, 0.0025250837206840515, 0.0816325768828392, 0.017062045633792877, 0.06203680485486984, -0.023130755871534348, 0.06039293482899666, 0.02065218798816204, 0.0040483735501766205, -0.09727766364812851, 0.05534961819648743, 0.041667621582746506, 0.0016686408780515194, -0.03321829438209534, -0.04353281110525131, -0.04242924600839615, -0.010209623724222183, 0.05086109787225723, 0.022009864449501038, 0.04411732405424118, 0.010923843830823898, 0.015415599569678307, 0.047783929854631424, 0.07683369517326355, 0.06699466705322266, -0.003345413599163294, -0.0015128576196730137, -0.020348871126770973, -0.0014409958384931087, -0.00633148942142725, -0.0011266004294157028, 0.02142736315727234, -0.04222307726740837, 0.010716225951910019, 0.01540196593850851, -0.001948578399606049, -0.013118671253323555, -0.01886524073779583, -0.007399334572255611, -0.0020423871465027332, -0.03278518095612526, -0.0196488369256258, 0.030932368710637093, 0.0019008361268788576, -0.03230343014001846, -0.012116353027522564, 0.007596305571496487, -0.03880123794078827, -0.005278724245727062, -0.040737394243478775, 0.01329700369387865, 0.05135995149612427, 0.003917733673006296, -0.009378594346344471, 0.03377140685915947, -0.0586867593228817, -0.028150370344519615, 0.05188654363155365, 0.0020818589255213737, 0.012209040112793446, 0.03302878886461258, -0.05945888161659241, 0.03404785320162773, 0.05446065217256546, -0.00985557958483696, 0.04450523108243942, -0.04811069369316101, 0.04676022380590439, -0.0005520498380064964, 0.019571343436837196, -0.009787405841052532, 0.009281580336391926, -0.02968861162662506, -0.044357430189847946, -0.007727982942014933, 0.02306593768298626, 0.05945185199379921, 0.024812765419483185, 0.003705493872985244, 0.014590595848858356, 0.03308193385601044, -0.034055013209581375, -0.010946827940642834, -0.009837274439632893, -0.04743171110749245, -0.058683667331933975, 0.009489435702562332, -0.07283449918031693, 0.021144328638911247, 0.06127696856856346, 0.02202673628926277, -0.06290264427661896, 0.08049175888299942, -0.03689291700720787, 0.06615041196346283, -0.02591024711728096, 0.024341436102986336, 0.022528134286403656, 0.019950302317738533, -0.004851717967540026, 0.0007777160499244928, -0.019879378378391266, 0.010658313520252705, -0.05748194083571434, -0.0003418798150960356, -0.0169291403144598, -0.09212596714496613, -0.029582412913441658, 0.019811509177088737, -0.022677309811115265, 0.019494570791721344, -0.04549311101436615, 0.002587759168818593, -0.016485998407006264, -0.010280254296958447, -0.009351457469165325, -0.009020188823342323, -0.004883608315140009, -0.023828111588954926, -0.00974505115300417, 0.023801151663064957, 0.0036842836998403072, -0.03003579005599022, -0.05166257172822952, 0.0176569614559412, 0.04500434175133705, -0.028008360415697098, 0.025579920038580894, -0.005891100969165564, -0.03773804381489754, -0.0663316398859024, -0.04649616405367851, -0.005303008481860161, 0.00819930899888277, 0.016223425045609474, -0.11403694748878479, -0.037149831652641296, 0.0041286395862698555, 0.012170236557722092, 0.024961302056908607, 0.019533764570951462, -0.04309077933430672, -0.017599593847990036, -0.010703196749091148, -0.005344909615814686, 0.023960739374160767, 0.013925354927778244, -0.007521520368754864, 0.009252586401998997, -0.0016822462202981114, -0.01481848955154419, 0.0068172854371368885, 0.003726267721503973, 0.04701035097241402, 0.02209676429629326, -0.006065627560019493, -0.0043623847886919975, 0.03200775757431984, 0.06523273140192032, 0.037111420184373856, -0.002004286041483283, -0.03975384309887886, -0.015065799467265606, -0.05127624049782753, -0.07167679071426392, -0.06255489587783813, -0.05989953130483627, 0.007467798423022032, 0.017517298460006714, -0.027771126478910446, 0.02649683505296707, -0.04700824245810509, -0.023640010505914688, -0.043328091502189636, -0.0672425851225853, -0.01134653203189373, -0.010436329059302807, -0.026772774755954742, 0.016673443838953972, -0.019561905413866043, -0.10505633801221848, 0.01639389805495739, 0.033238735049963, -0.028034957125782967, -0.03398068621754646, 0.05382847040891647, -0.003553464775905013, -0.032725460827350616, -0.026021292433142662, -0.011942297220230103, -0.05141095817089081, 0.05932530388236046, -0.03917476534843445, -0.035887379199266434, -0.014637988992035389, -0.007892255671322346, -0.024906432256102562, 0.027790289372205734, 0.014790385030210018, 0.05538791045546532, 0.004539031069725752, 0.024969391524791718, -0.03763024881482124, 0.03520558029413223, 0.009357549250125885, 0.03304113820195198, 0.0048332205042243, -0.006359643302857876, 0.028888029977679253, 0.0031760558485984802, 0.005902162753045559, -0.023101644590497017, -0.031781282275915146, 0.011726339347660542, 0.03752392530441284, -0.0038385491352528334, -0.033691469579935074, 0.0238998644053936, 0.03339676931500435, -0.07854296267032623, 0.022326553240418434, 0.0693022683262825, -0.013204729184508324, -0.05893377587199211, -0.026549512520432472, -0.0154580594971776, -0.004800182301551104, -0.023477209731936455, 0.007060056086629629, -0.11257592588663101, -0.027723634615540504, 0.03572343662381172, 0.059293996542692184, 0.0660751536488533, -0.01734606735408306, -0.016899624839425087, -0.10500101000070572, 0.02718544751405716, 0.03743753582239151, -0.01817619800567627, -0.07083684951066971, -0.03132136911153793, -0.016844823956489563, -0.027215413749217987, 0.02699071541428566, 0.05903853848576546, -0.028237389400601387, -0.013979177922010422, 0.03165418282151222, -0.05401216447353363, 0.00896789412945509, 0.019475450739264488, -0.014706035144627094, 0.07092271000146866, 0.05662146210670471, 0.019421571865677834, -0.036919087171554565, -0.042086564004421234, -0.018304090946912766, -0.039561424404382706, 0.0008091600611805916, 0.011950002983212471, 0.023892764002084732, 0.007139076478779316, -0.013976170681416988, 0.00036239836481399834, 0.08323977142572403, -0.058045610785484314, 0.02640967071056366, 0.030059291049838066, 0.046326007694005966, -0.02840229496359825, 0.00021181866759434342, -0.011101357638835907, 0.07606951892375946, 0.03340786695480347, 0.05835562199354172, 0.05124768987298012, -0.015198105946183205, -0.020647022873163223, -0.02317149005830288, 0.02364521101117134, -0.04036523029208183, -0.08609974384307861, -0.009998329915106297, 0.05024382472038269, -0.06485302746295929, -0.053398292511701584, -0.03133166953921318, -0.01390822883695364, 0.022281577810645103, 0.040994904935359955, 0.024656740948557854, 0.003566691419109702, 0.010660409927368164, 0.016848936676979065, -0.002452197251841426, 0.020883789286017418, 0.024082081392407417, -0.08777682483196259, -0.00938956718891859, -0.010832036845386028, -0.02477863058447838, -0.009743773378431797, -0.010541641153395176, -0.05940599367022514, -0.02572779543697834, 0.06763523072004318, -0.007999219931662083, 0.03372481092810631, 0.02321731299161911, -0.05128573253750801, -0.02377832680940628, -0.0039336346089839935, -0.03632264956831932, -0.046644099056720734, 0.011083237826824188, 0.04578113928437233, -0.003464640351012349, 0.0008325928938575089, 0.019747458398342133, -0.02011161483824253, 0.053345490247011185, -0.018225781619548798, -0.020078042522072792, -0.017627747729420662, -0.05304448679089546, -0.011510729789733887, 0.012487843632698059, 0.0557645782828331, -0.013242206536233425, 0.01827877014875412, -0.05499393492937088, 0.020702224224805832, 0.0032377182506024837, 0.038710180670022964, -0.04264054819941521, -0.01254729088395834, 0.03883754834532738, 0.07243706285953522, 0.00937671959400177, -0.04792856052517891, 0.019766833633184433, -0.0058471462689340115, -0.008061187341809273, 0.0824630856513977, 0.020237302407622337, -0.010601378977298737, 0.015698349103331566, 0.0067192139104008675, -0.013408642262220383, 0.07840095460414886, 0.0019562714733183384, 0.05712138116359711, -0.008270650170743465, -0.015264525078237057, -0.005538030061870813, 0.02270381525158882, 0.013002181425690651, 0.027234435081481934, -0.0354294627904892, -0.02649158239364624, -0.02533596009016037, -0.006902063265442848, 0.05418919399380684, -0.010513772256672382, 0.017850160598754883, 0.011356702074408531, 0.021694984287023544, -0.014989087358117104, 0.05758636072278023, -0.04544530808925629, 0.03388997167348862, 0.0101699847728014, 0.008001499809324741, -0.03435077518224716, -0.019748888909816742, 0.04223311319947243, 0.008488412015140057, 0.0036100936122238636, 0.02097330614924431, 0.027633395045995712, -0.04621116444468498, 0.013605189509689808, -0.02143010124564171, 0.015262546017765999, -0.04459248483181, -0.0005707904929295182, -0.029691189527511597, -0.061386123299598694, 0.027147455140948296, -0.03360291197896004, 0.04088321328163147, -0.004982922691851854, 0.03431890904903412, -0.016915179789066315, 0.014329042285680771, 0.03690806403756142, -0.0010684126755222678, -0.0003702959220390767, 0.05478552356362343, -0.04924643784761429, -0.011453317478299141, -6.21398493002515e-33, -0.04624636843800545, -0.0069032832980155945, -0.015484021045267582, 0.051420290023088455, -0.04316261410713196, 0.0025173150934278965, -0.03074125573039055, 0.024975847452878952, -0.009619873017072678, -0.009690538048744202, -0.024330414831638336, 0.029295209795236588, 0.030033379793167114, 0.026399973779916763, 0.05492096766829491, -0.011570943519473076, 0.03597225621342659, -0.018133575096726418, 0.022538654506206512, -0.0033965171314775944, 0.04398593306541443, 0.06085363030433655, 0.0830087959766388, -0.06226752698421478, -0.017960553988814354, 0.038211457431316376, 0.008570076897740364, -0.03310175612568855, 0.005108808632940054, 0.011687051504850388, -0.049594588577747345, 0.05022980272769928, -0.020332008600234985, -0.01926037110388279, -0.040481843054294586, 0.04976922273635864, -0.09730494022369385, 0.0015131330583244562, -0.004242949187755585, 0.02761797234416008, -0.02886553667485714, -0.026609132066369057, 0.03556760773062706, -0.011175816878676414, -0.03825708106160164, 0.007573665585368872, 0.03244125097990036, -0.04238065332174301, -0.026461968198418617, 0.008960770443081856, -0.030053507536649704, 0.022061221301555634, -0.023341739550232887, -0.005875204689800739, 0.03275291249155998, 0.038029491901397705, -0.02943667396903038, 0.008658727630972862, -0.117820143699646, 0.05598298832774162, 0.013018446043133736, 0.06518189609050751, 0.013541217893362045, -0.004034313838928938, -0.041990894824266434, 0.043585989624261856, 0.07537531852722168, -0.08776635676622391, -0.009378733113408089, 0.002246235962957144, 0.0029946824070066214, 0.04154278337955475, 0.0767674446105957, -0.008028264157474041, 0.02715502493083477, -0.02387804351747036, -0.05394792556762695, 0.0077375378459692, -0.004817154258489609, 0.023441364988684654, 0.0026404147502034903, 0.02552887052297592, -0.04078846797347069, 0.01767464354634285, 0.017865270376205444, 0.010845840908586979, -0.009917414747178555, 0.013092045672237873, 0.024290774017572403, -0.017906783148646355, 0.033026713877916336, -0.011931451968848705, 0.051855530589818954, -0.04501057788729668, 0.029904695227742195, 0.002474664943292737, 0.004812082275748253, -0.022193651646375656, -0.014032945036888123, 0.01949521154165268, -0.08489380031824112, -0.0015292338794097304, 0.03302943333983421, 0.05036259442567825, 0.02547384798526764, -0.0033599811140447855, 0.0300130732357502, 0.036717966198921204, -0.05592896789312363, -0.010797088034451008, -0.015685897320508957, 0.014638036489486694, 0.04394715279340744, 0.05686180666089058, 0.018739860504865646, -0.0786200761795044, 0.016346203163266182, 0.04639989510178566, -0.00856360886245966, 0.011705114506185055, -0.011637449264526367, -0.0606253445148468, -0.021969830617308617, 0.0199148990213871, -0.08108536899089813, 0.028437824919819832, -0.06048169732093811, -0.014040140435099602, 0.0655544176697731, -0.015812791883945465, 0.006891168188303709, -0.0029909934382885695, 2.9403491907942225e-07, 0.010015084408223629, -0.016215350478887558, 0.04337068647146225, 0.02943822182714939, 0.04048991575837135, -0.001510539324954152, -0.02629340998828411, 0.04767046868801117, 0.005128870252519846, 0.02699827216565609, -0.01988702081143856, -0.038114916533231735, 0.08527523279190063, 0.013205626979470253, -0.10679464787244797, -0.06989419460296631, -0.06922131031751633, 0.03779923543334007, -0.024237632751464844, 0.0024506812915205956, 0.021844495087862015, 0.10591000318527222, -0.0009719652007333934, -0.034454818814992905, 0.025207791477441788, -0.01292266696691513, -0.008890281431376934, 0.017432458698749542, -0.009423407725989819, -0.020168999210000038, 0.0845007449388504, 0.013239632360637188, -0.02285105735063553, -0.01412450522184372, -0.05814259126782417, 0.04825764149427414, 0.02683158591389656, 0.02751564420759678, -0.012226914055645466, -0.05699651688337326, 0.023180758580565453, 0.013098829425871372, 0.0029863466043025255, -0.002265348332002759, 0.03873581811785698, 0.03401864692568779, -0.019596321508288383, 0.03144465759396553, -0.007345172576606274, -0.003650376806035638, -0.004780445713549852, 0.009947773069143295, -0.009960707277059555, -0.00016688500181771815, 0.008770294487476349, -0.02717333659529686, -0.02070539817214012, -0.0503159835934639, -0.013914485462009907, -0.009586259722709656, -0.0282029639929533, -0.020702356472611427, 0.003791331546381116, -0.05526593700051308, 0.007091739680618048, -0.03366280347108841, -0.050694163888692856, 2.891167845110764e-34, 0.024496056139469147, -0.0003970074176322669, 0.016219260171055794, 0.04608847200870514, -0.013919428922235966, -0.04440990090370178, 0.03603283315896988, 0.01811756007373333, 0.0289725661277771, -0.07973792403936386, -0.06084071099758148]

['Shihao Ji', 'S. V. N. Vishwanathan', 'Nadathur Satish', 'Michael J. Anderson', 'Pradeep Dubey']

1511.06909v7

We propose BlackOut, an approximation algorithm to efficiently train massive recurrent neural network language models (RNNLMs) with million word vocabularies. BlackOut is motivated by using a discriminative loss, and we describe a new sampling strategy which significantly reduces computation while improving stability, sample efficiency, and rate of convergence. One way to understand BlackOut is to view it as an extension of the DropOut strategy to the output layer, wherein we use a discriminative training loss and a weighted sampling scheme. We also establish close connections between BlackOut, importance sampling, and noise contrastive estimation (NCE). Our experiments, on the recently released one billion word language modeling benchmark, demonstrate scalability and accuracy of BlackOut; we outperform the state-of-the art, and achieve the lowest perplexity scores on this dataset. Moreover, unlike other established methods which typically require GPUs or CPU clusters, we show that a carefully implemented version of BlackOut requires only 1-10 days on a single machine to train a RNNLM with a million word vocabulary and billions of parameters on one billion words. Although we describe BlackOut in the context of RNNLM training, it can be used to any networks with large softmax output layers.

BlackOut: Speeding up Recurrent Neural Network Language Models With Very Large Vocabularies

http://arxiv.org/pdf/1511.06909v7

Title BlackOut Speeding Recurrent Neural Network Language Models Large Vocabularies Summary propose BlackOut approximation algorithm efficiently train massive recurrent neural network language model RNNLMs million word vocabulary BlackOut motivated using discriminative loss describe new sampling strategy significantly reduces computation improving stability sample efficiency rate convergence One way understand BlackOut view extension DropOut strategy output layer wherein use discriminative training loss weighted sampling scheme also establish close connection BlackOut importance sampling noise contrastive estimation NCE experiment recently released one billion word language modeling benchmark demonstrate scalability accuracy BlackOut outperform stateofthe art achieve lowest perplexity score dataset Moreover unlike established method typically require GPUs CPU cluster show carefully implemented version BlackOut requires 110 day single machine train RNNLM million word vocabulary billion parameter one billion word Although describe BlackOut context RNNLM training used network large softmax output layer Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0006652222364209592, 0.041236214339733124, 0.009081205353140831, 0.0381535068154335, -0.011480504646897316, -0.007721998263150454, 0.034583013504743576, 0.014878233894705772, -0.025639204308390617, -0.028501413762569427, -0.01765325292944908, -0.05223629251122475, 0.01297624222934246, 0.04424270987510681, 0.005263077560812235, -0.01614168845117092, 0.039650239050388336, 0.013920803554356098, -0.037694260478019714, -0.029713215306401253, 0.018436957150697708, 0.012194855138659477, 0.010734555311501026, 0.03872896730899811, 0.01588146574795246, -0.0244816355407238, 0.013175065629184246, -0.03796974569559097, -0.05356082320213318, -0.0564776174724102, -0.013634582981467247, 0.038359738886356354, 0.026187226176261902, 0.04592190682888031, 2.200573362642899e-06, -0.03930072858929634, -0.003761396510526538, -0.011521723121404648, 0.0010669701732695103, 0.0501030795276165, 0.032046351581811905, 0.0031729855109006166, 0.0423014760017395, 0.02227364294230938, -0.020977893844246864, -0.01498735323548317, 0.048596158623695374, 0.05895310267806053, -0.009527446702122688, 0.016352344304323196, -0.0016789495712146163, -0.03270222991704941, 0.03657936304807663, -0.05736936256289482, 0.003915851004421711, -0.04571615532040596, 0.018219415098428726, -0.014303017407655716, -0.007898879237473011, -0.0668526440858841, -0.05407707393169403, 0.07109398394823074, 0.0237501859664917, 0.0226112250238657, 0.0029360868502408266, 0.04484174773097038, 0.010283209383487701, -0.009426507167518139, 0.014540690928697586, 0.06122327223420143, -0.051835499703884125, -0.00709477998316288, 0.0002232326805824414, 0.01776708848774433, -0.050282351672649384, -0.022724699229002, -0.04256100207567215, 0.029166772961616516, 0.027775965631008148, 0.03902707248926163, -0.03236282244324684, -0.0007404692005366087, 0.05597363039851189, 0.026927240192890167, -0.027173591777682304, 0.021992219612002373, 0.008591161109507084, -0.011978108435869217, -0.015541523694992065, 0.010134393349289894, -0.00855350960046053, -0.04670802503824234, 0.023443086072802544, 0.010776192881166935, -0.019488811492919922, 0.02728184498846531, -0.03385273367166519, -0.07507448643445969, 0.0075219664722681046, -0.025378631427884102, 0.04339221119880676, 0.017876913771033287, 0.02785470336675644, 0.03641181439161301, -0.02304939366877079, 0.017852522432804108, -0.019792236387729645, 0.004769901279360056, 0.015402897261083126, -0.007414830382913351, -0.01781310699880123, -0.008319288492202759, -0.04678240045905113, 0.061831533908843994, -0.012819488532841206, -0.04084714129567146, -0.01935754530131817, -0.02450726367533207, -0.020695317536592484, -0.05417078733444214, -0.003799043595790863, 0.03550412505865097, -0.040768858045339584, -0.01732633449137211, 0.011228763498365879, 0.03634015470743179, 0.0011925192084163427, -0.004123020451515913, -0.010865315794944763, -0.05355193838477135, -0.012407241389155388, -0.00970517285168171, 0.007047452498227358, 0.006594058591872454, -0.004843908362090588, 0.0675811693072319, 0.029155699536204338, 0.0022248278837651014, -0.05356700345873833, 0.004351235460489988, 0.014972733333706856, -0.028396669775247574, -0.037064362317323685, -0.09449419379234314, 0.0068250177428126335, -0.02960425801575184, 0.005502983927726746, -0.027568500488996506, 0.03849463164806366, 0.022002385929226875, 0.004682803060859442, 0.08089122176170349, -0.04294668883085251, -0.022038407623767853, 0.029554927721619606, -0.009892546571791172, 0.06759350001811981, 0.0673658549785614, 0.04033961892127991, 0.004760985728353262, 0.03588588163256645, -0.00608037831261754, 0.022053925320506096, 0.028796222060918808, 0.0241752527654171, -0.005006440449506044, -0.10972680896520615, -0.06852123886346817, 0.029427360743284225, 0.03554859012365341, 0.053587429225444794, 0.0610591396689415, -0.02580876648426056, -0.027995316311717033, 0.03331650421023369, 0.023669863119721413, 0.015384180471301079, 0.08141690492630005, -0.020230187103152275, 0.008967746049165726, -0.021797697991132736, -0.026253655552864075, -0.017018921673297882, 0.040506646037101746, 0.010300914756953716, -0.008792705833911896, 0.051692865788936615, 0.007029721979051828, -0.04909329488873482, -0.025584565475583076, -0.004363800399005413, 0.007226679008454084, 0.05638233944773674, 0.011726629920303822, 0.047196827828884125, 0.007046191021800041, -0.041927553713321686, 0.08307355642318726, 0.03751892223954201, -0.009753973223268986, 0.020623408257961273, -0.033376261591911316, -0.004087989218533039, 0.016775628551840782, 0.06738079339265823, -0.029596395790576935, -0.009631757624447346, -0.02623339742422104, 0.030821427702903748, 0.03564779832959175, -0.03639411926269531, 0.006024998612701893, 0.036012567579746246, -0.09542498737573624, 0.0006274083280004561, 0.017251411452889442, -0.011391846463084221, 0.036561187356710434, -0.02696409821510315, 0.04921886324882507, 0.01802830956876278, -0.008743107318878174, -0.04281018674373627, 0.03466905280947685, -0.02555205672979355, -0.04280956834554672, 0.023631766438484192, 0.012146861292421818, 0.04011319577693939, 0.007839826866984367, -0.0019381237216293812, 0.020975841209292412, 0.03291871398687363, -0.07402509450912476, -0.024245113134384155, -0.03447975963354111, -0.0875384509563446, -0.03928809240460396, 0.029456770047545433, -0.02355443499982357, 0.06277988106012344, 0.09556826949119568, -0.02288067899644375, -0.044804368168115616, 0.050172146409749985, -0.0426042377948761, 0.06056642532348633, -0.05893159285187721, 0.008078720420598984, -0.015152199193835258, 0.06761206686496735, -0.005627658683806658, 0.0038448430132120848, -0.058860376477241516, 0.026253625750541687, -0.019360389560461044, 0.03925296291708946, 0.007820847444236279, -0.041781555861234665, -0.04937412589788437, 0.02439248375594616, -0.04492756724357605, 0.008923185989260674, -0.04479413479566574, 0.00305364141240716, -0.009786536917090416, 0.013439774513244629, -0.05864135921001434, 0.002703003352507949, -0.009638131596148014, -0.006222550757229328, 0.005336935631930828, 0.03355976566672325, 0.036650799214839935, -0.03224871680140495, -0.02535036951303482, 0.04064682498574257, -0.03064669296145439, 0.01473999209702015, 0.013377646915614605, 0.02227800339460373, -0.03076532483100891, -0.00222960882820189, -0.06764448434114456, 0.02854957990348339, 0.03780538961291313, -0.028090599924325943, -0.0702400729060173, -0.0043402197770774364, 0.02828351780772209, -0.00601395545527339, 0.06216183677315712, 0.0009086862555705011, -0.058935604989528656, -0.016576077789068222, -0.01417351234704256, 0.020899619907140732, 0.034646883606910706, 0.03466559946537018, -0.030255284160375595, 0.00991884246468544, -0.004873228725045919, -0.019446661695837975, 0.02703532576560974, -0.02435251697897911, -0.007184267975389957, 0.01682092435657978, -0.004857722204178572, -0.026966048404574394, 0.06428153812885284, -0.007149023469537497, -0.0005779479397460818, -0.023068798705935478, -0.05367196723818779, -0.03455056622624397, -0.024995075538754463, -0.03810712695121765, 0.005573106463998556, -0.021988091990351677, -0.021253492683172226, -0.015196179039776325, 0.009872970171272755, 0.009431087411940098, -0.012356080114841461, 0.004151319153606892, -0.02986982837319374, -0.03603901341557503, -0.033080000430345535, 0.03781701251864433, 0.0027170944958925247, 0.0014593013329431415, -0.038457926362752914, -0.04478411376476288, -0.025993453338742256, -0.017343835905194283, -0.04683556780219078, -0.026439119130373, 0.024512222036719322, -0.0025627135764807463, 0.012199688702821732, -0.017736384645104408, -0.014588183723390102, -0.022495390847325325, -0.010308659635484219, -0.02708415687084198, -0.013980677351355553, 0.048661768436431885, 0.0010264345910400152, -0.028120068833231926, 0.0584343820810318, 0.004155138041824102, 0.05532969906926155, -0.011636568233370781, 0.020234443247318268, 0.01016018632799387, 0.02342960610985756, 0.04215029627084732, -0.00588052487000823, 0.020202992483973503, 0.00613004295155406, 0.021394969895482063, 0.04957214742898941, 0.011299754492938519, 0.02731049619615078, -0.03383920341730118, 0.004641365725547075, 0.014786658808588982, 0.012303406372666359, -0.03231891989707947, 0.00981366541236639, 0.02367883175611496, -0.0779765173792839, 0.010311635211110115, 0.07821089774370193, 0.004347776062786579, -0.11069276928901672, -0.012784026563167572, -0.015835842117667198, 0.011458729393780231, 0.022646423429250717, -0.012009787373244762, -0.05065549537539482, -0.027608228847384453, -0.007524382323026657, 0.017901135608553886, -0.0031520873308181763, -0.06637541204690933, -0.01306867878884077, -0.11280448734760284, 0.0014161065919324756, -0.0050463080406188965, -0.06812143325805664, -0.034192487597465515, -0.023077700287103653, -0.007556075695902109, -0.026813898235559464, 0.027709512040019035, 0.04110223427414894, 0.017327116802334785, -0.035608869045972824, 0.03641476482152939, -0.020319193601608276, 0.031069613993167877, 0.04679584875702858, -0.05243393033742905, 0.011656825430691242, 0.04436261206865311, 0.0261010080575943, -0.03711239993572235, -0.03506822511553764, 0.012929851189255714, -0.043363530188798904, -0.04173857346177101, -0.003260360099375248, 0.01494844350963831, 0.015015637502074242, -0.02881125919520855, 0.03709913045167923, 0.03372592851519585, -0.04710344597697258, 0.01552535966038704, 0.0013435081345960498, 0.023169852793216705, 0.021371979266405106, -0.027807921171188354, -0.025130221620202065, 0.02007453888654709, 0.019107675179839134, 0.047284454107284546, 0.05075063928961754, -0.05726699158549309, -0.03923410549759865, 0.008342931978404522, 0.019501395523548126, -0.11981718242168427, 0.016553737223148346, -0.014635988511145115, 0.004948990885168314, -0.07832853496074677, -0.05603425204753876, -0.0017740637995302677, -0.014561007730662823, 0.04794808477163315, 0.023745376616716385, 0.06641197204589844, 0.04916379600763321, 0.004458886105567217, -0.03272528573870659, -0.012645338661968708, -0.025362297892570496, 0.010539204813539982, -0.05742824450135231, 0.02349422313272953, -0.016764691099524498, -0.009704616852104664, -0.01752980798482895, 0.016176875680685043, -0.10841041803359985, -0.011588482186198235, 0.04213132709264755, -0.01021221186965704, 0.014871715568006039, 0.029118644073605537, -0.018565746024250984, -0.08632858842611313, 0.05706712603569031, 0.04317153990268707, 0.013494132086634636, 0.03471718356013298, 0.0229111909866333, 0.0023542444687336683, 0.015449350699782372, 0.05201633274555206, -0.032632045447826385, 0.029641300439834595, -0.0013421208132058382, 0.02841571532189846, -0.018888285383582115, 0.023645909503102303, -0.02111089788377285, -0.009176627732813358, 0.010761710815131664, -0.005503668915480375, 0.001524697756394744, -0.035439882427453995, 0.028446851298213005, 0.0024548443034291267, 0.01663520187139511, -0.06963593512773514, 0.046349573880434036, 0.02515438385307789, -0.015103158541023731, 0.0025060672778636217, -0.049716174602508545, 0.05777456611394882, -0.04130830243229866, 0.008000650443136692, 0.013051201589405537, 0.0017927667358890176, -0.0075166975148022175, 0.02318573370575905, 0.013607120141386986, -0.04588019475340843, -0.015606263652443886, 0.023608803749084473, 0.016720280051231384, -0.042668793350458145, 0.019276157021522522, 0.01867230050265789, -0.017010869458317757, -0.05267646163702011, 0.021148310974240303, -0.018821725621819496, -0.004988777916878462, -0.05439390242099762, 0.04026303440332413, 0.034693505614995956, 0.0019536693580448627, -0.03340630978345871, -0.008392058312892914, 0.003736194223165512, -0.03714976832270622, 0.03193014860153198, -0.02552015893161297, 0.008392784744501114, 0.030202776193618774, 0.047081638127565384, -0.02672361582517624, 0.05462481081485748, 0.06997447460889816, 0.05806607007980347, 0.01986309327185154, 0.056154511868953705, -0.0009893708629533648, -0.0105946259573102, 0.006590521428734064, -0.0219122301787138, 0.06011621281504631, -0.020940113812685013, 0.010607103817164898, -0.00911985244601965, -0.05568249151110649, 0.08002184331417084, -0.017219657078385353, 0.02397027239203453, -0.007852449081838131, 0.03231586888432503, 0.0024389466270804405, 0.021300077438354492, 0.0206570066511631, -0.008508927188813686, 0.06933553516864777, 0.02482728846371174, -0.028882121667265892, -0.038212958723306656, -6.578514544422772e-33, -0.0004579652159009129, -0.04231607913970947, -0.002750647021457553, -0.053267184644937515, -0.050638217478990555, 0.03306683152914047, -0.03698697313666344, -0.025556646287441254, -0.015058640390634537, 0.0025785730686038733, -0.023857619613409042, 0.01800890825688839, 0.02302519790828228, 0.057876184582710266, 0.005099091213196516, -0.010445726104080677, 0.03537750616669655, -0.001639047753997147, 0.04592176526784897, 0.032595425844192505, 0.020539846271276474, 0.057447608560323715, 0.04170907661318779, 0.008496910333633423, -0.040111344307661057, -0.034960854798555374, -0.017979184165596962, -0.010426808148622513, 0.009319771081209183, 0.0418173223733902, -0.05966976284980774, 0.054856251925230026, 0.017745690420269966, -0.04038845747709274, -0.03753792122006416, 0.003117149230092764, -0.05196341499686241, -0.028414219617843628, -0.023782964795827866, 0.018070008605718613, -0.048105739057064056, 0.03132685646414757, 0.07337220013141632, 0.028512511402368546, 0.006313077174127102, 0.035627707839012146, 0.030029715970158577, -0.018839245662093163, -0.10642022639513016, 0.01304179709404707, 5.145904651726596e-05, 0.01559092104434967, 0.00866649392992258, -0.020391635596752167, -0.0007225574227049947, -0.020721711218357086, -0.034303419291973114, 0.04633057862520218, -0.09519171714782715, -0.03555585443973541, 0.02993101440370083, 0.07948405295610428, 0.025346167385578156, 0.04579351097345352, 0.05813632532954216, 0.03716270253062248, 0.011607334949076176, -0.025981096550822258, -0.04107469320297241, 0.007763230707496405, 0.0559159480035305, 0.01916523464024067, 0.05574598163366318, 0.01463755127042532, 0.10552190989255905, -0.05537033826112747, -0.06464456021785736, -0.04253022372722626, -0.0423959344625473, 0.09124778211116791, 0.07343688607215881, 0.023797251284122467, -0.015219785273075104, -0.022506937384605408, 0.01020943745970726, -0.030376316979527473, -0.04376513510942459, -0.007188227493315935, 0.019359534606337547, 0.021194735541939735, 0.005848676431924105, 0.029398269951343536, 0.007348817307502031, -0.03701017424464226, -0.0006196593167260289, 0.022858871147036552, 0.018102338537573814, 0.022550860419869423, 0.0032175653614103794, 0.016153747215867043, -0.03464420884847641, -0.010010121390223503, -0.0283010583370924, 0.02755044586956501, -0.009139136411249638, -0.0011562468716874719, 0.0466311015188694, 0.02324451133608818, -0.01588134653866291, -0.045041169971227646, -0.0284566730260849, -0.0050530764274299145, 0.034638866782188416, 0.1074984148144722, 0.027162611484527588, -0.02606862224638462, 0.019846584647893906, 0.060107141733169556, 0.017235584557056427, -0.04477936401963234, 0.017906401306390762, -0.030473511666059494, 0.054613009095191956, 0.019181804731488228, -0.06158839166164398, -0.023697247728705406, -0.05230386555194855, -0.02256772108376026, 0.02355213649570942, -0.03259192779660225, -0.03152576833963394, 0.026022182777523994, 2.7859451279255154e-07, -0.0073061478324234486, -0.0001383706257911399, 0.0028205127455294132, -0.03353175148367882, -0.010284841991961002, -0.01030808687210083, 0.041618574410676956, 0.03346747159957886, -0.02755635976791382, 0.03457734361290932, 0.004941719118505716, 0.003845771076157689, 0.038572538644075394, 0.013204635120928288, -0.11964622884988785, 0.007246361114084721, -0.07336009293794632, 0.0716489776968956, 0.0010297041153535247, -0.022044530138373375, -0.0015085870400071144, 0.12742352485656738, 0.03935086727142334, -0.02734610065817833, 0.03233722597360611, -0.05993005260825157, -0.0008315967861562967, 0.005375244654715061, 0.012330234982073307, 0.0003816236276179552, 0.021453235298395157, 0.08434420824050903, -0.015719030052423477, -0.02976856380701065, -0.015906095504760742, 0.03531497344374657, 0.011697467416524887, 0.028330489993095398, -0.03965781629085541, -0.058352962136268616, 0.027209747582674026, -0.01888399012386799, -0.019887642934918404, -0.02713763900101185, 0.04808339849114418, 0.0008697265293449163, -0.017353644594550133, -0.029724329710006714, 0.024669161066412926, 0.012804907746613026, 0.027094129472970963, -0.03086625039577484, -0.007300399709492922, -0.011989993043243885, -0.005964183248579502, -0.07236325740814209, -0.03911999240517616, -0.06454678624868393, 0.005747130140662193, 0.002881530439481139, -0.04966680705547333, -0.01443270593881607, -0.0429207868874073, -0.019123634323477745, 0.03559190034866333, -0.012125475332140923, 0.03581129014492035, 2.7705710786772728e-34, 0.04051639512181282, -0.039339542388916016, -0.01039178017526865, 0.060444630682468414, -0.0008764344383962452, -0.014506684616208076, -0.023321053013205528, 0.01969705894589424, -0.029587896540760994, -0.10890203714370728, -0.04108325392007828]

['Marta R. Costa-Jussà', 'José A. R. Fonollosa']

1603.00810v3

Neural Machine Translation (MT) has reached state-of-the-art results. However, one of the main challenges that neural MT still faces is dealing with very large vocabularies and morphologically rich languages. In this paper, we propose a neural MT system using character-based embeddings in combination with convolutional and highway layers to replace the standard lookup-based word representations. The resulting unlimited-vocabulary and affix-aware source word embeddings are tested in a state-of-the-art neural MT based on an attention-based bidirectional recurrent neural network. The proposed MT scheme provides improved results even when the source language is not morphologically rich. Improvements up to 3 BLEU points are obtained in the German-English WMT task.

Character-based Neural Machine Translation

http://arxiv.org/pdf/1603.00810v3

Title Characterbased Neural Machine Translation Summary Neural Machine Translation MT reached stateoftheart result However one main challenge neural MT still face dealing large vocabulary morphologically rich language paper propose neural MT system using characterbased embeddings combination convolutional highway layer replace standard lookupbased word representation resulting unlimitedvocabulary affixaware source word embeddings tested stateoftheart neural MT based attentionbased bidirectional recurrent neural network proposed MT scheme provides improved result even source language morphologically rich Improvements 3 BLEU point obtained GermanEnglish WMT task Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.014114925637841225, 0.035114072263240814, 0.002446637023240328, 0.09347090870141983, -0.000986468861810863, -0.0038921234663575888, -0.020763492211699486, 0.016344992443919182, -0.04062526300549507, -0.023435117676854134, -0.0058680386282503605, -0.0912121906876564, 0.0344366617500782, 0.04694531857967377, 0.0838363841176033, -0.03573345020413399, 0.007237262558192015, 0.005802425555884838, -0.006593325175344944, 0.006552442908287048, 0.03394795209169388, 0.016464384272694588, 0.04090599715709686, 0.026975203305482864, -0.014029650017619133, 0.025718269869685173, -0.006087447516620159, 0.026266280561685562, -0.007374695967882872, -0.033020444214344025, -0.02119695395231247, 0.0071930354461073875, 0.0298505537211895, 0.09812260419130325, 2.221663862655987e-06, -0.004571732133626938, -0.02900906279683113, -0.019272541627287865, 0.007783771026879549, 0.012027266435325146, 0.04973207414150238, -0.055035464465618134, -0.02156051993370056, 0.030105743557214737, 0.01250520534813404, -0.012710239738225937, 0.05305373668670654, 0.04725749045610428, 0.037816304713487625, 0.0655970424413681, -0.014016840606927872, -0.08379975706338882, 0.0041397735476493835, -0.042230453342199326, 0.0049121445044875145, -0.021559085696935654, -0.023627134039998055, -0.05463799461722374, -0.002780459588393569, 0.03335025534033775, -0.03538620471954346, 0.050598710775375366, -0.010129274800419807, -0.013942189514636993, -0.0023312699049711227, 0.03137876093387604, 0.01373347733169794, 0.014478215016424656, 0.0272821094840765, 0.11365172266960144, -0.046506118029356, 0.003418656997382641, -0.031068991869688034, -0.0006605738890357316, 0.0024594715796411037, -0.04661707207560539, -0.02434069663286209, 0.015107863582670689, -0.0038363919593393803, 0.0169383492320776, 0.0171011034399271, 0.023033076897263527, 0.057586848735809326, 0.009583941660821438, -0.06109251827001572, -0.05493074283003807, 0.036519937217235565, -0.02960168942809105, -0.04378902167081833, -0.012648883275687695, -0.019436433911323547, -0.013480925001204014, 0.040717605501413345, 0.052422355860471725, 0.022147534415125847, 0.027781061828136444, -0.01908850111067295, -0.0725400373339653, 0.03331036865711212, -0.08477478474378586, 0.061124954372644424, 0.0436071902513504, -0.03687886521220207, 0.014218711294233799, -0.04812799394130707, 0.043524306267499924, -0.060880228877067566, -0.029897956177592278, -0.02341705746948719, -0.01699347235262394, -0.03675301373004913, -0.003919446375221014, -0.04432946816086769, 0.014962940476834774, -0.025642257183790207, 0.012224549427628517, -0.014773787930607796, 0.018652494996786118, 0.03637170046567917, -0.04237563535571098, 0.00665003526955843, 0.004602112807333469, -0.065763458609581, -0.023206615820527077, -0.0192435160279274, 0.07815776765346527, -0.017731651663780212, -0.053201548755168915, -0.04384661465883255, 0.007459900341928005, -0.010487403720617294, 0.021551702171564102, -0.0026155044324696064, -0.027074463665485382, -0.005881554912775755, 0.09233126789331436, 0.017774051055312157, -0.0632292777299881, -0.000909603841137141, 0.017313534393906593, -0.03850233554840088, -0.03821905329823494, -0.011533908545970917, -0.05056324973702431, 0.05084536224603653, -0.03266283497214317, -0.027190128341317177, -0.023100323975086212, 0.02514990046620369, 0.019110066816210747, -0.02239951118826866, 0.08185554295778275, 0.009758230298757553, -0.042261864989995956, 0.012114794924855232, 0.004097505938261747, 0.020151229575276375, -0.013694182969629765, 0.0705222561955452, 0.02812991477549076, -0.030823418870568275, -0.0053649283945560455, -0.007198915351182222, 0.04051899537444115, 0.0025051573757082224, 0.001281234435737133, -0.0619082935154438, -0.011833961121737957, 0.00250403955578804, 0.07896965742111206, 0.029422208666801453, 0.10051004588603973, -0.008144049905240536, -0.02218056097626686, 0.031665753573179245, 0.04615806043148041, 0.05865611508488655, 0.04751656949520111, 0.01931753382086754, 0.008618516847491264, -0.009472455829381943, -0.01084230188280344, -0.02105964906513691, 0.041725143790245056, -0.0353628471493721, 0.007613737601786852, -0.0536973737180233, 0.04435276985168457, -0.005609655287116766, 0.002534331288188696, 0.026221133768558502, -0.013403983786702156, -0.0045598833821713924, -0.05561237782239914, 0.0301519725471735, -0.023983219638466835, -0.07897120714187622, 0.007961973547935486, -0.0010389978997409344, -0.038865335285663605, 0.03656145930290222, -0.025201519951224327, -0.025653116405010223, 0.054711971431970596, 0.06007075682282448, -0.004816823173314333, -0.04375142976641655, -0.023275280371308327, -0.025599246844649315, 0.06753628700971603, 0.010660885833203793, 0.014415380544960499, 0.004236660432070494, -0.06565817445516586, 0.02072717249393463, 0.02541750855743885, -0.014246206730604172, 0.04906165599822998, -0.06760305911302567, 0.049609433859586716, 0.03940852731466293, 0.047290999442338943, -0.030854377895593643, 0.05019297078251839, 0.00785158108919859, -0.013689402490854263, 0.006495801266282797, 0.013714131899178028, -0.009345279075205326, 0.008703112602233887, -0.015905683860182762, 0.026130590587854385, 0.02297339029610157, -0.05520855262875557, 0.0025717674288898706, 0.030491648241877556, -0.05834574997425079, -0.05883486196398735, 0.055304717272520065, -0.022540628910064697, 0.0031378548592329025, -0.014146535657346249, -0.00923597440123558, -0.04503600299358368, 0.019211987033486366, -0.07871241122484207, 0.03516716510057449, -0.03306575119495392, 0.06499914079904556, -0.004797548055648804, 0.04524043947458267, -0.03589608892798424, 0.04575188830494881, -0.013985507190227509, -0.018902264535427094, 0.010721174068748951, 0.005936900153756142, 0.029834676533937454, -0.02330125868320465, -0.036388762295246124, 0.05638744309544563, 0.03571036458015442, 0.015105229802429676, -0.00907185673713684, 0.00030349715962074697, 0.003814560594037175, -0.057629965245723724, -0.03803033381700516, -0.000894856930244714, -0.005108208395540714, 0.01835373044013977, 0.012338604778051376, 0.05047934502363205, 0.028699565678834915, -0.002976791700348258, -0.017092041671276093, 0.03779313340783119, -0.003167469287291169, 0.001606218982487917, 0.03451285883784294, -0.02627309411764145, 0.02461976557970047, -0.02396991476416588, -0.024179348722100258, 0.0011003424879163504, 0.02825898677110672, 0.0357179269194603, -0.06603796035051346, -0.06212381273508072, -0.03695542365312576, -0.015121360309422016, 0.024157609790563583, -0.007868192158639431, -0.07833842933177948, -0.005427046213299036, -0.04601293429732323, 0.0476718470454216, 0.00991739146411419, 0.009731877595186234, -0.007959126494824886, 0.03307881951332092, -0.012263303622603416, -0.02153206802904606, 0.0005260028410702944, 0.013827084563672543, 0.016613831743597984, -0.014530947431921959, -0.008229044266045094, 0.002124237595126033, 0.06033847853541374, -0.03489619120955467, 0.008563960902392864, -0.04554830491542816, -0.019035035744309425, -0.024728579446673393, 0.007761327084153891, -0.010049181990325451, 0.015725387260317802, -0.04245113581418991, -0.03453166410326958, -0.026947021484375, -0.0054177939891815186, 0.06178971007466316, -0.02447618916630745, -0.02862267568707466, -0.05415155738592148, -0.003703799331560731, -0.033979833126068115, 0.045961424708366394, 0.0036044756416231394, 0.019653445109725, 0.009507997892796993, -0.05405760556459427, -0.018973099067807198, 0.020716959610581398, -0.051635898649692535, -0.044525932520627975, 0.05021877586841583, 0.01077986042946577, -0.0069787646643817425, -0.050727616995573044, 0.0029795386362820864, -0.0272587388753891, -0.024037880823016167, -0.019591543823480606, -0.0249614417552948, 0.05239507928490639, -0.056990623474121094, -0.002274178434163332, 0.03543100133538246, -0.0077672842890024185, 0.026828216388821602, -0.01412022951990366, -0.006775536574423313, -0.013643220067024231, 0.05547462776303291, 0.005871373228728771, -0.0012444346211850643, 0.005640511866658926, 0.006967771798372269, 0.03827608376741409, 0.024852048605680466, -0.06896413117647171, -0.028819754719734192, -0.05110808461904526, -0.009919487871229649, 0.01653025485575199, -0.02559223584830761, -0.04044787585735321, -0.010897488333284855, 0.022310631349682808, -0.07752066105604172, -0.01932523213326931, 0.10387805104255676, 0.0409446619451046, -0.05390949547290802, -0.011328285560011864, 0.014614083804190159, 0.03332831710577011, 0.01105122547596693, 0.04204961284995079, -0.07292914390563965, -0.01786784455180168, 0.00947023555636406, 0.01791873387992382, 0.03464644029736519, -0.030510904267430305, -0.017021939158439636, -0.06954854726791382, 0.002728851279243827, 0.03365261107683182, -0.05575181171298027, -0.022109175100922585, 0.020518071949481964, -0.040025532245635986, 0.01156756654381752, 0.01729435659945011, 0.035380855202674866, 0.007673005573451519, -0.026177380234003067, -0.004485247656702995, 0.019827956333756447, -0.009995038621127605, 0.004859537351876497, -0.06415661424398422, 0.027890469878911972, 0.03506116196513176, 0.07861127704381943, -0.0298550296574831, -0.009200460277497768, -0.00988257396966219, 0.014924462884664536, 0.012212713249027729, -0.02677307464182377, 0.03599708899855614, -0.009287109598517418, -0.04661852866411209, -0.017524491995573044, -0.007611346896737814, -0.02440502494573593, 0.040323011577129364, -0.011772927828133106, 0.10484469681978226, -0.006097553297877312, 0.018351972103118896, -0.024524342268705368, -0.019063817337155342, -0.007853696122765541, 0.019667893648147583, 0.020748306065797806, -0.0426960363984108, -0.01386856660246849, -0.029273120686411858, -0.0037677402142435312, -0.08053071051836014, -0.03324181213974953, 0.0007080485811457038, -0.009864671155810356, -0.009695254266262054, -0.11290131509304047, -0.07376544177532196, 0.00036024150904268026, 0.0474671870470047, 0.028983302414417267, 0.008201430551707745, 0.016914021223783493, -0.03241516277194023, -0.07398339360952377, 0.020381979644298553, -0.0018040474969893694, 0.049609292298555374, -0.06694827228784561, 0.007240493781864643, 0.051668573170900345, -0.017348874360322952, 0.04013544321060181, -0.030332211405038834, -0.025757307186722755, -0.06423652917146683, -0.03333829343318939, 0.015327023342251778, -0.0026211203075945377, -0.011923650279641151, -0.06343168765306473, -0.07220995426177979, 0.023979127407073975, -0.06350350379943848, -0.02456391230225563, -0.023814044892787933, 0.05595922842621803, -0.0007593206246383488, -0.010001257993280888, 0.02944350428879261, 0.006873703096061945, 0.011507440358400345, -0.022567488253116608, 0.0340590663254261, 0.02629624679684639, -0.032569512724876404, 0.020103104412555695, 0.009665719233453274, 0.0003134549770038575, -0.010135199874639511, 0.03800933063030243, -0.032373055815696716, -0.012524421326816082, -0.003895736765116453, -0.008986038155853748, -0.04791567102074623, 0.019129112362861633, 0.07329889386892319, -0.01522495411336422, -0.007787078153342009, -0.0403297059237957, -0.016953155398368835, -0.04674534499645233, 0.04534338414669037, 0.06938956677913666, 0.0008146832697093487, 0.014589103870093822, 0.01922902837395668, 0.04499302804470062, -0.011233581230044365, -0.008682352490723133, -0.019795114174485207, 0.01947799138724804, -0.03368121385574341, 0.04423549026250839, -0.005976223386824131, 0.01829879730939865, -0.020557213574647903, 0.027557216584682465, 0.02070225588977337, 0.036273106932640076, -0.029132861644029617, 0.0181723739951849, 0.08597695827484131, -0.013593670912086964, 0.04721672087907791, -0.004107032902538776, 0.0033229703549295664, -0.02069525234401226, 0.0314573235809803, -0.05028494819998741, 0.005437721032649279, 0.03959694132208824, 0.017862077802419662, -0.008425979875028133, -0.01651047356426716, 0.04889292269945145, 0.01779843494296074, 0.00991937704384327, 0.035152267664670944, 0.009794230572879314, 0.0022901291958987713, 0.001573466113768518, 0.006729763466864824, 0.015563779510557652, -0.047539886087179184, -0.016578221693634987, -0.01940058544278145, -0.08045139908790588, 0.0588085874915123, 0.0037512737326323986, 0.013281246647238731, 0.014422422274947166, -0.018458658829331398, -0.01658451370894909, 0.013286244124174118, 0.03427862003445625, -0.02029331959784031, 0.07066585123538971, 0.03246195241808891, -0.04246699810028076, -0.043090756982564926, -5.9830774319053426e-33, 0.0006861381116323173, -0.00488608842715621, -0.0027126611676067114, -0.07168016582727432, -0.06531969457864761, -0.0027448704931885004, -0.04106135293841362, 0.0035083319526165724, -0.02083674818277359, 0.0256465133279562, -0.021778171882033348, 0.022488700225949287, 0.0010761540615931153, 0.0256363358348608, 0.010782214812934399, 0.01544424332678318, 0.013002496212720871, 0.0014371871948242188, 0.016672849655151367, 0.021072031930088997, 0.039913780987262726, 0.07686970382928848, 0.095609650015831, -0.019854767248034477, 0.003235833253711462, -0.013726466335356236, 0.04273718595504761, 0.02998565323650837, 0.018653428182005882, 0.007978343404829502, -0.039176154881715775, 0.01734810508787632, 0.008525390177965164, 0.004582654219120741, -0.03472378849983215, 0.005543634295463562, -0.08161584287881851, -0.0073196543380618095, -0.0265418142080307, 0.02792532369494438, -0.016876716166734695, -0.013180178590118885, 0.07024247199296951, -0.030482495203614235, 0.03465190902352333, -0.0009214570745825768, 0.010910682380199432, -0.03906374052166939, -0.05513157323002815, 0.017794545739889145, -0.07978765666484833, 0.019887160509824753, 0.015043755061924458, 0.006937441881746054, 0.05739503353834152, -0.018270859494805336, 0.025177672505378723, 0.02299652434885502, -0.06036602705717087, -0.024950390681624413, -0.03484153002500534, 0.03103186935186386, 0.02905779704451561, 0.04446735233068466, -0.028578629717230797, -0.002147708786651492, 0.012334992177784443, -0.03374796360731125, 0.007005817256867886, 0.031079933047294617, 0.03738909214735031, -0.003422795096412301, 0.09111401438713074, 0.02319302223622799, 0.04616899415850639, -0.026500489562749863, -0.03645547851920128, 0.009462688118219376, 0.008405307307839394, 0.04801037162542343, 0.01865648664534092, 0.013715033419430256, -0.06195005774497986, -0.005522174295037985, 0.022553736343979836, -0.007204833440482616, -0.025472629815340042, -0.0320996530354023, -0.005099388770759106, -0.01531364768743515, -0.010753083974123001, 0.025416208431124687, 0.049836739897727966, -0.039099980145692825, 0.029422208666801453, 0.02146301232278347, 0.0017703808844089508, 0.007007393054664135, -0.011135358363389969, 0.06891074031591415, -0.015005731023848057, -0.010913482867181301, -0.0279762651771307, 0.02038680948317051, -0.017731886357069016, -0.01780841313302517, 0.04215076565742493, 0.002034697448834777, -0.013254779390990734, -0.0015737767098471522, -0.0391790047287941, -0.0496787466108799, 0.0051706088706851006, 0.0681857243180275, 0.0021635047160089016, -0.04100633040070534, 0.0027632100973278284, 0.03134162351489067, 0.04633164033293724, -0.013357564806938171, -0.03981705754995346, -0.0024317284114658833, 0.057511236518621445, 0.022974342107772827, -0.05227482691407204, 0.019342688843607903, -0.044846780598163605, 0.06907086819410324, 0.054218050092458725, -0.09009601175785065, -0.017169009894132614, -0.0017835464095696807, 2.9506031751225237e-07, 0.05067429691553116, 0.055271245539188385, 0.02699245885014534, -0.02901836484670639, 0.008921264670789242, 0.0026142895221710205, -0.04384692385792732, 0.028493687510490417, -0.014658196829259396, 0.029991311952471733, 0.0316600427031517, -0.011258021928369999, 0.04275763779878616, 0.004107522312551737, -0.08002173900604248, -0.014215894043445587, -0.06410475075244904, 0.05587669089436531, -0.04023072123527527, -0.01201519276946783, 0.081794373691082, 0.1341697871685028, -0.0021295074839144945, -0.014105191454291344, 0.026271173730492592, -0.008970707654953003, 0.05840030685067177, 0.026672091335058212, 0.0008001412497833371, -0.007633497007191181, 0.042526159435510635, 0.015254904516041279, -0.05397588014602661, -0.054648540914058685, -0.03125477209687233, 0.03922896459698677, 0.01696840673685074, 0.023962922394275665, -0.009951520711183548, -0.027112390846014023, 0.027611833065748215, -0.03711753338575363, -0.005782341118901968, -0.0019042688654735684, 0.03060096874833107, -0.03879541531205177, -0.050376929342746735, 0.0032383280340582132, 0.029981987550854683, 0.016645824536681175, 0.024833744391798973, -0.020210569724440575, -0.003860518801957369, 0.013945656828582287, 0.04869087040424347, -0.06781231611967087, -0.028583070263266563, -0.09772748500108719, -0.011865083128213882, -0.012204212136566639, -0.013733654282987118, 0.029537031427025795, -0.05198616907000542, -0.010588888078927994, 0.04515460506081581, -0.01803014613687992, 0.006580116227269173, 2.7645599862762515e-34, 0.011384647339582443, -0.04792261868715286, 0.020884085446596146, 0.019462820142507553, 0.01275855302810669, -0.003580986289307475, 0.04578957334160805, 0.01379567850381136, 0.01934710144996643, -0.06970149278640747, -0.06409130990505219]

['Yangfeng Ji', 'Gholamreza Haffari', 'Jacob Eisenstein']

1603.01913v2

This paper presents a novel latent variable recurrent neural network architecture for jointly modeling sequences of words and (possibly latent) discourse relations between adjacent sentences. A recurrent neural network generates individual words, thus reaping the benefits of discriminatively-trained vector representations. The discourse relations are represented with a latent variable, which can be predicted or marginalized, depending on the task. The resulting model can therefore employ a training objective that includes not only discourse relation classification, but also word prediction. As a result, it outperforms state-of-the-art alternatives for two tasks: implicit discourse relation classification in the Penn Discourse Treebank, and dialog act classification in the Switchboard corpus. Furthermore, by marginalizing over latent discourse relations at test time, we obtain a discourse informed language model, which improves over a strong LSTM baseline.

A Latent Variable Recurrent Neural Network for Discourse Relation Language Models

http://arxiv.org/pdf/1603.01913v2

Title Latent Variable Recurrent Neural Network Discourse Relation Language Models Summary paper present novel latent variable recurrent neural network architecture jointly modeling sequence word possibly latent discourse relation adjacent sentence recurrent neural network generates individual word thus reaping benefit discriminativelytrained vector representation discourse relation represented latent variable predicted marginalized depending task resulting model therefore employ training objective includes discourse relation classification also word prediction result outperforms stateoftheart alternative two task implicit discourse relation classification Penn Discourse Treebank dialog act classification Switchboard corpus Furthermore marginalizing latent discourse relation test time obtain discourse informed language model improves strong LSTM baseline Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.06390361487865448, 0.02962624467909336, 0.0004280621069483459, 0.055127594619989395, -0.02473086304962635, -0.014818601310253143, 0.012562375515699387, -0.007152600213885307, -0.023706721141934395, -0.07547377049922943, 0.010420695878565311, -0.022652819752693176, 0.023212887346744537, 0.028981022536754608, -0.00939810648560524, -0.04173964634537697, 0.007335085887461901, 0.0064222305081784725, 0.05313446745276451, 0.003146494971588254, 0.029746945947408676, 0.026814859360456467, -0.0010553642641752958, 0.02228350192308426, -0.021532170474529266, -0.043559834361076355, 0.00033806273131631315, -0.024830922484397888, -0.017398837953805923, -0.04236561059951782, 0.07568377256393433, 0.048038214445114136, 0.03395381197333336, 0.01930384524166584, 2.004678663070081e-06, -0.01968761906027794, 0.02978329546749592, -0.047518227249383926, 0.02288137376308441, 0.026487741619348526, 0.04317411780357361, 0.022962868213653564, 0.02356608398258686, 0.042665429413318634, -0.039252087473869324, -0.04182374104857445, 0.02529495768249035, 0.1078966036438942, 0.0437910370528698, 0.03788723796606064, -0.009550157934427261, -0.04519807547330856, -0.02207745797932148, -0.025387195870280266, -0.03279504552483559, -0.03746435418725014, 0.040792692452669144, 0.0006588608957827091, -0.03097952902317047, 0.05126199871301651, 0.018811410292983055, 0.0055425167083740234, -0.015764780342578888, -0.04076143354177475, -0.00025483162607997656, 0.028495201840996742, 0.020402222871780396, -0.001831047353334725, 0.015604418702423573, 0.03300412371754646, 0.07571814209222794, -0.02163770981132984, 0.027375368401408195, 0.037112247198820114, -0.015282842330634594, 0.006142333149909973, -0.0020734502468258142, 0.004074665252119303, -0.03530142828822136, 0.020433973520994186, 0.04679861664772034, -0.005598288029432297, 0.008960333652794361, 0.04009517654776573, 0.021030064672231674, 0.005974938161671162, -0.001638932852074504, -0.026415450498461723, -0.02720426209270954, -0.014164510183036327, -0.039897628128528595, -0.08092577755451202, 0.03780260682106018, 0.03430894762277603, -0.025337468832731247, 0.012431538663804531, 0.002933356910943985, -0.0541263148188591, 0.031977806240320206, -0.10841894894838333, 0.037511903792619705, -0.007796281483024359, 0.0056019495241343975, -0.016514532268047333, 0.02710188925266266, 0.06035008653998375, -0.02246699295938015, -0.06220660358667374, -0.014775047078728676, 0.007364843972027302, -0.05821877717971802, -0.0541914664208889, -0.023794502019882202, 0.06503286212682724, -0.04576847329735756, -0.027562109753489494, -0.04498977214097977, 0.005736038088798523, 0.011989963240921497, -0.023545773699879646, 0.027633363381028175, 0.07857668399810791, -0.020891282707452774, 0.02425345964729786, -0.03812388703227043, 0.012229926884174347, -0.03954312577843666, 0.03697735443711281, -0.029236674308776855, 0.005522106308490038, 0.010275601409375668, 0.048216722905635834, 0.008238738402724266, 0.0215508621186018, -0.04198222607374191, 0.04937554895877838, 0.01018951553851366, -0.004925020504742861, -0.02506435103714466, -0.0039661843329668045, -0.029588742181658745, -0.02801653742790222, -0.01039395947009325, -0.052619777619838715, -0.03459008038043976, -0.0279323011636734, -0.04168924689292908, -0.017088333144783974, 0.04349331185221672, 0.05082947388291359, -0.018317848443984985, 0.06858982145786285, 0.025294117629528046, -0.017383551225066185, 0.08055416494607925, 0.02257576957345009, 0.06914839893579483, 0.020026378333568573, 0.05013201758265495, -0.0094301113858819, 0.002575409598648548, 0.001814907300285995, -0.006310774479061365, -0.014752466231584549, -0.0050482978112995625, -0.06671962887048721, -0.004422440659254789, 0.016093501821160316, -0.00831848569214344, 0.059845902025699615, 0.010838980786502361, 0.05242912843823433, -0.0006080068415030837, -0.060444895178079605, 0.032380808144807816, 0.07260970026254654, -0.03502701222896576, 0.04782290756702423, 0.03867361322045326, 0.055968400090932846, 0.005287524312734604, 0.019942641258239746, 0.019798455759882927, -0.008856445550918579, 0.012571807950735092, -0.031094487756490707, -0.010277023538947105, -0.014703536406159401, -0.017009619623422623, -0.04734642803668976, -0.011197145096957684, -0.004961605649441481, 0.01597258821129799, -0.059436749666929245, 0.031109489500522614, 0.016142798587679863, -0.05574139952659607, 0.03940734639763832, 0.03859269991517067, -0.022917840629816055, -0.03799382597208023, -0.010520407930016518, 0.024224594235420227, -0.0029768578242510557, 0.010324354283511639, -0.007469621486961842, -0.02992919087409973, -0.034927137196063995, 0.0523952916264534, 0.0633893832564354, 0.008646759204566479, -0.012762908823788166, -0.018902890384197235, -0.03366156294941902, 0.010416196659207344, -0.040877871215343475, 0.015632152557373047, 0.07686831802129745, -0.02337687462568283, -0.010284094139933586, 0.009387942962348461, 0.07563354074954987, 0.006546481978148222, 0.01866876892745495, -0.024120589718222618, -0.017769740894436836, 0.04228464514017105, -0.010260703042149544, 0.04917386919260025, 0.027693085372447968, 0.0026574910152703524, 0.003984022419899702, 0.04129551351070404, -0.022408125922083855, -0.023216620087623596, 0.0026386494282633066, -0.06945711374282837, -0.00529824011027813, 0.015420978888869286, -0.031886208802461624, 0.008871248923242092, 0.0012846756726503372, -0.023581083863973618, -0.030866947025060654, 0.08288279175758362, -0.04795842245221138, 0.003611353924497962, -0.056438181549310684, -0.01379701029509306, 0.009472557343542576, 0.01713275909423828, 0.00046707040746696293, 0.04362974315881729, -0.01879872940480709, 0.0037871678359806538, 0.02635268121957779, 0.004871071316301823, 0.03623335808515549, -0.010777212679386139, 0.007750544231384993, -0.004672996234148741, 0.014413203112781048, 0.0003033879620488733, 0.027578862383961678, 0.0062506357207894325, -0.009260514751076698, -0.03769354894757271, -0.12119646370410919, 0.007848188281059265, -0.011618757620453835, 0.01333510223776102, -0.002638334408402443, -0.02991735376417637, 0.01909559778869152, -0.013343852944672108, -0.024267379194498062, 0.006865738891065121, 0.011839409358799458, -0.013139331713318825, 0.0892597883939743, 0.00879879854619503, 0.03065742552280426, -0.03756321594119072, 0.017118491232395172, -0.019134093075990677, 0.05960998684167862, 0.038287203758955, -0.036311980336904526, -0.020533591508865356, 0.005343687254935503, -0.024540646001696587, 0.03532325103878975, -0.022216828539967537, -0.07238908112049103, 0.015098164789378643, 0.02481718175113201, 0.07409872859716415, 0.014992909505963326, 0.071269191801548, 0.0591927208006382, -0.0017051838804036379, -0.04627157375216484, -0.014239282347261906, 0.024699682369828224, -0.021171055734157562, 0.034608203917741776, -0.010059193708002567, 0.01823561079800129, -0.044179774820804596, 0.07517109811306, 0.028253594413399696, 0.007009865250438452, -0.020376471802592278, 0.0753251239657402, 0.010737827979028225, -0.004272363148629665, 0.021451415494084358, -0.05018310248851776, -0.029615065082907677, -0.013167859986424446, -0.029453089460730553, 0.013501571491360664, 0.02855842001736164, -0.022110924124717712, 0.008955448865890503, -0.06406824290752411, -0.038501523435115814, -0.024602478370070457, 0.048124369233846664, 0.009188899770379066, -0.024340903386473656, 0.02624785155057907, -0.045901983976364136, -0.007144671864807606, -0.027167847380042076, 0.0038527101278305054, -0.03088267333805561, 0.044725336134433746, -0.05331491678953171, 0.0028868047520518303, -0.007879202254116535, -0.03840978071093559, -0.025099916383624077, -0.029242148622870445, 0.004923120141029358, -0.009073189459741116, -0.0287688747048378, -0.02979501336812973, -0.003881750861182809, 0.009202591143548489, -0.014120250940322876, 0.010205338709056377, -0.03235280513763428, 0.02338719181716442, -0.024395044893026352, 0.06897532939910889, 0.041848327964544296, 0.004789057653397322, -0.04253799840807915, 0.011709646321833134, 0.015379024669528008, 0.03801259398460388, -0.07451637834310532, 0.00700270663946867, -0.06741271913051605, -0.015119224786758423, -0.023884298279881477, -0.03791932761669159, -0.0469299741089344, -0.005223628133535385, 0.009193703532218933, -0.07654381543397903, -0.015410390682518482, 0.11604850739240646, -0.010664906352758408, -0.030853360891342163, -0.020443782210350037, -0.03606894984841347, -0.003856152296066284, 0.02675805799663067, 0.018061473965644836, -0.04839923232793808, 0.012767855077981949, -0.031492095440626144, -0.02500254474580288, -0.027786901220679283, -0.06917667388916016, -0.021520551294088364, -0.0578799694776535, -0.007622038945555687, -0.04199538379907608, -0.0009385336306877434, -0.0014296669978648424, -0.031231965869665146, -0.025557909160852432, 0.02859836257994175, 0.01013498567044735, -0.011870453134179115, -0.018819201737642288, -0.010447138920426369, 0.04505525901913643, -0.0531158521771431, 0.011835931800305843, 0.013851813040673733, -0.024123037233948708, 0.04140152782201767, -0.008634918369352818, 0.10127038508653641, -0.03447214886546135, 0.03455553576350212, 0.017390111461281776, -0.06607665121555328, -0.020841289311647415, -0.013520713895559311, 0.04456512629985809, -0.01602521724998951, 3.6950303183402866e-05, -0.021780282258987427, 0.021077655255794525, -0.01013349462300539, 0.004383385647088289, 0.029049312695860863, 0.0318785235285759, -0.022562164813280106, -0.038570139557123184, -0.03299078345298767, 0.07127656042575836, 0.023891620337963104, 0.03297197446227074, 0.04206221178174019, -0.014575246721506119, -0.060466963797807693, -0.021624771878123283, 0.013999265618622303, -0.015962567180395126, 0.009670895524322987, -0.07421643286943436, 0.04259562864899635, -0.017956847324967384, -0.0882306918501854, -0.09123940765857697, -0.027535969391465187, -0.011477071791887283, 0.012980001047253609, 0.06120573356747627, 0.020813781768083572, -0.024351807311177254, -0.06016761064529419, -0.029276125133037567, 0.03768271952867508, -0.01523854024708271, -0.011866984888911247, -0.006707719061523676, 0.08357485383749008, -0.022947097197175026, -0.033976346254348755, -0.05795089527964592, -0.047914568334817886, -0.062234342098236084, 0.0017693586414679885, 0.01635083742439747, 0.008290168829262257, 0.06266111135482788, -0.03367438539862633, -0.03949498012661934, 0.04666665196418762, 0.005715677049010992, -0.0435127392411232, 0.013087919913232327, 0.05203736200928688, 0.05950009077787399, 0.01666250266134739, 0.008733103983104229, 0.017130713909864426, 0.05905326455831528, -0.020541612058877945, -0.02583535574376583, -0.054178137332201004, -0.057885363698005676, -0.035159721970558167, -0.05684744194149971, 0.03996956720948219, 0.04866660758852959, 0.023155974224209785, -0.06462276726961136, 0.02060251496732235, -0.03938876837491989, -0.029000330716371536, -0.0348479226231575, 0.03036360628902912, 0.01732276938855648, 0.0014020432718098164, -0.04829725995659828, -0.07584719359874725, -0.015032474882900715, 0.05083698034286499, 0.009419208392500877, 0.05577683076262474, 0.035396672785282135, 0.05087045207619667, -0.0436827689409256, -0.004858016036450863, -0.02259691432118416, -0.0020712276455014944, 0.0016483402578160167, 0.0408187136054039, -0.02349219098687172, 0.07898273319005966, 0.004796857479959726, -0.0019622468389570713, 0.03518614172935486, 0.015300966799259186, -0.01768241822719574, 0.05348337069153786, -0.03423524647951126, 0.022496670484542847, 0.027618633583188057, -0.041458550840616226, 0.028096873313188553, 0.007104598917067051, 0.020864857360720634, -0.014223463833332062, 0.08530533313751221, -0.023610329255461693, -0.021298488602042198, 0.04774607717990875, 0.006248330231755972, -0.026247937232255936, 0.027623744681477547, 0.05440494790673256, 0.03497782349586487, 0.022203661501407623, 0.09219218790531158, -0.01595381274819374, -0.03728041797876358, -0.051088303327560425, 2.0010429579997435e-05, 0.0011696352157741785, 0.0047793942503631115, 0.05713622644543648, 0.0007187050068750978, -0.0075302934274077415, 0.07943173497915268, -0.011935750022530556, 0.03472251817584038, -0.004332056734710932, 0.026513108983635902, 0.04464956745505333, 0.04259735718369484, -0.012064430862665176, -0.06172556057572365, -0.01044796034693718, 0.014376244507730007, -0.036342933773994446, -0.07652482390403748, -6.011241541867075e-33, -0.077707938849926, -0.05388582870364189, 0.02129373326897621, 0.05805860459804535, -0.03128204494714737, 0.018887432292103767, -0.07401872426271439, -0.019271640107035637, -0.009276239201426506, 0.05635697394609451, -0.008641653694212437, 0.03015715256333351, 0.005665701348334551, 0.02717037871479988, 0.03452266752719879, -0.029399430379271507, 0.03551843762397766, -0.015294046141207218, 0.024871237576007843, 0.02164383977651596, 0.043933216482400894, 0.04357535392045975, 0.06593397259712219, -0.07016182690858841, 0.005613693036139011, -0.026316799223423004, 0.02157529443502426, 0.025309981778264046, 0.002551825949922204, 0.046311113983392715, -0.03653838858008385, 0.02203911542892456, 0.033701878041028976, 0.00935592595487833, 0.014721078798174858, 0.06411092728376389, -0.08481169492006302, -0.08296878635883331, 0.015706457197666168, -0.021115751937031746, -0.02132038027048111, -0.02238532155752182, 0.011666632257401943, 0.02850019931793213, 0.007794769946485758, 0.02767878584563732, 0.06933149695396423, -0.003878186456859112, 0.000886817870195955, -0.03173651546239853, -0.045719269663095474, 0.01827053539454937, -0.0052416762337088585, 0.02367076463997364, 0.020093392580747604, 0.0032563386484980583, 0.010885024443268776, -0.010787665843963623, -0.06041572242975235, -0.015303158201277256, -0.059884849935770035, 0.027316085994243622, -0.02776002511382103, 0.0017165839672088623, -0.007127446122467518, 0.05930803716182709, -0.0198826901614666, -0.007445963099598885, -0.08236164599657059, 0.022501176223158836, -0.020076943561434746, -0.014969760552048683, 0.02893095649778843, -0.0014580526622012258, 0.000989946536719799, -0.014394163154065609, -0.06648893654346466, -0.02343318983912468, 0.03428303822875023, 0.06901533156633377, 0.03042864426970482, -0.055121760815382004, 0.0024019910488277674, -0.026519713923335075, -0.017544014379382133, -0.03810872137546539, -0.030169498175382614, -0.04931148141622543, 0.010839918628334999, -0.034591592848300934, 0.015228161588311195, -0.00807724054902792, -0.024081358686089516, -0.01504580955952406, -0.017322154715657234, 0.03423049673438072, 0.017037823796272278, -0.03011801466345787, 0.025058424100279808, 0.03022455982863903, -0.05334408953785896, -0.007321425247937441, -0.0019212141633033752, 0.028686294332146645, 0.005417197477072477, -0.0022885077632963657, -0.005224487744271755, -0.02814977616071701, -0.03619929030537605, -0.02325684204697609, -0.007685244549065828, -0.005718120373785496, -0.03537726029753685, 0.08196931332349777, -0.02638496458530426, 0.018470266833901405, -0.00045794970355927944, 0.07401411980390549, 0.011263992637395859, -0.006638742983341217, -0.043930284678936005, -0.027159810066223145, 0.005251671187579632, 0.024224678054451942, -0.02857566438615322, 0.0013921877834945917, -0.02213527262210846, 0.04575061425566673, -0.00639901589602232, -0.03122391551733017, 0.004145095590502024, 0.014973933808505535, 2.515301105177059e-07, 0.004446635488420725, 0.05550794675946236, 0.04805869236588478, -0.017419788986444473, 0.02254682034254074, 0.006348894443362951, 0.012764840386807919, 0.06442656368017197, 0.01262985821813345, -0.027774179354310036, 0.003346027573570609, 0.013553362339735031, 0.013360857032239437, 0.013380746357142925, -0.10601262748241425, -0.03970520943403244, -0.12297279387712479, -0.02031206153333187, -0.028362348675727844, -0.007146773859858513, 0.08349781483411789, 0.06997483223676682, 0.04513333737850189, 0.008082830347120762, -0.02937779575586319, 0.013136070221662521, 0.020125703886151314, -0.019381379708647728, -0.01984846033155918, 0.019986793398857117, 0.022677253931760788, -0.008205596357584, -0.011446050368249416, 0.007740642409771681, -0.0071916766464710236, 0.04770487919449806, -0.02755563147366047, 0.04763286933302879, 0.005060947500169277, -0.03653044253587723, -0.00998608861118555, 0.0040099709294736385, 0.0024795406498014927, 0.007241183426231146, 0.030059831216931343, -0.039185766130685806, -0.04926731064915657, -0.02493302710354328, -0.01192206796258688, -0.0020791050046682358, 0.04256313666701317, 0.01648232713341713, -0.0068132104352116585, -0.01243108231574297, 0.0008860877715051174, -0.03354048728942871, 0.012536317110061646, -0.07823976874351501, 0.028154676780104637, -0.0038144385907799006, -0.047355812042951584, 0.039329130202531815, -0.00702378386631608, -0.005199609324336052, 0.03631683811545372, -0.009790540672838688, 0.028496691957116127, 2.2041120600417726e-34, 0.042882151901721954, -0.04258739948272705, -0.03428058698773384, 0.023823155090212822, 0.04204699397087097, 0.013847628608345985, 0.022360561415553093, 0.003602215787395835, 0.03501645848155022, -0.05265423655509949, -0.001365459873341024]

['Zhiyuan Tang', 'Lantian Li', 'Dong Wang']

1603.09643v4

Although highly correlated, speech and speaker recognition have been regarded as two independent tasks and studied by two communities. This is certainly not the way that people behave: we decipher both speech content and speaker traits at the same time. This paper presents a unified model to perform speech and speaker recognition simultaneously and altogether. The model is based on a unified neural network where the output of one task is fed to the input of the other, leading to a multi-task recurrent network. Experiments show that the joint model outperforms the task-specific models on both the two tasks.

Multi-task Recurrent Model for Speech and Speaker Recognition

http://arxiv.org/pdf/1603.09643v4

Title Multitask Recurrent Model Speech Speaker Recognition Summary Although highly correlated speech speaker recognition regarded two independent task studied two community certainly way people behave decipher speech content speaker trait time paper present unified model perform speech speaker recognition simultaneously altogether model based unified neural network output one task fed input leading multitask recurrent network Experiments show joint model outperforms taskspecific model two task Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.018811749294400215, 0.028306886553764343, -7.840494072297588e-05, 0.04581144079566002, -0.023841267451643944, 0.01702040806412697, 0.04916604980826378, -0.04716957360506058, -0.017879294231534004, -0.0043065547943115234, -0.07053326070308685, -0.05154119059443474, 0.05155247077345848, -0.006731683854013681, 0.0012477351119741797, -0.03943261876702309, 0.015395193360745907, 0.004475318361073732, 0.009077822789549828, -0.0072902487590909, 0.006542196497321129, -0.003709180047735572, -0.01698973961174488, 0.01310637779533863, 0.00022634249762631953, 0.006314821075648069, 0.016430620104074478, -0.007629061117768288, 0.02093709632754326, 0.014861643314361572, 0.02329653687775135, 0.018022336065769196, 0.0017889135051518679, 0.05180077627301216, 2.1532721348194173e-06, -0.015720758587121964, -0.0026225608307868242, -0.03751635551452637, -0.007533836644142866, -0.0661383867263794, 0.02593422867357731, 0.07138051837682724, 0.002113024704158306, 0.044993650168180466, -0.022553887218236923, 0.02027883380651474, 0.015309229493141174, 0.083465076982975, 0.018009833991527557, 0.01850265823304653, 1.889986015157774e-05, -0.04332365468144417, 0.0029420487117022276, -0.016302645206451416, -0.012293185107409954, -0.024247534573078156, 0.033234186470508575, -0.02400144375860691, -0.008247995749115944, -0.04377908632159233, 0.001721539767459035, 0.022032693028450012, -0.01777034066617489, 0.0327480211853981, 0.007312871981412172, 0.012077892199158669, -0.003822418162599206, -0.03874120116233826, -0.0016266910824924707, 0.0708809420466423, -0.03272860869765282, 0.007171341683715582, 0.06910555809736252, 0.04272531718015671, -0.05271761119365692, 0.006417324300855398, -0.023854974657297134, -0.015004860237240791, -0.03673074394464493, -0.02693815343081951, -0.01438081730157137, 0.021398834884166718, 0.03763280436396599, -0.009079220704734325, -0.03324638307094574, 0.027515148743987083, -0.03143990784883499, -0.022343341261148453, 0.02197861857712269, -0.031700603663921356, 0.014039643108844757, -0.04072796180844307, 0.051386862993240356, 0.03167188912630081, -0.034806571900844574, -0.024572579190135002, -0.020181279629468918, -0.1172427386045456, -0.025172626599669456, -0.04941845312714577, 0.03683978691697121, 0.025618163868784904, -0.028889916837215424, 0.014652826823294163, 0.003971877042204142, 0.0440279021859169, -0.015390215441584587, -0.0017149434424936771, -0.00020298073650337756, -0.012806768529117107, -0.07018923759460449, 0.006890900898724794, -0.005489449482411146, 0.050408314913511276, 0.03672942891716957, -0.010784119367599487, -0.05341874435544014, 0.023131081834435463, -0.06096014007925987, -0.012113738805055618, 0.02801152691245079, 0.01571941375732422, -0.04151888191699982, 0.020024454221129417, 0.025722570717334747, 0.056074101477861404, 0.006667783483862877, 0.05385459214448929, -0.030143264681100845, -0.03902972489595413, 0.0084213363006711, 0.03386709466576576, 0.04178048297762871, 0.013580950908362865, 0.012751596979796886, 0.027393357828259468, 0.04667900130152702, -0.007090288680046797, -0.022839482873678207, -0.005173730198293924, -0.03635115921497345, -0.06180397421121597, 0.004060768987983465, -0.06966596841812134, 0.05024025961756706, 0.0002224398631369695, -0.003978780936449766, 0.004749261308461428, -0.004263779614120722, -0.022232213988900185, -0.007652375381439924, 0.07240119576454163, 0.05504041910171509, 0.026615085080266, 0.09298234432935715, -0.011401569470763206, 0.0006858527776785195, 0.020272940397262573, 0.046380653977394104, -0.0071486542001366615, -0.025146884843707085, -0.01693957857787609, 0.0202822033315897, 0.04779507964849472, -0.04714958369731903, -0.0681077092885971, 0.01722053810954094, -0.03639188036322594, 0.028898289427161217, 0.025828080251812935, 0.01709614507853985, 0.02154359221458435, -0.013027658686041832, 0.0025572525337338448, 0.03582843765616417, 0.04662302881479263, 0.03969710320234299, 0.009933565743267536, 0.021574530750513077, 0.01416101772338152, -0.0115653770044446, 0.023015979677438736, -0.013584612868726254, 0.017118429765105247, 0.0017475365893915296, -0.0221830066293478, -0.011916585266590118, 0.021701592952013016, -0.032759297639131546, 0.003742900677025318, 0.029342593625187874, -0.06241092458367348, 0.015355476178228855, 0.015545220114290714, 0.05392160639166832, -0.012102835811674595, -0.029136035591363907, -0.011476986110210419, 0.023973578587174416, -0.013983876444399357, 0.0016530423890799284, -0.0328826941549778, -0.007261814083904028, 0.024203864857554436, -0.02063770592212677, -0.021790605038404465, 0.02063252590596676, -0.053817491978406906, 0.011966302059590816, -0.034372780472040176, -0.03406748175621033, 0.0007154941558837891, 0.06381843239068985, -0.04369940236210823, -0.01312266755849123, 0.028204653412103653, -0.011915692128241062, 0.04704838618636131, -0.04842054471373558, 0.0019437220180407166, 0.038029205054044724, 0.061940696090459824, 0.0069166263565421104, -0.004434968810528517, -0.04577670991420746, 0.004622252658009529, 0.017744703218340874, 0.023327987641096115, 0.07012217491865158, 0.02477920986711979, -0.01963842660188675, -0.014252115972340107, 0.0306827574968338, -0.033722057938575745, 0.005908846855163574, 0.04625896364450455, -0.034667059779167175, -0.0195339135825634, 0.03792349994182587, -0.013930181041359901, 0.009720507077872753, 0.10533754527568817, 0.025083675980567932, -0.09868252277374268, 0.04843953996896744, -0.022399943321943283, 0.010985421016812325, -0.019122596830129623, 0.010504637844860554, 0.020517617464065552, 0.04619988799095154, 0.019395289942622185, 0.013711648061871529, 0.019069112837314606, -0.0005393600440584123, 0.013268896378576756, -0.023978983983397484, 0.008042036555707455, -0.0995517373085022, -0.04299156740307808, -0.0035679214634001255, -0.0021509204525500536, -0.012161334045231342, -0.056335411965847015, 0.007373217027634382, -0.008306660689413548, -0.07233355194330215, -0.08627988398075104, -0.0014422312378883362, -0.03721436858177185, -0.004424355924129486, -0.021382393315434456, 0.012520457617938519, 0.02300911769270897, -0.04609442502260208, -0.010132747702300549, 0.014127785339951515, 0.024195995181798935, 0.007715923711657524, -0.003114980412647128, 0.02318359538912773, -0.02221391722559929, -0.014167262241244316, -0.02705458737909794, -0.00779750244691968, -0.006581316702067852, 0.029349304735660553, -0.09314757585525513, 0.0010661176638677716, -0.0021435702219605446, 0.01984747312963009, 0.03370729088783264, 0.007536500226706266, 0.04954422265291214, -0.02381335385143757, 0.025797223672270775, 0.06982303410768509, 0.03137002885341644, 0.0023126646410673857, -0.007773182354867458, -0.034478023648262024, -0.016695097088813782, 0.002890977542847395, 0.014773521572351456, 0.011584277264773846, 0.05121122673153877, -0.0023974261712282896, 0.014976453967392445, -0.03418359532952309, 0.03622041270136833, 0.020409738644957542, 0.02564583718776703, 0.017310576513409615, -0.011385978199541569, -0.030414078384637833, -0.05076180770993233, -0.025078998878598213, -0.056997012346982956, -0.037208616733551025, -0.01110925991088152, -0.01220231968909502, -0.002339843427762389, 0.008807978592813015, -0.02349984273314476, -0.016311224550008774, -0.006583474576473236, -0.04306235536932945, -0.012018641456961632, 0.011924193240702152, 0.004051965661346912, -0.00015054210962262005, 0.0042693219147622585, -0.07232636958360672, -0.03048102930188179, 0.01694977469742298, -0.01252997200936079, -0.054298676550388336, 0.01763194426894188, -0.0057273199781775475, -0.004303663969039917, -0.027172263711690903, -0.051707424223423004, -0.03194846957921982, 0.020706230774521828, -0.045558568090200424, 0.003898927243426442, -0.032462313771247864, -0.026192709803581238, -0.014909700490534306, 0.01952660270035267, 0.04752683266997337, -0.016088509932160378, -0.018709808588027954, 0.01767432689666748, -0.014621786773204803, 0.08487782627344131, 0.03872304782271385, 0.07007778435945511, -0.0708148181438446, -0.015548838302493095, -0.021529939025640488, -0.036460019648075104, 0.05126262083649635, 0.030348021537065506, -0.057393599301576614, -0.0402943417429924, 0.015655018389225006, -0.0051077185198664665, -0.0638410747051239, 0.025339093059301376, 0.020107276737689972, -0.039792727679014206, 0.03756863251328468, 0.09869614988565445, -0.0359211266040802, -0.040092069655656815, -0.06012406200170517, -0.02905469387769699, -0.05091188848018646, 0.02007952705025673, 0.0189093928784132, -0.006366748362779617, -0.01922289840877056, 0.0350196547806263, 0.01133766956627369, 0.03904047980904579, -0.03757454454898834, -0.016575487330555916, -0.03569234162569046, 0.02396477945148945, 0.011696775443851948, -0.03694937378168106, -0.011621433310210705, -0.04316916689276695, -0.015920884907245636, -0.04829411581158638, 0.04975266009569168, 0.0016775227850303054, 0.011484178714454174, -0.03789448365569115, 0.05006451904773712, -0.0888182520866394, -0.007299110759049654, 0.07517892122268677, -0.056854356080293655, 0.0596865750849247, 0.060044728219509125, 0.0676008015871048, -0.04522461071610451, -0.05198858305811882, -0.018350772559642792, 0.002515227999538183, 0.03493519127368927, -0.02371497079730034, 0.0037994487211108208, -0.010091815143823624, -0.028266331180930138, -0.015504753217101097, 0.03707090765237808, -0.039006557315588, 0.03821706399321556, 0.017232248559594154, 0.05870644748210907, -0.024750176817178726, -0.0102661969140172, -0.017682228237390518, 0.018986713141202927, 0.060969796031713486, 0.04088590666651726, 0.0038267041090875864, -0.04557216539978981, -0.035178396850824356, 0.04770451784133911, 0.008759042248129845, -0.02610687166452408, -0.00721793994307518, -0.018100494518876076, 0.032438162714242935, -0.03105013258755207, -0.036662351340055466, -0.03060857579112053, -0.010970890522003174, 0.0220292080193758, 0.05094710364937782, 0.04903724417090416, 0.03143677860498428, 0.029182976111769676, -0.036287128925323486, 0.012336901389062405, -0.009912557899951935, 0.07213538140058517, -0.057357821613550186, 0.0015323625411838293, 0.02815670147538185, -0.05112401023507118, -0.01753915846347809, 0.009560760110616684, -0.13744668662548065, -0.015789400786161423, 0.022761186584830284, -0.03156866505742073, 0.01954902894794941, 0.07462023943662643, -0.056909773498773575, -0.05782223492860794, -0.009976192377507687, -0.04467711225152016, -0.019985496997833252, 0.042072050273418427, 0.08185788244009018, 0.010815997608006, -0.039225269109010696, 0.0021130330860614777, -0.03439055755734444, 0.05039328709244728, -0.007924288511276245, -0.05108671262860298, -0.05011634901165962, -0.05994059890508652, -0.0406157448887825, 0.00402094004675746, 0.05822806805372238, 0.01691747084259987, 0.03525536507368088, -0.0677444189786911, 0.0018250750144943595, 0.05594446137547493, 0.055966172367334366, -0.018775170668959618, 0.0021617277525365353, 0.04200441390275955, 0.021002519875764847, 0.011325348168611526, -0.02772531844675541, 0.019987016916275024, -0.034243833273649216, -0.01647198759019375, 0.03387731686234474, -0.02476534992456436, -0.007103301119059324, -0.01756291836500168, 0.008682159706950188, -0.021271467208862305, 0.028302134945988655, 0.07544403523206711, 0.01474851369857788, 0.0210000891238451, 0.022124364972114563, -0.025851409882307053, -0.01053033396601677, 0.010692807845771313, 0.017583727836608887, -0.012757708318531513, -0.02568179741501808, -0.03609701618552208, -0.0015701667871326208, 0.03179994598031044, -0.0014275886351242661, 0.009461257606744766, 0.027697311714291573, 0.049498300999403, -0.07576727122068405, 0.04190872237086296, -0.03543698042631149, 0.025055646896362305, 0.03462322801351547, -0.0075516668148338795, -0.0177910253405571, 0.03488469496369362, 0.07537685334682465, 0.0073996651917696, -0.012881264090538025, -0.01196654886007309, 0.020390721037983894, -0.05110444128513336, -0.044245798140764236, -0.010536154732108116, 0.01216184627264738, -0.04143739864230156, -0.02631094679236412, 0.012811041437089443, -0.013289197348058224, 0.08283358812332153, -0.040514107793569565, 0.04584573954343796, -0.009916587732732296, 0.012606792151927948, -0.015407565049827099, -0.03343455120921135, 0.049063242971897125, -0.005783911794424057, -0.053587719798088074, 0.028208352625370026, -0.014156411401927471, 0.02452518790960312, -6.1441017908687644e-33, -0.016031332314014435, 0.023980826139450073, -0.014119918458163738, 0.009145001880824566, -0.03334162011742592, -0.023489343002438545, -0.020621228963136673, 0.012596177868545055, -0.016147272661328316, -0.05234581232070923, -0.028161361813545227, 0.018310310319066048, 0.040856532752513885, 0.008454365655779839, 0.02519717440009117, -0.01829502172768116, 0.08306381851434708, -0.005154627375304699, 0.07135530561208725, 0.020311547443270683, 0.06610532104969025, 0.06461753696203232, 0.039993032813072205, -0.09473668783903122, -0.00879159290343523, -0.021884718909859657, 0.008229528553783894, -0.03661062940955162, -0.004212942905724049, 0.004037901759147644, -0.025609076023101807, 0.030915632843971252, 0.0234250258654356, -0.04791642725467682, -0.026361597701907158, 0.09034387767314911, -0.09646084904670715, -0.01547938585281372, -0.05882059410214424, 0.03422054648399353, -0.06218285486102104, 0.0007477123290300369, 0.06529373675584793, 0.030192071571946144, -0.0014812365407124162, 0.007233642041683197, 0.07944749295711517, -0.02410873770713806, -0.014449804089963436, -0.009811569936573505, 0.0021957841236144304, -0.0013165337732061744, -0.008876044303178787, -0.0013911460991948843, 0.03814497962594032, 0.06061655282974243, -0.026694372296333313, -0.014649266377091408, -0.11393141746520996, 0.031064605340361595, -0.024723246693611145, 0.0008394840406253934, 0.023338574916124344, 0.08033066987991333, 0.01609552837908268, 0.03224075585603714, 0.022266831248998642, -0.012575389817357063, -0.0040598842315375805, -0.04593738913536072, -0.0032398041803389788, 0.0571758933365345, 0.016105685383081436, 0.009409863501787186, 0.016920192167162895, -0.05498560890555382, -0.0693138912320137, 0.012889623641967773, 0.056042514741420746, 0.003937972709536552, 0.023727672174572945, -0.0032689974177628756, -0.03603501617908478, 0.009384775534272194, 0.0013586137210950255, 0.005133539903908968, -0.024488842114806175, -0.009857269935309887, 0.02603730373084545, -0.001466193119995296, 0.025589236989617348, -0.012604353949427605, 0.03694919869303703, -0.07020585238933563, 0.023813487961888313, -0.02084621973335743, -0.0031812014058232307, -0.0051974765956401825, 0.008736466988921165, 0.008925150148570538, -0.04998369514942169, -0.039417676627635956, 0.03977318853139877, 0.0755850076675415, 0.007044995669275522, -0.001967269228771329, 0.035600341856479645, 0.0300485510379076, -0.016052041202783585, -0.03258335962891579, 0.0012483566533774137, 0.020500516518950462, 0.01927998661994934, 0.08025697618722916, 0.04808958247303963, -0.023118743672966957, -0.011019331403076649, 0.019404632970690727, 0.01669502444565296, -0.03228563815355301, -0.01626960188150406, -0.01190157700330019, 0.03473067656159401, -0.0018733859760686755, -0.051970578730106354, -0.009892493486404419, -0.010927495546638966, -0.009631641209125519, 0.036267682909965515, -0.017621710896492004, 0.002825316274538636, 0.005694547668099403, 2.874662925478333e-07, -0.0670817419886589, -0.007987579330801964, 0.020846741273999214, -0.06317771226167679, 0.04445037990808487, 0.002670042682439089, -0.017768030986189842, 0.03761846572160721, -0.0015991118270903826, -0.006398554425686598, 0.01705191098153591, -0.017246544361114502, 0.06782381981611252, -0.004427262116223574, -0.10549710690975189, -0.04480264335870743, -0.08191723376512527, 0.06339003145694733, -0.02620384655892849, 0.03765234351158142, 0.013607414439320564, 0.08470986038446426, 0.0323219932615757, -0.029149934649467468, 0.0034514525905251503, -0.019551457837224007, 0.03993155434727669, -0.020575739443302155, 0.04462183266878128, -0.03195096179842949, 0.03475380688905716, 0.0017283614724874496, -0.021476304158568382, 0.04072418436408043, -0.02277248352766037, 0.048317573964595795, 0.040696002542972565, 0.04346639662981033, -0.017110655084252357, -0.00482205580919981, -0.017594482749700546, 0.04559047147631645, -0.0056870924308896065, 0.008948057889938354, 0.05289873853325844, -0.03350327908992767, -0.062168508768081665, -0.025297515094280243, 0.030575446784496307, 0.004695413634181023, 0.022606708109378815, 0.04117944836616516, 0.04791687801480293, -0.016967544332146645, -0.018020430579781532, -0.019085010513663292, -0.011787417344748974, -0.052487779408693314, 0.011301180347800255, 0.02057085558772087, -0.08917435258626938, -0.022920023649930954, 0.012210055254399776, -0.0654972493648529, 0.07361093908548355, -0.04924054443836212, 0.007704563904553652, 1.7859500337515283e-34, -0.016381332650780678, 0.014486964792013168, 0.004956788383424282, 0.016066424548625946, -0.023825757205486298, -0.04157130420207977, -0.09734394401311874, 0.00948890671133995, 0.034470491111278534, -0.036845721304416656, -0.03747756406664848]

['Sarath Chandar', 'Sungjin Ahn', 'Hugo Larochelle', 'Pascal Vincent', 'Gerald Tesauro', 'Yoshua Bengio']

1605.07427v1

Memory networks are neural networks with an explicit memory component that can be both read and written to by the network. The memory is often addressed in a soft way using a softmax function, making end-to-end training with backpropagation possible. However, this is not computationally scalable for applications which require the network to read from extremely large memories. On the other hand, it is well known that hard attention mechanisms based on reinforcement learning are challenging to train successfully. In this paper, we explore a form of hierarchical memory network, which can be considered as a hybrid between hard and soft attention memory networks. The memory is organized in a hierarchical structure such that reading from it is done with less computation than soft attention over a flat memory, while also being easier to train than hard attention over a flat memory. Specifically, we propose to incorporate Maximum Inner Product Search (MIPS) in the training and inference procedures for our hierarchical memory network. We explore the use of various state-of-the art approximate MIPS techniques and report results on SimpleQuestions, a challenging large scale factoid question answering task.

Hierarchical Memory Networks

http://arxiv.org/pdf/1605.07427v1

Title Hierarchical Memory Networks Summary Memory network neural network explicit memory component read written network memory often addressed soft way using softmax function making endtoend training backpropagation possible However computationally scalable application require network read extremely large memory hand well known hard attention mechanism based reinforcement learning challenging train successfully paper explore form hierarchical memory network considered hybrid hard soft attention memory network memory organized hierarchical structure reading done le computation soft attention flat memory also easier train hard attention flat memory Specifically propose incorporate Maximum Inner Product Search MIPS training inference procedure hierarchical memory network explore use various stateofthe art approximate MIPS technique report result SimpleQuestions challenging large scale factoid question answering task Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.008692226372659206, 0.014331907965242863, -0.02022092044353485, 0.03938573971390724, 0.021290449425578117, 0.004444582387804985, 0.00995647069066763, -0.019644591957330704, -0.015351303853094578, -0.05517832189798355, -0.03843724727630615, -0.0025149635039269924, -0.006596947554498911, 0.020143985748291016, 0.030484670773148537, -0.09159400314092636, 0.03349696472287178, -0.013278252445161343, 0.0052095940336585045, 0.007149407174438238, 0.01706698164343834, -0.021349556744098663, 0.006632583681493998, 0.022025668993592262, -0.0267124492675066, -0.03185821697115898, -0.04460544511675835, 0.020081575959920883, 0.02777860127389431, -0.07232573628425598, 0.045330047607421875, 0.005985500290989876, 0.05020814761519432, 0.04565461352467537, 2.3964830688782968e-06, -0.006867050658911467, -0.010544756427407265, -0.027754027396440506, 0.029082590714097023, 0.008783026598393917, 0.014773830771446228, -0.018308617174625397, -0.011140458285808563, 0.00887638796120882, -0.0228955689817667, -0.005414103157818317, 0.03276590257883072, 0.037651125341653824, 0.038011547178030014, 0.05757061764597893, 0.0029820995405316353, -0.08205527067184448, 0.049788642674684525, -0.007824378088116646, 0.03292609751224518, -0.05246346443891525, 0.022387463599443436, 0.014872328378260136, -0.026936642825603485, -0.0016161776147782803, 0.015731750056147575, 0.012562909163534641, 0.030300557613372803, 0.0302366204559803, 0.04392054304480553, 0.03650661185383797, 0.026015087962150574, 0.02362409420311451, -0.032322850078344345, 0.05352332442998886, -0.0360298752784729, 0.0074805147014558315, 0.010150326415896416, -0.018633540719747543, -0.038618896156549454, -0.029561294242739677, 0.02018946409225464, 0.0540403313934803, -0.022516751661896706, -0.007332031149417162, 0.011024613864719868, 0.04618261381983757, 0.013740329071879387, 0.02979411743581295, 0.008623949252068996, 0.0414399653673172, -0.017260471358895302, -0.013397599570453167, 0.01418167445808649, -0.03122442401945591, 0.031133366748690605, -0.015272964723408222, 0.03280673176050186, 0.038201864808797836, -0.003859726246446371, 0.009370851330459118, -0.007162601687014103, -0.06266385316848755, 0.04478068649768829, -0.12084021419286728, 0.048516109585762024, -0.012706835754215717, 0.023226529359817505, 0.02517065964639187, -0.009936129674315453, 0.030057718977332115, -0.07027474045753479, -0.0007832503179088235, -0.0220845527946949, 0.019905248656868935, -0.02899968810379505, -0.023703863844275475, 0.00023265239724423736, 0.060865238308906555, 0.02328415960073471, -0.023912405595183372, -0.0829896554350853, -0.03522544354200363, -0.03107260912656784, -0.009659744799137115, -0.024615658447146416, 0.03905588760972023, -0.03079376555979252, 0.003185536479577422, -0.0408024899661541, 0.028014320880174637, -0.06216568499803543, 0.003622699063271284, -0.006930460687726736, 0.03221287205815315, 0.01623503491282463, 0.020159639418125153, -0.008507582359015942, 0.0294504277408123, 0.02805439941585064, 0.09340599924325943, 0.015817763283848763, 0.0019485319498926401, -0.11158207803964615, 0.00016538650379516184, 0.02748042345046997, -0.0703994631767273, 0.02986370027065277, -0.054758913815021515, 0.014308655634522438, -0.0486680269241333, -0.03677276521921158, 0.06410352885723114, 0.015224444679915905, 0.021373750641942024, -0.03240390121936798, 0.035017505288124084, -0.0010181540856137872, -0.039422910660505295, 0.09370969235897064, -0.0008110539638437331, -0.006277628242969513, 0.03599792346358299, 0.06537289172410965, 0.0537068247795105, -0.0018962451722472906, -0.004023173823952675, -0.009426918812096119, 0.008294541388750076, -0.015421481803059578, -0.037891749292612076, -0.03247794508934021, -0.010471617802977562, -0.03548083454370499, 0.03857708349823952, 0.02029435895383358, 0.025719963014125824, -0.007064768113195896, -0.016140233725309372, 0.031425271183252335, 0.0286310613155365, -0.00419717887416482, 0.009889982640743256, 0.012791058048605919, -0.0378262996673584, -0.02005545236170292, -0.02491096220910549, -0.01528092660009861, 0.06740141659975052, -0.003920322749763727, -0.006399298552423716, -0.025075716897845268, -0.031656671315431595, -0.027175484225153923, -0.01647770032286644, 0.008509631268680096, -0.014318373054265976, 0.0019722713623195887, -0.0500553622841835, 0.05959095060825348, 0.015378037467598915, -0.023163486272096634, 0.009357284754514694, 0.01895666867494583, 0.0398804172873497, -0.03364714980125427, -0.022112471982836723, 0.0057537248358130455, 0.017683908343315125, -0.013144966214895248, -0.08058717846870422, -0.020333444699645042, -0.0038173296488821507, -0.058159004896879196, -0.004921048879623413, -0.02210156060755253, -0.0064328694716095924, -0.0002511913189664483, -0.0698244571685791, 0.043562643229961395, 0.018088161945343018, 0.010534310713410378, 0.022499890998005867, -0.012837099842727184, -0.009543037042021751, 0.031946562230587006, 0.08169214427471161, -0.019743792712688446, 0.022131022065877914, 0.010922722518444061, 0.023648886010050774, 0.019041763618588448, 0.044077347964048386, 0.030800066888332367, 0.005250328220427036, 0.02556203119456768, -0.00309850019402802, 0.029598696157336235, -0.020589159801602364, -0.03137888386845589, -0.09471115469932556, -0.07885942608118057, -0.018698876723647118, -6.168508843984455e-05, -0.018612271174788475, 0.0040522050112485886, 0.020601043477654457, -0.03518896922469139, -0.036661770194768906, 0.022694889456033707, -0.050553396344184875, 0.03878950700163841, -0.03352004662156105, 0.030245983973145485, 0.042742323130369186, -0.007794956676661968, -0.03011363185942173, 0.07867391407489777, -0.025027669966220856, 0.021607032045722008, -0.02711278200149536, 0.02468549832701683, 0.02364133857190609, -0.03889472037553787, -0.010787813924252987, 0.00950953271239996, -0.04191286489367485, 0.0034937686286866665, -0.016813911497592926, 0.027710596099495888, -0.050732873380184174, 0.012859104201197624, -0.013686652295291424, 0.03305017948150635, -0.0014299140311777592, -0.021215448155999184, 0.014472010545432568, -0.026422826573252678, 0.03474543243646622, -0.04590713605284691, -0.022796476259827614, 0.12270770967006683, -0.01774691231548786, -0.00990188680589199, 0.037188801914453506, 0.010846621356904507, 0.0406331904232502, -0.029716556891798973, -0.06187386438250542, -0.03180963546037674, 0.056968189775943756, 0.027286894619464874, -0.06284444034099579, 0.025771770626306534, -0.012254676781594753, -0.038032472133636475, 0.04790951684117317, -0.010785824619233608, -0.04813222959637642, -0.011253617703914642, -0.04101952537894249, 0.03789698705077171, 0.12860623002052307, 0.027882631868124008, -2.5026363800861873e-05, 0.025101356208324432, 0.006067322567105293, -0.0374208502471447, 0.022671187296509743, -0.01086499635130167, 0.020792512223124504, 0.040355633944272995, -0.003901726333424449, -0.033580925315618515, 0.08648495376110077, 0.013105004094541073, 0.04552285373210907, -0.005795846693217754, -0.0018788946326822042, -0.008423770777881145, 0.0015418808907270432, -0.02858981303870678, -0.010507655330002308, -0.009792557917535305, 0.007295031100511551, -0.007047812454402447, -0.03359191492199898, 0.03208692744374275, 0.0044724890030920506, 4.733567402581684e-05, 0.004503706004470587, -0.02423364482820034, -0.013338095508515835, 0.05483970046043396, 0.03042011708021164, 0.0404583141207695, -0.01785990409553051, -0.05703878775238991, -0.008680739440023899, -0.00440113665536046, 0.008804171346127987, -0.033073823899030685, -0.01642046496272087, -0.01792341284453869, -0.01512982603162527, -0.01664484478533268, -0.052511803805828094, -0.032761622220277786, 0.0633556991815567, 0.014493526890873909, -0.002609233371913433, 0.012026301585137844, -0.04951433092355728, -0.04678213223814964, 0.013406598009169102, 0.027932168915867805, 0.04893060773611069, -0.018664982169866562, -0.010244560427963734, -0.015922831371426582, 0.029589371755719185, 0.02065153233706951, -0.00028883552295155823, 0.02339794486761093, -0.0033340491354465485, 0.0017273854464292526, 0.03934035077691078, 0.005348329432308674, -0.0028038006275892258, -0.04962184652686119, 0.01718842051923275, -0.01597481593489647, -0.031217502430081367, -0.022792212665081024, 0.019973866641521454, -0.015085183084011078, -0.09937718510627747, 0.007010001223534346, 0.027529513463377953, 0.013729952275753021, -0.10278452932834625, -0.008429285138845444, 0.0180816687643528, -0.034805797040462494, 0.008401677943766117, 0.025161754339933395, -0.014208280481398106, 0.015342159196734428, -0.02368125505745411, 0.01917513646185398, -0.026545749977231026, -0.06406620889902115, 0.03667070344090462, -0.10162652283906937, 0.015075196512043476, -0.009961160831153393, -0.06393135339021683, -0.05581321194767952, -0.009317714720964432, -0.03712574020028114, 0.025413690134882927, -0.026744509115815163, 0.029101064428687096, -0.004910103976726532, -0.08487088978290558, 0.02063833735883236, -0.06134060397744179, 0.0384022481739521, 0.04618137329816818, -0.06765678524971008, -0.0008994434610940516, 0.05744015797972679, 0.03103232942521572, -0.026250377297401428, -0.019918551668524742, -0.008395176380872726, -0.014945331029593945, -0.014814862981438637, -0.04012764245271683, 0.030440831556916237, -0.0026610789354890585, 0.012425875291228294, -0.03537481278181076, 0.053351327776908875, 0.0034475079737603664, 0.012994840741157532, 0.02384122647345066, 0.033173222094774246, 0.02362027019262314, -0.02404504083096981, -0.03975292667746544, 0.04742656648159027, -0.0019118692725896835, -0.013536853715777397, -0.02041570097208023, -0.015979928895831108, -0.05235881358385086, -0.015253663063049316, -0.014529085718095303, -0.018547317013144493, 0.044000476598739624, 0.06930649280548096, -0.02059580385684967, -0.008382112719118595, -0.08563827723264694, -0.011197696439921856, 0.003589518368244171, 0.0530095100402832, 0.008087574504315853, -0.03763020411133766, 0.05339682847261429, -0.014008798636496067, -0.039740994572639465, -0.014179904013872147, 0.016261864453554153, -0.0030983807519078255, -0.03416435420513153, 0.003989118151366711, 0.05263233929872513, 0.0014537652023136616, -0.003032772336155176, -0.01911088265478611, -0.023140566423535347, -0.04184582084417343, -0.013005251064896584, 0.10473648458719254, 0.0057909670285880566, -0.00044699423597194254, -0.009957443922758102, -0.04617433622479439, 0.0076871635392308235, -0.02976003661751747, -0.05574153736233711, 0.004349636845290661, 0.038846082985401154, 0.00894759688526392, -0.013430154882371426, 0.009898601099848747, -0.02318592555820942, 0.05028475821018219, 0.0343310609459877, 0.0054924385622143745, 0.0005198956932872534, 0.006456974893808365, 0.01945328898727894, -0.024329759180545807, 0.03677777945995331, 0.028245924040675163, -0.006675278302282095, -0.03462560102343559, 0.047253720462322235, -0.020093124359846115, -0.01383939664810896, -0.008902028203010559, 0.024351691827178, 0.0014520108234137297, 0.027463750913739204, -0.01698926091194153, -0.09605707973241806, 0.10303502529859543, -0.05029676482081413, 0.046648602932691574, 0.010901983827352524, -0.010321957059204578, 0.033317361027002335, -0.0003987514937762171, 0.020740758627653122, -0.05482129007577896, -0.0017888766014948487, 0.0018074441468343139, 0.06926041841506958, -0.02483842894434929, 0.08051029592752457, 0.02974748983979225, 0.002655147109180689, -0.0873330608010292, -0.003485386958345771, 0.020964885130524635, -0.007408985868096352, -0.04422815889120102, -0.009855225682258606, 0.06243433803319931, -0.027405614033341408, -0.038109783083200455, -0.036765024065971375, 0.033991437405347824, -0.015871256589889526, 0.024727052077651024, -0.03856824338436127, 0.0071030776016414165, 0.000388930959161371, 0.004225575365126133, -0.032839611172676086, 0.005527079571038485, 0.012360864318907261, 0.053578779101371765, -0.029292967170476913, 0.0011335747549310327, -0.010033505968749523, -0.02536010555922985, 0.026948988437652588, 0.019902758300304413, 0.08107779920101166, -0.007431425154209137, 0.00021596949954982847, -0.03133842721581459, -0.04050792381167412, -0.005781533662229776, 0.03979073092341423, 0.03768067806959152, 0.01398859266191721, 0.028301574289798737, 0.009005059488117695, 0.01622207835316658, -0.013993633911013603, -0.023596888408064842, -0.013431471772491932, -0.02130904793739319, 0.015206282958388329, -0.05648687854409218, -6.804101461237169e-33, -0.023872997611761093, -0.0461110882461071, -0.011270149610936642, -0.015844877809286118, -0.056740809231996536, 0.050910644233226776, -0.02514173835515976, -0.00879944022744894, 0.003242811420932412, -0.00395191228017211, -0.03484693169593811, 1.8376631487626582e-05, 0.0038923665415495634, 0.025361541658639908, 0.05490218475461006, 0.006514469627290964, -0.020607413724064827, 0.009722094982862473, 0.027294529601931572, 0.0013523390516638756, 0.04975947365164757, 0.044475480914115906, 0.07192284613847733, -0.024145949631929398, -0.06480956077575684, -0.012438054196536541, 0.0042212833650410175, 0.032716602087020874, -0.035959478467702866, 0.008440647274255753, -0.020982692018151283, -0.007433803752064705, 0.033605482429265976, -0.02897094190120697, 0.03534776717424393, 0.0254069771617651, -0.10795220732688904, -0.023660190403461456, -0.049070365726947784, 0.0061605279333889484, -0.032885778695344925, 0.005823253188282251, 0.08801838755607605, 0.01343800313770771, 0.021508652716875076, -0.01657150313258171, 0.03430432826280594, 0.0038858484476804733, -0.026362953707575798, -0.0373322069644928, -0.05976482108235359, 0.012892828322947025, 0.014134577475488186, 0.052627082914114, -0.03304504230618477, -0.035752035677433014, -0.025351284071803093, 0.031808096915483475, -0.09311467409133911, 0.014978772029280663, -0.015466448850929737, 0.04398674517869949, 0.003660538699477911, 0.06547278165817261, 0.05296606943011284, 0.055540572851896286, 0.02894933521747589, 0.04735778272151947, -0.013256118632853031, -0.00797102227807045, 0.021435683593153954, 0.044174108654260635, 0.060667816549539566, -0.054005250334739685, 0.09934146702289581, -0.013406544923782349, -0.0627056285738945, -0.006223488133400679, 0.022345885634422302, 0.04069511964917183, -0.013532468117773533, -0.0016568939900025725, -0.05196771398186684, 0.019217101857066154, 0.014062684029340744, 0.04049484431743622, -0.025401094928383827, -0.06749415397644043, 0.011019496247172356, 0.009100326336920261, -0.00690581975504756, 0.03720155730843544, 0.0038893164601176977, -0.009649522602558136, 0.04021980240941048, -0.03936193883419037, 0.07148721814155579, 0.02541595697402954, -0.012271077372133732, 0.024303803220391273, -0.06331197917461395, -0.040292710065841675, -0.04062454774975777, -0.0037611641455441713, 0.012448630295693874, 0.040585245937108994, 0.00021352256590034813, 0.0016294962260872126, -0.025930166244506836, -0.012344901449978352, 0.010130729526281357, -0.01043738704174757, 0.0051214685663580894, 0.057624924927949905, 0.03298021852970123, -0.032661862671375275, -0.004463283810764551, 0.08385547995567322, 0.01695283316075802, -0.013369748368859291, -0.0005996543914079666, 0.007395952474325895, 0.0024205404333770275, 0.031161537393927574, -0.029738478362560272, 0.009320330806076527, -0.09400389343500137, -0.014447608031332493, 0.00025490016560070217, -0.06937069445848465, 0.007792133837938309, 0.04765034466981888, 3.081581212427409e-07, -0.0313897542655468, 0.033289987593889236, 0.0015861800638958812, 0.00289395940490067, 0.028638308867812157, 0.007351798005402088, 0.017162740230560303, 0.014886312186717987, -0.030049176886677742, -0.012536337599158287, 0.04868080094456673, -0.015997830778360367, 0.031213561072945595, 0.013479741290211678, -0.10453768074512482, -0.06223239377140999, -0.0783107802271843, -0.022351833060383797, -0.03138859197497368, 0.0029561782721430063, 0.0505533367395401, 0.10824231803417206, 0.04334133118391037, 0.01413559727370739, 0.033129557967185974, -0.01156746968626976, 0.0046818070113658905, 0.060254182666540146, 0.04309549927711487, -0.0030943292658776045, -0.013383588753640652, 2.5549075871822424e-05, -0.07294943928718567, 0.05332136154174805, -0.016274571418762207, 0.041512951254844666, 0.011441675946116447, 0.028055325150489807, -0.012443498708307743, -0.05555034056305885, 0.06972690671682358, -0.0003685957635752857, 0.01493053138256073, -0.051947157829999924, 0.012902271933853626, -0.06809088587760925, -0.04685244336724281, 0.03479410335421562, 0.015275629237294197, 0.024076897650957108, 0.009223905391991138, -0.023471711203455925, 0.009680461138486862, 0.007178966887295246, -0.026010612025856972, -0.030880486592650414, 0.015062915161252022, -0.10497946292161942, 0.025296831503510475, 0.059163618832826614, -0.010373467579483986, -0.03238476812839508, -0.024651281535625458, -0.01337040588259697, 0.056565407663583755, -0.021082842722535133, -0.030907878652215004, 2.8820922022029506e-34, -0.010411417111754417, -0.039937056601047516, -0.03670399263501167, 0.035233959555625916, 0.020850615575909615, 0.02864636853337288, -0.018865935504436493, 0.03307051211595535, 0.012791198678314686, -0.04166657477617264, -0.022880634292960167]

['Sam Wiseman', 'Alexander M. Rush']

1606.02960v2

Sequence-to-Sequence (seq2seq) modeling has rapidly become an important general-purpose NLP tool that has proven effective for many text-generation and sequence-labeling tasks. Seq2seq builds on deep neural language modeling and inherits its remarkable accuracy in estimating local, next-word distributions. In this work, we introduce a model and beam-search training scheme, based on the work of Daume III and Marcu (2005), that extends seq2seq to learn global sequence scores. This structured approach avoids classical biases associated with local training and unifies the training loss with the test-time usage, while preserving the proven model architecture of seq2seq and its efficient training approach. We show that our system outperforms a highly-optimized attention-based seq2seq system and other baselines on three different sequence to sequence tasks: word ordering, parsing, and machine translation.

Sequence-to-Sequence Learning as Beam-Search Optimization

http://arxiv.org/pdf/1606.02960v2

Title SequencetoSequence Learning BeamSearch Optimization Summary SequencetoSequence seq2seq modeling rapidly become important generalpurpose NLP tool proven effective many textgeneration sequencelabeling task Seq2seq build deep neural language modeling inherits remarkable accuracy estimating local nextword distribution work introduce model beamsearch training scheme based work Daume III Marcu 2005 extends seq2seq learn global sequence score structured approach avoids classical bias associated local training unifies training loss testtime usage preserving proven model architecture seq2seq efficient training approach show system outperforms highlyoptimized attentionbased seq2seq system baseline three different sequence sequence task word ordering parsing machine translation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.06399953365325928, 0.0633859634399414, 0.011333177797496319, 0.021156882867217064, -0.0031690301839262247, -0.010915356688201427, 0.008128847926855087, -0.021023651584982872, 0.016098977997899055, -0.030058465898036957, -0.016497142612934113, -0.021620193496346474, 0.010177547112107277, 0.08310149610042572, 0.015923965722322464, -0.04420726001262665, 0.04760976880788803, 0.0034712746273726225, 0.02661530300974846, 0.03950206935405731, 0.02816520445048809, -0.0023999810218811035, 0.008562679402530193, 0.03831874206662178, 0.0032679017167538404, -0.0014835878973826766, 0.002068408066406846, -0.0032396328169852495, 0.005810867063701153, -0.06324931979179382, 0.052873846143484116, 0.08026264607906342, 0.019736677408218384, 0.03679554909467697, 2.3271338704944355e-06, -0.009633718058466911, -0.025689508765935898, -0.01805802620947361, 0.0326073057949543, 0.032566171139478683, 0.008471428416669369, -0.029994942247867584, -0.006061107385903597, 0.021156908944249153, -0.055752627551555634, -0.014539500698447227, 0.03165707364678383, 0.03533037379384041, 0.044512033462524414, 0.05452742055058479, -0.007554502226412296, -0.07074456661939621, -0.0008608633652329445, -0.032692793756723404, 0.042815789580345154, -0.04901077598333359, 0.002772723091766238, -0.01027103140950203, 0.02913041040301323, 0.05168227106332779, -0.016889236867427826, 0.06036543846130371, -0.0021130589302629232, -0.025320174172520638, 0.016741862520575523, 0.02721576951444149, -0.010991161689162254, -0.030070168897509575, -0.01303255558013916, 0.08514225482940674, -0.04450131207704544, -0.02054133079946041, 0.030446430668234825, 0.003494411241263151, -0.014255928806960583, -0.05241422727704048, -0.020199721679091454, 0.027863403782248497, -0.005627312697470188, -0.008822095580399036, 0.05052652955055237, 0.036781299859285355, 0.0151960588991642, 0.0068238843232393265, -0.018545392900705338, 0.021944714710116386, 0.011247429996728897, -0.023204682394862175, -0.04277358204126358, -0.05171710252761841, -0.030278390273451805, -0.03658754378557205, 0.08142994344234467, 0.016171112656593323, -0.017290130257606506, 0.016612010076642036, -0.012576999142765999, -0.07100105285644531, 0.03312363475561142, -0.06933518499135971, -0.0032143599819391966, 0.027955245226621628, -0.002893472323194146, 0.012070435099303722, -0.019293278455734253, 0.034845076501369476, 0.0514143668115139, -0.023399215191602707, -0.064435213804245, 0.016827113926410675, -0.028626352548599243, -0.012089923955500126, -0.029417365789413452, 0.015485190786421299, -0.050108201801776886, -0.04311700165271759, -0.05259918421506882, -0.003809330053627491, 0.05600069463253021, -0.05743635818362236, 0.02513057179749012, 0.030779363587498665, -0.026569927111268044, 0.009518684819340706, -0.002911212155595422, -1.2740127203869633e-05, -0.01744953729212284, -0.008964160457253456, -0.0072149536572396755, -0.023032180964946747, -0.008348140865564346, 0.027139611542224884, -0.011968632228672504, -0.004988060798496008, -0.006750050000846386, 0.03338591754436493, -0.001314624329097569, -0.06881486624479294, 0.00451640784740448, 0.0007583518163301051, -0.03407742455601692, 0.004419525619596243, -0.036681000143289566, -0.07087040692567825, 0.016775665804743767, -0.0011027066502720118, -0.05677638575434685, 0.0028335507959127426, 0.033006638288497925, 0.020121430978178978, -0.045018039643764496, 0.05265070125460625, -0.004435866605490446, -0.0029196462128311396, 0.027423767372965813, 0.013596590608358383, 0.056322693824768066, 0.004933098331093788, 0.04534289985895157, 0.03897056356072426, 0.022685658186674118, -0.02192731201648712, 0.0038218821864575148, 0.038268741220235825, -0.008815555833280087, -0.042194660753011703, -0.02175559289753437, -0.007708398159593344, 0.009339925833046436, 0.041546780616045, 0.046767354011535645, 0.0704306960105896, -0.012334836646914482, 0.013786629773676395, 0.006860742811113596, 0.0780935063958168, 0.0395408496260643, 0.004170726519078016, 0.043278370052576065, 0.04839920625090599, -0.014243717305362225, -0.0017039020312950015, -0.02724554017186165, 0.0226843673735857, 0.0337565653026104, -0.0008978249970823526, 0.054444655776023865, 0.020373089239001274, -0.0023552090860903263, -0.022293539717793465, 0.013564313761889935, -0.009906441904604435, -0.0021254487801343203, -0.03714999184012413, 0.005645683966577053, 0.03714411333203316, -0.07945563644170761, 0.04147307202219963, -0.0005333300214260817, -0.054126519709825516, -0.0021410416811704636, 0.0015717879869043827, -0.029331233352422714, 0.04295245558023453, 0.042717549949884415, -0.007848038338124752, -0.03419818356633186, 0.011198105290532112, -0.029858004301786423, 0.02930981107056141, 0.030285345390439034, -0.016713593155145645, -0.026309264823794365, -0.05787854641675949, -0.015149552375078201, 0.03221031278371811, -0.012730433605611324, 0.009223740547895432, -0.02809297852218151, -0.010964796878397465, 0.05669360235333443, 0.04716430604457855, -0.07586291432380676, 0.05222785100340843, -0.07441683858633041, -0.04573850706219673, 0.019756654277443886, -0.007951471954584122, 0.006959829479455948, 0.023673132061958313, 0.010492240078747272, 0.050084929913282394, 0.05816467106342316, -0.008273733779788017, -0.00020547324675135314, 0.0054137930274009705, -0.08990008383989334, -0.06853549182415009, 0.023777907714247704, -0.03529287129640579, 0.03625386580824852, 0.013888458721339703, -0.04021252319216728, -0.04528319463133812, 0.009033413603901863, -0.02377810887992382, -0.009872425347566605, -0.01885151118040085, 0.04374757781624794, 0.028487032279372215, 0.005794655531644821, -0.05714588612318039, 0.04079421982169151, -0.040267329663038254, 0.046201739460229874, -0.02957257442176342, 0.018300579860806465, -0.0015367843443527818, -0.03554864227771759, -0.016478028148412704, -0.0009838301921263337, -0.019106727093458176, -0.02210703305900097, 0.03343583643436432, 0.024903636425733566, -0.03573651611804962, -0.005079546011984348, -0.05615846812725067, 0.039405617862939835, -0.0032456712797284126, 0.03687725216150284, 0.013531986624002457, 0.0538741871714592, -0.010104447603225708, -0.0413040928542614, -0.04311405122280121, 0.0039670816622674465, 0.022016743198037148, -0.008303144946694374, 0.044695574790239334, 0.020159369334578514, -0.002102876780554652, -0.05803179368376732, -0.01797611266374588, -0.03603542968630791, 0.03665224462747574, 0.016335822641849518, -0.055410951375961304, -0.044614050537347794, 0.05735476315021515, -0.02177581377327442, 0.0439034141600132, -0.006558548659086227, -0.0366353765130043, -0.011513893492519855, -0.04268239811062813, 0.04373485594987869, 0.022320201620459557, 0.06194888800382614, -0.04294441267848015, 0.0011889400193467736, -0.005252794362604618, 0.0016971621662378311, -0.017089512199163437, -0.03492341935634613, 0.05720936134457588, 0.02110893279314041, -0.034570738673210144, 0.01366938091814518, 0.08954659849405289, 0.01511507760733366, 0.0183908399194479, -0.010719923302531242, 0.007096723187714815, 0.009388276375830173, -0.018144525587558746, -0.010635830461978912, 0.014444918371737003, -0.03743656724691391, -0.00975035224109888, -0.03794734552502632, -0.01494054589420557, 0.046155910938978195, -0.00694070803001523, 0.004948499612510204, -0.0902642011642456, -0.01315257791429758, -0.02650320716202259, 0.022407270967960358, 0.014168741181492805, 0.02232254110276699, -0.012551411986351013, -0.06380552798509598, -0.03451862186193466, 0.0004416857264004648, -0.0297707486897707, -0.059045400470495224, 0.042601294815540314, -0.034310802817344666, -0.016883911564946175, -0.04822893068194389, -0.014967468567192554, -0.06828320026397705, -0.03023480251431465, 0.01216284092515707, 0.00019193651678506285, 0.07328572869300842, 0.0004749794607050717, -0.03868906944990158, 0.040479037910699844, -0.004475336521863937, 0.07150299102067947, -0.03785727173089981, 0.008871978148818016, -0.01683240570127964, 0.05417559668421745, 0.04803751781582832, -0.03453024476766586, 0.02809830754995346, 0.02857530117034912, 0.006559527944773436, 0.027405083179473877, -0.004662159830331802, 0.025412525981664658, -0.019054267555475235, -0.02520822547376156, 0.03658038005232811, -0.06965981423854828, -0.06214155629277229, 0.030592573806643486, 0.0347345769405365, -0.07228555530309677, -0.006106122396886349, 0.1127457469701767, 0.0603058859705925, -0.05478658899664879, 0.016494253650307655, 0.0018141604959964752, -0.026776250451803207, 0.018461357802152634, 0.029974080622196198, -0.06750468909740448, -0.01586412452161312, -0.007832007482647896, 0.00951449666172266, 0.0166490375995636, -0.024393752217292786, -0.03951232135295868, -0.08607736974954605, -0.004640414845198393, -0.0026183738373219967, -0.03727349638938904, -0.008050196804106236, -0.016259798780083656, -0.03355243057012558, 0.012106213718652725, 0.00044882448855787516, 0.05029870197176933, -0.011468381620943546, 0.021016951650381088, 0.03195446357131004, -0.03201207146048546, -0.03893306478857994, 0.000397519557736814, -0.05635987967252731, 0.0313388966023922, 0.07966812700033188, 0.0554259829223156, -0.002933457726612687, -0.023340586572885513, 0.0020397379994392395, -0.022427072748541832, -0.015925489366054535, -0.03476230800151825, 0.022265732288360596, -0.02910691313445568, 0.002434757072478533, -0.030589798465371132, 0.02162248268723488, -0.013319539837539196, 0.03753254935145378, 0.007556591182947159, 0.012773026712238789, 0.010960130952298641, 0.001116676372475922, -0.040786415338516235, 0.02050623670220375, 0.0034748187754303217, 0.03284091502428055, 0.02801690064370632, -0.0337338000535965, -0.02650495432317257, -0.05263790488243103, 0.030685273930430412, -0.06818331032991409, -0.048577167093753815, -0.0022315543610602617, -0.010875923559069633, -0.018790418282151222, -0.09730777144432068, -0.059936679899692535, -0.02882814034819603, 0.020449308678507805, 0.026853786781430244, 0.03816304728388786, -0.04865429177880287, -0.04260969161987305, -0.04014639928936958, -0.008092873729765415, 0.04510108008980751, 0.0025390356313437223, -0.09841461479663849, 0.02895023487508297, 0.058347638696432114, -0.02344265766441822, -0.028607357293367386, -0.022103499621152878, -0.0349360853433609, -0.04438973218202591, -0.01717444509267807, 0.06594914942979813, 0.0018127155490219593, -0.02025122009217739, -0.03544709086418152, -0.06101512908935547, 0.01376616396009922, 0.07337697595357895, -0.0347297228872776, -0.05502944067120552, 0.03308439627289772, 0.0012045369949191809, -0.02279030717909336, 0.009272035211324692, -0.0067605325020849705, 0.048914503306150436, -0.026062767952680588, 0.0800585001707077, 0.015530608594417572, -0.08576754480600357, -0.006344804540276527, -0.022139940410852432, 0.08096376806497574, -0.028171969577670097, -0.005392859689891338, -0.025324085727334023, 0.012713488191366196, 0.0021061445586383343, 0.0013403266202658415, -0.020733358338475227, 0.051778506487607956, 0.04197482019662857, 0.031000828370451927, -0.010021207854151726, -0.005690744612365961, -0.026668505743145943, -0.01376004796475172, -0.033572543412446976, 0.06332924216985703, 0.01073941495269537, 0.03789644315838814, -0.015242495574057102, -0.018743976950645447, -0.011064903810620308, 0.003356223925948143, 0.012080632150173187, 0.046333372592926025, -0.05193455144762993, 0.030537519603967667, 0.0003310847096145153, 0.04260372370481491, 0.0123720932751894, 0.06533260643482208, -0.03292396292090416, 0.012974047102034092, -0.036103568971157074, -0.02301952615380287, 0.0967053472995758, -0.04291260614991188, 0.05346011370420456, 0.032836850732564926, 0.03067728877067566, -0.040953122079372406, 0.05652857571840286, -0.020008523017168045, -0.01151537150144577, -0.014796365983784199, 0.007726671174168587, -0.019204750657081604, -0.004057525657117367, 0.08009298890829086, 0.010152475908398628, -0.009013860486447811, 0.04421243071556091, -0.036748141050338745, -0.016526198014616966, 0.005551422480493784, 0.017996909096837044, 0.0018746857531368732, -0.06927487999200821, 0.010689939372241497, -0.013396453112363815, -0.03625088557600975, 0.05881939083337784, -0.0030122012831270695, 0.01972142979502678, 0.008458035998046398, 0.06582307070493698, 0.037804167717695236, -0.01781187765300274, -0.02360638789832592, -0.06169929727911949, 0.004249224904924631, 0.020964365452528, -0.06902614235877991, -0.04813409596681595, -6.39977328154055e-33, -0.031048156321048737, -0.03736705332994461, 0.008027670904994011, 0.025376245379447937, 0.0038501075468957424, 0.011741301976144314, -0.04977114871144295, -0.021500451490283012, -0.00779548566788435, -0.02696870267391205, -0.009220498614013195, -0.00022905944206286222, 0.010478660464286804, -0.008643655106425285, 0.02279343642294407, 0.020391173660755157, 0.019677506759762764, 0.01121709868311882, -8.498064562445506e-05, 0.0162977185100317, 0.017014769837260246, 0.08810567110776901, 0.09970059990882874, -0.029530365020036697, -0.001318106660619378, -0.005457989405840635, 0.052066922187805176, -0.013681500218808651, 0.04876691848039627, 0.018309153616428375, -0.0220097154378891, -0.008874760009348392, 0.012327327392995358, -0.040164776146411896, -0.02507091499865055, 0.0219121016561985, -0.06070531904697418, -0.016338897868990898, -0.027760302647948265, -0.007395672146230936, -0.0078749880194664, -0.019906558096408844, 0.03951937332749367, -0.02349291928112507, -0.051385872066020966, 0.049536995589733124, 0.05514635890722275, -0.001766237779520452, -0.06138501316308975, -0.038343314081430435, -0.04441962391138077, 0.02689581923186779, 0.01887895166873932, -0.013371706940233707, 0.023026207461953163, 0.04348643124103546, 0.012685563415288925, -0.012644319795072079, -0.04475140944123268, 0.02541770413517952, -0.010197486728429794, 0.10198549926280975, 0.04458281025290489, 0.036371827125549316, 0.01836501806974411, 0.025195665657520294, 0.036601047962903976, -0.03852279484272003, 0.03474428132176399, 0.04458430036902428, 0.020159466192126274, -0.0001597545633558184, 0.03273311257362366, -0.013150662183761597, 0.055560510605573654, -0.006773696281015873, -0.061435434967279434, 0.0614461712539196, 0.021788539364933968, 0.025594038888812065, 0.03593764081597328, 0.005203737411648035, -0.014530709944665432, 0.0047489553689956665, -0.011312130838632584, -0.024275407195091248, -0.0006240080110728741, -0.040728695690631866, 0.022492729127407074, 0.012423388659954071, 0.003159652231261134, 0.012232297100126743, 0.04664342850446701, -0.011370135471224785, -0.02007385529577732, 0.04485273361206055, -0.00952785275876522, -0.014356969855725765, -0.01866932027041912, 0.05696532130241394, -0.10292109102010727, -0.021458692848682404, 0.010043876245617867, -0.005170776043087244, -0.011283773928880692, -0.00821260642260313, 0.0006854769308120012, -0.024639785289764404, -0.012195676565170288, -0.007968086749315262, -0.0007651261985301971, -0.020762691274285316, -0.002457033609971404, 0.08394300937652588, 0.011540945619344711, -0.016057979315519333, 0.009402191266417503, 0.09075944125652313, 0.03324342146515846, -0.0022854928392916918, -0.037624750286340714, -0.044522788375616074, 0.028912844136357307, 0.05045672506093979, -0.05218062177300453, 0.015955597162246704, -0.06686531007289886, 0.0449138805270195, -0.012600974179804325, -0.07382600009441376, -0.026507733389735222, 0.031498849391937256, 2.9373092047535465e-07, 0.02539311908185482, 0.022274095565080643, 0.030162615701556206, -0.006273327860981226, 0.00936073623597622, 0.00021160398318897933, -0.005338085815310478, 0.05545371025800705, -0.01913260668516159, 0.022647462785243988, -0.009442894719541073, -0.008409079164266586, -0.008148111402988434, -0.03092912957072258, -0.13984031975269318, -0.021909626200795174, -0.09866659343242645, 0.06010740250349045, -0.033188555389642715, -0.007873175665736198, 0.03297751396894455, 0.10629841685295105, -0.027756912633776665, -0.007248681038618088, 0.011126845143735409, -0.014983703382313251, 0.026362158358097076, 0.03921204060316086, -0.05355770140886307, 0.014471648260951042, 0.014193429611623287, 0.002913256175816059, -0.038420744240283966, -0.038242045789957047, -0.04683886468410492, 0.027193456888198853, 0.017259864136576653, 0.05425563082098961, -0.012642358429729939, -0.03986392915248871, 0.03806041553616524, 0.007570626679807901, 0.02251552976667881, 0.002491347724571824, 0.061887383460998535, 0.0045250775292515755, -0.005434310529381037, 0.0134572209790349, -0.020491046831011772, 0.028312696143984795, -0.014836211688816547, -0.027827372774481773, -0.02771201729774475, 0.006627989001572132, 0.04085617884993553, -0.03469331935048103, -0.023204386234283447, -0.07886497676372528, -0.017783552408218384, -0.006802520714700222, 0.03028869815170765, 0.0018179892795160413, -0.04916808754205704, 0.014544297941029072, 0.0071584079414606094, 0.009028640575706959, 0.005963827949017286, 3.249852497519915e-34, 0.029898403212428093, -0.03210707753896713, -0.011609412729740143, 0.017957918345928192, 0.012851264327764511, -0.011363871395587921, -0.04699682071805, 0.03702356666326523, 0.02561347559094429, -0.08692525327205658, -0.05345829203724861]

['Ankit Vani', 'Yacine Jernite', 'David Sontag']

1705.08557v1

In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large numbers of concepts from text. We apply the new model to address an important problem in healthcare of understanding what medical concepts are discussed in clinical text. Using a publicly available dataset derived from Intensive Care Units, we learn to label a patient's diagnoses and procedures from their discharge summary. Our evaluation shows a clear advantage to using our proposed architecture over a variety of strong baselines.

Grounded Recurrent Neural Networks

http://arxiv.org/pdf/1705.08557v1

Title Grounded Recurrent Neural Networks Summary work present Grounded Recurrent Neural Network GRNN recurrent neural network architecture multilabel prediction explicitly tie label specific dimension recurrent hidden state call process grounding approach particularly wellsuited extracting large number concept text apply new model address important problem healthcare understanding medical concept discussed clinical text Using publicly available dataset derived Intensive Care Units learn label patient diagnosis procedure discharge summary evaluation show clear advantage using proposed architecture variety strong baseline Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03502779081463814, 0.003919562324881554, -0.008802095428109169, 0.014723682776093483, 0.0010392939439043403, 0.0014341771602630615, 0.022555751726031303, 0.002775089582428336, -0.010944842360913754, -0.02333691529929638, -0.006412681192159653, -0.02209273912012577, 0.03233269602060318, 0.08150706440210342, 0.006033760495483875, -0.04603736847639084, 0.03416471183300018, 0.04224845767021179, 0.01098746806383133, 0.02658008597791195, 0.004109629895538092, 0.017222080379724503, 0.008931792341172695, 0.06405703723430634, -0.017219847068190575, -0.002483331598341465, 0.018678532913327217, -0.03697558864951134, -0.011101622134447098, -0.11398138105869293, 0.04282314330339432, 0.011444690637290478, 0.0353134386241436, 0.021673640236258507, 2.3068034806783544e-06, -0.022494569420814514, -0.033684030175209045, -0.029000384733080864, 0.020555783063173294, -0.04663506895303726, -0.009956562891602516, -0.06706252694129944, 0.024706583470106125, 0.0032705827616155148, -0.037827618420124054, -0.030840104445815086, 0.02127687819302082, 0.1444391906261444, 0.05725527182221413, 0.01879233866930008, -0.017838114872574806, -0.06022799387574196, -0.01615994982421398, -0.021798621863126755, 0.0049952850677073, -0.05148015916347504, 0.05217882990837097, 0.008891896344721317, -0.005315293092280626, -0.010224452242255211, -0.010233024135231972, 0.0432128831744194, 0.008894847705960274, 0.027456536889076233, 0.03786928206682205, 0.06983225792646408, 0.02827095426619053, -0.014498366042971611, 0.005160338710993528, 0.07237030565738678, -0.030122173950076103, 0.00864001177251339, 0.03306078165769577, 0.01763995550572872, -0.02414483018219471, -0.05663249269127846, -0.028867747634649277, -0.01443235669285059, -0.033011194318532944, 0.020535456016659737, -0.008618131279945374, 0.0452442392706871, 0.013840979896485806, -0.003948863595724106, -0.015186893753707409, 0.041724685579538345, -0.02309807576239109, -0.0323389396071434, 0.03012303076684475, -0.003867124207317829, 0.01380312629044056, -0.024935882538557053, 0.027788836508989334, 0.05096276476979256, -0.006617155857384205, 0.017949126660823822, 0.014914100989699364, -0.051966678351163864, 0.04604407772421837, -0.08655234426259995, 0.027933930978178978, -0.006579496432095766, 0.0076970672234892845, -0.012406336143612862, -0.007965593598783016, 0.010386315174400806, -0.03779231011867523, 0.003683585673570633, -0.012574048712849617, 0.04498550295829773, -0.06837476789951324, -0.023648258298635483, -0.014965361915528774, 0.08148448914289474, 0.03249465674161911, -0.015025725588202477, -0.07872036844491959, -0.028760798275470734, -0.0048135994002223015, 0.00582472700625658, 0.012602129019796848, 0.07377579808235168, -0.030933121219277382, 0.017704276368021965, -0.016674792394042015, 0.04124553129076958, -0.04858794063329697, 0.03923661634325981, -0.01124945841729641, -0.018786096945405006, 0.013515359722077847, 0.02363436482846737, 0.016978325322270393, 0.02208985574543476, -0.02341374009847641, 0.0218255203217268, 0.016180433332920074, -6.078219666960649e-05, -0.07316280156373978, -0.0401463583111763, -0.020821036770939827, -0.00497021758928895, -0.009886021725833416, -0.046964097768068314, 0.0004617329395841807, -0.03185829147696495, -0.01654125191271305, -0.042197227478027344, 0.02452554553747177, 0.013358082622289658, -0.017549026757478714, 0.08296312391757965, -0.021497365087270737, -0.029376348480582237, 0.08371897786855698, 0.03503430634737015, 0.036832764744758606, 0.02556050755083561, 0.01646096259355545, 0.0337224081158638, 0.00113369757309556, -0.012881618924438953, 0.02647726610302925, -0.016971156001091003, 0.015413192100822926, -0.06515245884656906, -0.030315406620502472, -0.027835706248879433, 0.01560689602047205, 0.07456471025943756, -0.039390597492456436, 0.011524821631610394, 0.026900460943579674, 0.014157264493405819, 0.024880988523364067, 0.07045160979032516, 0.0012656287290155888, 0.027882976457476616, -0.010135382413864136, -0.04999159276485443, -0.012716508470475674, -0.011660177260637283, 0.011331163346767426, 0.02401244267821312, 0.024245673790574074, 0.011968209408223629, -0.04025062918663025, -0.026239795610308647, -0.03371475636959076, -0.030134128406643867, -0.011838817968964577, -0.01182816457003355, -0.015203597024083138, -0.06552788615226746, 0.045767899602651596, 0.021398665383458138, -0.0667535588145256, 0.030060751363635063, 0.02523830533027649, 0.021517183631658554, -0.02468772791326046, -0.03292218595743179, -0.020192591473460197, -0.009197450242936611, 0.029696373268961906, -0.028634022921323776, -0.03944260999560356, -0.056173063814640045, 0.012619463726878166, -0.00801030732691288, -0.002193351276218891, -0.006154102738946676, -0.007556799799203873, -0.055890042334795, 0.006144755519926548, 0.010159098543226719, -0.004448119085282087, 0.030635109171271324, -0.04366173967719078, 0.04569972679018974, 0.01126833725720644, 0.011372486129403114, -0.016059134155511856, 0.05792796611785889, -0.015594519674777985, -0.02808963693678379, 0.011839662678539753, 0.016111599281430244, 0.04710689187049866, 0.004655031953006983, 0.03883535414934158, 0.006211009807884693, 0.04705177992582321, -0.04258043318986893, -0.04600822553038597, -0.029579585418105125, -0.07029598951339722, -0.00942531879991293, 0.0009546171058900654, -0.007064651232212782, 0.03362957388162613, -0.0016333356034010649, -0.04540853574872017, -0.040984056890010834, 0.016621647402644157, -0.029573621228337288, 0.014294303953647614, -0.0069828578270971775, -0.023018373176455498, 0.03501325100660324, 0.044094108045101166, -0.017219217494130135, 0.02722112089395523, -0.03180323913693428, 0.0067068529315292835, -0.030897920951247215, -0.018630292266607285, 0.008520856499671936, -0.0035281397867947817, 0.00253375805914402, 0.00490441732108593, -0.043394509702920914, -0.0056266398169100285, -0.03397976607084274, 0.025754304602742195, -0.019426587969064713, -0.011526062153279781, -0.05888126790523529, 0.00518724275752902, 0.0073432037606835365, -0.037810493260622025, 0.011537530459463596, -0.005990311969071627, 0.01752079650759697, -0.04461662843823433, -0.060667622834444046, 0.02092668227851391, 0.0051113455556333065, -0.012006083503365517, 0.06475099921226501, 0.08860345929861069, 0.017188403755426407, 0.00020709546515718102, 0.002709078835323453, -0.03196922317147255, 0.03395438194274902, 0.036195058375597, -0.09011070430278778, -0.005919598042964935, 0.012441123835742474, -0.047849301248788834, 0.005208291113376617, -0.0028203781694173813, -0.05092431232333183, -0.019471464678645134, -0.013783578760921955, -0.008179862052202225, 0.01564955897629261, 0.028703853487968445, 0.044735800474882126, -0.0026349981781095266, 0.016382353380322456, 0.013857314363121986, 0.005732943303883076, -0.06139906123280525, 0.007404963485896587, 0.05780104920268059, 0.023694247007369995, 0.00537971593439579, 0.0792279988527298, 0.05594126135110855, 0.03244246542453766, -0.009908738546073437, 0.0164062287658453, -0.022507458925247192, 0.02366064116358757, -0.09469935297966003, 0.021035313606262207, -0.026922406628727913, 0.043032459914684296, 0.02670941688120365, -0.0211397185921669, 0.06286658346652985, 0.03317714110016823, 0.012120027095079422, -0.06472291052341461, -0.03800011798739433, -0.03486379235982895, 0.012971934862434864, -0.040088504552841187, -0.005911034997552633, 0.04403766989707947, -0.03430898115038872, 0.0047101788222789764, 0.020349424332380295, -0.033546075224876404, -0.029821068048477173, 0.047661859542131424, -0.007883287966251373, 0.01916452869772911, 0.001268258085474372, -0.030346810817718506, -0.05959463119506836, 0.020025499165058136, -0.018182076513767242, -0.014592104591429234, -0.05559581518173218, 0.03174898773431778, -0.051488082855939865, 0.029036233201622963, -0.014142954722046852, 0.07373306155204773, -0.022921821102499962, -0.006008091848343611, 0.002709015505388379, 0.02899906598031521, 0.05210172384977341, -0.03590897098183632, -0.03893275186419487, 0.0005209947121329606, 0.03673485666513443, 0.02336566522717476, -0.03190717473626137, 0.033866316080093384, -0.02169562503695488, 0.021206730976700783, -0.0035137017257511616, -0.016799332574009895, -0.005428567063063383, 0.028150850906968117, -0.029914263635873795, -0.0843764916062355, -0.016972262412309647, 0.10782164335250854, 0.011211619712412357, -0.05169403925538063, 0.013901226222515106, -0.029456745833158493, -0.03196439892053604, 0.010886896401643753, 0.008835694752633572, 0.010097537189722061, 0.005192444659769535, -0.029603200033307076, 0.024108681827783585, 0.008764293976128101, -0.0605822317302227, -0.014168629422783852, -0.03039998933672905, 0.01730029284954071, -0.0187193863093853, -0.09154284745454788, -0.0625690221786499, -0.04277065396308899, -0.025561384856700897, 0.03918925300240517, -0.03591961786150932, 0.003802578430622816, 0.034424349665641785, -0.03567767143249512, 0.03894641250371933, -0.09631120413541794, -0.04503452032804489, 0.04656730964779854, -0.011698639951646328, 0.016188345849514008, 0.06564196199178696, 0.07332736998796463, -0.051785118877887726, -0.04298506677150726, 0.020169617608189583, -0.016841519623994827, 0.013412182219326496, -0.04267299547791481, 0.06687799841165543, 0.016133315861225128, -0.0017312588170170784, -0.00977172888815403, 0.06462337076663971, -0.0781557634472847, 0.019923867657780647, 0.01917007565498352, 0.09419936686754227, -0.024781666696071625, -0.06628632545471191, -0.04840032756328583, 0.046526167541742325, 0.044566888362169266, 0.008344844914972782, 0.0064458115957677364, -0.015219499357044697, -0.02715175226330757, 0.008992486633360386, 0.05506323277950287, 0.002657622564584017, -0.01138679962605238, -0.0035270615480840206, -0.02506670542061329, -0.04514199495315552, -0.07081393897533417, -0.02646542713046074, 0.01951713114976883, 0.02496454305946827, 0.04958685114979744, 0.029228948056697845, 0.03017045371234417, 0.00668450677767396, -0.032739076763391495, -0.012365403585135937, 0.05047350749373436, 0.0073271323926746845, -0.03720884770154953, 0.007906160317361355, 0.08348165452480316, 0.0037059327587485313, -0.028891636058688164, -0.05366026982665062, 0.014224095270037651, 0.0011970865307375789, 0.01248599961400032, 0.021647609770298004, 0.015435172244906425, 0.009912041015923023, -0.018276352435350418, -0.009076688438653946, 0.0288765300065279, -0.0062864478677511215, -0.015030727721750736, -0.029781948775053024, 0.03460446745157242, 0.0071535250172019005, 0.015172983519732952, 0.006808368489146233, -0.005726352799683809, 0.10947056114673615, 0.0036278830375522375, -0.03201533854007721, -0.004592999815940857, -0.03644415736198425, -0.030962031334638596, 0.004081582184880972, 0.06842388957738876, -0.00039881753036752343, -0.017931103706359863, -0.05469156429171562, 0.014623161405324936, 0.004530901089310646, -0.00935432966798544, -0.015269173309206963, 0.026094747707247734, 0.055516503751277924, 0.005913531873375177, -0.02657541073858738, -0.037364691495895386, 0.022750969976186752, -0.011471519246697426, 0.000831451965495944, 0.02520895190536976, 0.004864651244133711, 0.03358175605535507, -0.0025858175940811634, 0.03662623092532158, -0.03225986286997795, -0.00622587651014328, 0.023380253463983536, 0.06060631945729256, -0.018429163843393326, 0.08628898859024048, 0.025413012132048607, 0.029464436694979668, -0.004621684085577726, 0.025421231985092163, -0.012470453046262264, 0.019815918058156967, -0.06829369068145752, 0.0014561931602656841, -0.01421049702912569, 0.002748510567471385, -0.03504451364278793, 0.00939761009067297, 0.01639845222234726, -0.025288747623562813, 0.060319364070892334, -0.03810911253094673, 0.004097619093954563, 0.04556186497211456, -0.004195804242044687, -0.040042195469141006, 0.00024950719671323895, 0.05807819217443466, 0.029044870287179947, 0.027937812730669975, 0.01210466492921114, -0.02893606200814247, -0.045855794101953506, 0.047807786613702774, 0.016496362164616585, 0.027927733957767487, -0.005548705812543631, 0.011231105774641037, -0.05459023267030716, -0.02621244452893734, 0.0911245197057724, -0.023035597056150436, 0.028348324820399284, 0.009409003891050816, 0.0648927167057991, 0.015353250317275524, 0.04145153984427452, 0.032149482518434525, -0.02111324854195118, 0.02051984705030918, 0.01550800446420908, -0.05147653445601463, -0.027487503364682198, -6.0753405141334454e-33, -0.019371217116713524, -0.050359632819890976, 0.0021800589747726917, -0.019527053460478783, -0.0241075586527586, 0.05988992005586624, -0.059235624969005585, -0.019865550100803375, 0.006671019364148378, 0.016054827719926834, -0.018908416852355003, -0.007542193401604891, 0.0020406576804816723, 0.0447247251868248, 0.039148975163698196, -0.03959377482533455, 0.005212847143411636, -0.009043494239449501, 0.0334189236164093, 0.021486669778823853, 0.0183261651545763, 0.08163030445575714, 0.05428307130932808, -0.09206191450357437, -0.008927245624363422, -0.008625784888863564, -0.00016354980471078306, -0.004789690021425486, 0.013150906190276146, 0.03100813366472721, -0.05053763836622238, 0.03888783976435661, 0.04658118635416031, -0.05316903814673424, -0.0016859711613506079, 0.05034984275698662, -0.07232561707496643, -0.07461357116699219, -0.05069756880402565, -0.005854652263224125, -0.020271748304367065, 0.02178359217941761, 0.04273521155118942, -0.001543325139209628, 0.003824572777375579, 0.05152389779686928, 0.05592077597975731, -0.02045462466776371, -0.016694610938429832, -0.04355519264936447, -0.04161044955253601, 0.0036712728906422853, 0.023575590923428535, 0.025138476863503456, -0.023268140852451324, -0.014386502094566822, -0.021920310333371162, 0.08409284055233002, -0.09920373558998108, -0.041059378534555435, -0.027859022840857506, 0.0285175871104002, 0.00829132180660963, 0.011783832684159279, 0.0038786542136222124, 0.039936814457178116, -0.03275769203901291, 0.017981162294745445, -0.09048350900411606, -0.0038231154903769493, -0.013259527273476124, 0.029390985146164894, 0.07118688523769379, -0.028602559119462967, 0.04188491031527519, -0.0709075927734375, -0.08286000788211823, 0.03039686009287834, -0.017385434359312057, 0.04381367191672325, 0.005137222353368998, -0.022340089082717896, -0.031951241195201874, -0.014082487672567368, 0.027860112488269806, -0.01532724592834711, -0.019044697284698486, -0.028109759092330933, 0.031154243275523186, -0.015318470075726509, 0.038998398929834366, 0.03346532583236694, -0.038445692509412766, -0.04430537298321724, 0.023641087114810944, -0.04065898805856705, 0.05539468303322792, 0.00404294254258275, 0.0018269616411998868, -0.017818190157413483, -0.04709120839834213, -0.018046336248517036, -0.01440782006829977, 0.02974485233426094, 0.030928321182727814, -0.0008302318165078759, 0.022141411900520325, -0.03808815777301788, -0.03964553773403168, -0.04149601235985756, 0.012520860880613327, -0.043878279626369476, 0.028111625462770462, 0.059116214513778687, -0.021723687648773193, -0.01248700451105833, -0.012342400848865509, 0.08512185513973236, 0.03822104260325432, -0.016365595161914825, -0.030692534521222115, -0.05433907359838486, 0.026363400742411613, 0.008756117895245552, -0.07809611409902573, -0.04030648618936539, -0.02810535579919815, 0.014130414463579655, 0.04318546503782272, -0.04861917719244957, -0.01797415502369404, 0.005278349854052067, 2.963180065762572e-07, 0.028345707803964615, 0.028323590755462646, 0.020575253292918205, -0.07302649319171906, 0.025572972372174263, 0.022660696879029274, 0.007286811713129282, 0.023416003212332726, -0.02283572219312191, -0.05541180074214935, 0.0462811142206192, -0.03481058403849602, 0.01319758128374815, 0.011033851653337479, -0.09147556126117706, -0.039590053260326385, -0.08728799223899841, -0.0021581826731562614, -0.0316707044839859, -0.03327672556042671, 0.0326867401599884, 0.10733701288700104, 0.04106724262237549, -0.03457939252257347, 0.011598700657486916, 0.02971295639872551, -0.008491428568959236, 0.014251005835831165, 0.03934360295534134, -0.0032314222771674395, 0.0011901349062100053, 0.025948669761419296, -0.037443600594997406, -0.0009115388966165483, -0.023327892646193504, 0.010157101787626743, 0.026226500049233437, 0.043921541422605515, -0.060446225106716156, 0.001084781950339675, 0.025915812700986862, 0.008234526962041855, 0.023196974769234657, -0.039502497762441635, 0.046546097844839096, -0.05515405163168907, -0.051934633404016495, 0.0021535498090088367, 0.027552755549550056, 0.03989172354340553, 0.06945601850748062, 0.003731159260496497, -0.022850798442959785, 0.013294682838022709, 0.004396115429699421, -0.001100310473702848, -0.01733921840786934, -0.06931174546480179, 0.018775321543216705, 0.028213130310177803, -0.011122606694698334, 0.017932172864675522, 0.026576664298772812, -0.02312583103775978, 0.03981144726276398, -0.039979226887226105, -0.01659185066819191, 2.914112943825838e-34, -0.01759326085448265, -0.03715114668011665, -0.00988060887902975, 0.04563833773136139, -0.021023739129304886, -0.012845538556575775, -0.011254334822297096, 0.02059747464954853, 0.015558124519884586, -0.02516850084066391, -0.02213531732559204]

['Tsung-Hsien Wen', 'Yishu Miao', 'Phil Blunsom', 'Steve Young']

1705.10229v1

Developing a dialogue agent that is capable of making autonomous decisions and communicating by natural language is one of the long-term goals of machine learning research. Traditional approaches either rely on hand-crafting a small state-action set for applying reinforcement learning that is not scalable or constructing deterministic models for learning dialogue sentences that fail to capture natural conversational variability. In this paper, we propose a Latent Intention Dialogue Model (LIDM) that employs a discrete latent variable to learn underlying dialogue intentions in the framework of neural variational inference. In a goal-oriented dialogue scenario, these latent intentions can be interpreted as actions guiding the generation of machine responses, which can be further refined autonomously by reinforcement learning. The experimental evaluation of LIDM shows that the model out-performs published benchmarks for both corpus-based and human evaluation, demonstrating the effectiveness of discrete latent variable models for learning goal-oriented dialogues.

Latent Intention Dialogue Models

http://arxiv.org/pdf/1705.10229v1

Title Latent Intention Dialogue Models Summary Developing dialogue agent capable making autonomous decision communicating natural language one longterm goal machine learning research Traditional approach either rely handcrafting small stateaction set applying reinforcement learning scalable constructing deterministic model learning dialogue sentence fail capture natural conversational variability paper propose Latent Intention Dialogue Model LIDM employ discrete latent variable learn underlying dialogue intention framework neural variational inference goaloriented dialogue scenario latent intention interpreted action guiding generation machine response refined autonomously reinforcement learning experimental evaluation LIDM show model outperforms published benchmark corpusbased human evaluation demonstrating effectiveness discrete latent variable model learning goaloriented dialogue Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.10098562389612198, 0.06708446890115738, -0.01680503971874714, 0.022988336160779, -0.03346974030137062, -0.0035950455348938704, -0.0012845752062276006, -0.02798912487924099, 0.008067675866186619, -0.06890923529863358, 0.009950743988156319, 0.010213034227490425, -0.046132877469062805, 0.0958106741309166, 0.007869823835790157, -0.07604578137397766, 0.01851295307278633, 0.0009095752029679716, 0.05694097653031349, 0.012174734845757484, 0.04425961524248123, 0.01235037948936224, -0.03409133478999138, 0.040643878281116486, -0.027288461104035378, -0.002838567364960909, -0.07483398169279099, -0.0073000285774469376, -0.0018965931376442313, -0.01999506726861, 0.05177636444568634, 0.04768292233347893, 0.06269469112157822, 0.017846331000328064, 2.153864443243947e-06, -0.0537632592022419, 0.019571729004383087, -0.044105976819992065, -0.010949167422950268, -0.06352858990430832, 0.0399910993874073, 0.00668722577393055, -0.0028148542623966932, 0.028313346207141876, -0.04714246839284897, 0.0015938858268782496, 0.03647881746292114, 0.08941104263067245, 0.04782770574092865, 0.0740506649017334, -0.016430769115686417, -0.04221002757549286, -0.005826539359986782, 0.012999597936868668, 0.010662153363227844, -0.04324779286980629, 0.011406231671571732, 0.013039777055382729, -0.016044050455093384, -0.001682881498709321, -0.002469408791512251, -0.012231629341840744, -0.034146443009376526, -0.0718090608716011, -0.014335205778479576, 0.024165118113160133, 0.01530967466533184, -0.07300595194101334, -0.03681597113609314, 0.08426669239997864, 0.06940365582704544, -0.004582833964377642, 0.025357238948345184, -0.021261679008603096, 0.0024387920275330544, -0.001731253694742918, -0.013951433822512627, 0.02461576834321022, 0.0029515009373426437, -0.0006542947958223522, 0.02381615713238716, 0.02381664328277111, -0.010830143466591835, 0.041599374264478683, -0.000591169111430645, 0.026623062789440155, 0.00528490636497736, -0.031266454607248306, -0.021358471363782883, -0.0018068825593218207, -0.007337184622883797, -0.09463159739971161, -0.015831682831048965, 0.037110812962055206, -0.10681775957345963, 0.038958098739385605, -0.04290654882788658, -0.022819528356194496, 0.03454829379916191, -0.025386786088347435, 0.023992128670215607, 0.04785466566681862, 0.01586623676121235, 0.031198522076010704, 0.05394631251692772, 0.05457970127463341, -0.01724427193403244, 0.011644450016319752, -0.016497692093253136, 0.013696210458874702, -0.02022242732346058, -0.0007712746155448258, -0.04643283411860466, 0.030616257339715958, -0.027424490079283714, -0.039774954319000244, -0.027525385841727257, 0.06077858433127403, 0.021204492077231407, 0.02431604452431202, 0.007364979479461908, 0.046199981123209, -0.02730511501431465, 0.004863286390900612, -0.05915428698062897, 0.012707595713436604, -0.0555768646299839, 0.052028946578502655, 0.005465553142130375, -0.031674325466156006, 0.015258850529789925, 0.05131004378199577, 0.0069679152220487595, 0.03263244777917862, 4.416604497237131e-05, 0.0959303006529808, -0.016028720885515213, -0.015509111806750298, -0.02348916605114937, -0.001396623207256198, -0.02773589827120304, -0.07202870398759842, -0.01893966645002365, -0.03494013100862503, 0.014878581278026104, -0.011776674538850784, -0.029653428122401237, 0.01574764959514141, 0.017698442563414574, 0.03314191475510597, 0.011842108331620693, 0.05428779870271683, 0.0013399802846834064, -0.00435195118188858, 0.06674022227525711, 0.001486918656155467, 0.019380051642656326, 0.04987383633852005, 0.047865141183137894, 0.01007594633847475, 0.02629072219133377, 0.008895421400666237, 0.0014341312926262617, -0.00039177865255624056, -0.01752919889986515, -0.026172589510679245, 0.01514752022922039, 0.026629969477653503, -0.037895675748586655, 0.04929827153682709, 0.010298320092260838, 0.07498493045568466, -0.03464245796203613, -0.014742592349648476, 0.06258935481309891, 0.07719817012548447, -0.022393984720110893, -0.0042147086933255196, 0.0359414778649807, 0.08700484037399292, -0.014282045885920525, 0.003632613690569997, -0.013354722410440445, 0.04236014932394028, 0.024060416966676712, -0.02295227162539959, 0.018518494442105293, -0.02116023376584053, -0.012116029858589172, -0.04930282011628151, 0.015679026022553444, -0.012344622984528542, 0.04352910444140434, -0.003663338953629136, 0.023534098640084267, -0.0004477820184547454, -0.04982621222734451, -0.00276607321575284, -0.004362633917480707, -0.014856294728815556, -0.06035635620355606, -0.0377875417470932, 0.06335734575986862, 0.016419023275375366, 0.029726773500442505, 0.007946193218231201, -0.02662738598883152, -0.060785923153162, -0.033866818994283676, 0.050215885043144226, 0.027761325240135193, -0.0405464731156826, 0.000240653011132963, -0.058431610465049744, 0.0012086437782272696, -0.013943243771791458, -0.00527665950357914, 0.01371312141418457, -0.02110382542014122, -0.005773814395070076, -0.013346799649298191, 0.061928641051054, 0.03719399496912956, 0.0314350351691246, 0.01146914903074503, -0.016991736367344856, 0.018477007746696472, -0.009453830309212208, 0.06196162849664688, 0.026656778529286385, 0.009621590375900269, -0.008739052340388298, 0.023783519864082336, 0.029275374487042427, -0.05360130965709686, 0.025104638189077377, -0.03207810968160629, -0.0607382133603096, 0.010808274149894714, -0.014118008315563202, -0.003546009538695216, 0.01881350576877594, -0.023447997868061066, -0.0722927525639534, 0.0241981353610754, -0.04920255020260811, 0.003583417506888509, -0.05986536666750908, -0.00830561388283968, 0.00997597724199295, -0.007696556393057108, -0.02973802201449871, 0.02434595488011837, 0.010920433327555656, -0.014374581165611744, 0.022384466603398323, 0.05154164507985115, 0.04837130382657051, -0.04048994556069374, -0.008381064049899578, 0.003794457297772169, -0.008707228116691113, 0.011841039173305035, 0.04266238212585449, 0.038854457437992096, -0.05706297606229782, -0.02854079194366932, -0.08372480422258377, -0.01340243685990572, -0.031276509165763855, -0.0363474041223526, 0.00029193691443651915, 0.022329125553369522, -0.0071610757149755955, -0.03612256050109863, -0.0393124520778656, 0.0294563639909029, 0.061066579073667526, -0.01347389817237854, 0.06100527197122574, 0.0030931630171835423, -0.01121034100651741, -0.0645165741443634, 0.0397690050303936, -0.0037435926496982574, 0.0009230237919837236, 0.026339974254369736, -0.021866271272301674, -0.035750675946474075, 0.024339178577065468, -0.0242662001401186, 0.04186423122882843, -0.0332651361823082, -0.08202815800905228, 0.039831921458244324, -0.015304706059396267, 0.021606408059597015, 0.03144339099526405, 0.05277811735868454, 0.03672308474779129, 0.02474946528673172, 0.001382947899401188, -0.0662161260843277, 0.053231194615364075, -0.026251129806041718, 0.006411291658878326, -0.054721105843782425, 0.015296977013349533, 0.021908467635512352, 0.04599738493561745, 0.06311923265457153, 0.03906659781932831, -0.04056861251592636, 0.021244319155812263, 0.017147066071629524, -0.05581583455204964, -0.005482184235006571, -0.028406992554664612, -0.05759045481681824, 0.05374657362699509, 0.020445287227630615, -0.03567928820848465, 0.08342523872852325, 0.004873770289123058, -0.042900100350379944, -0.0528075136244297, -0.031058168038725853, -0.009244874119758606, 0.04261089861392975, -0.011098887771368027, 0.01872245781123638, -0.0031265709549188614, -0.035449665039777756, -0.038462717086076736, -0.016784049570560455, 0.021645313128829002, -0.011688168160617352, 0.03205639123916626, -0.05200207605957985, 0.012229455634951591, -0.0030112480744719505, -0.016988035291433334, -0.07515376806259155, -0.047297101467847824, -0.029995281249284744, 0.003937091678380966, 0.00892707146704197, -0.02316265180706978, -0.01585770584642887, 0.0033361874520778656, 0.011543002910912037, 0.018225518986582756, 0.00011953174544032663, -0.013472957536578178, -0.031097928062081337, 0.010695939883589745, 0.0832446813583374, 0.025209106504917145, -0.049394551664590836, 0.028190292418003082, 0.07801514863967896, 0.0339190773665905, -0.04062879830598831, 0.002142986748367548, -0.059411853551864624, 0.004367271903902292, 0.023089410737156868, -0.01009017787873745, -0.003646882250905037, 0.03266598656773567, 0.04969693720340729, -0.021054888144135475, 0.007444434799253941, 0.10381219536066055, 0.01391468197107315, -0.0548747293651104, -0.02623554691672325, -0.054493144154548645, 0.01409901399165392, 0.0073138149455189705, 0.0424405075609684, -0.0688469409942627, -0.021262597292661667, -0.03143558278679848, 0.0329778790473938, -0.02946828305721283, -0.027766235172748566, -0.008829791098833084, -0.06568131595849991, 0.047532662749290466, -0.03855519741773605, -0.0007419426110573113, 0.019972139969468117, -0.009436939842998981, 0.0054757436737418175, -0.02694585733115673, 0.012393400073051453, -0.00680104224011302, 0.01990245096385479, -0.009701751172542572, -0.004547358024865389, -0.007081999909132719, -0.02187514491379261, 0.010682612657546997, -0.029216064140200615, 0.0957551896572113, 0.07889476418495178, 0.06639063358306885, 0.011627818457782269, 0.012462508864700794, -0.024820245802402496, -0.0027158299926668406, -0.000693402485921979, -0.012574868276715279, 0.04269406571984291, -0.02725614793598652, 0.004521852359175682, -0.05028608441352844, 0.037229686975479126, -0.007536496501415968, 0.014296297915279865, 0.03430952876806259, 0.02661490999162197, -0.06377682834863663, 0.008207094855606556, -0.04757966846227646, 0.05880839750170708, 0.04670729115605354, 0.04597100615501404, 0.0034866612404584885, -0.04739554598927498, -0.05447059124708176, -0.023354854434728622, -0.028442971408367157, -0.009490687400102615, -0.003056006273254752, -0.03170351684093475, -0.008718207478523254, -0.007096681743860245, -0.08594077825546265, -0.0814705416560173, -0.0020718008745461702, 0.024013720452785492, 0.011625806801021099, -0.011393620632588863, 0.019783688709139824, 0.01288900338113308, 0.007679510861635208, -0.03826354071497917, 0.03576352819800377, 0.003881820710375905, -0.04932454600930214, -0.006998417433351278, 0.05754414200782776, -0.05337953194975853, 0.00560634583234787, -0.02747143618762493, -0.05459011346101761, -0.07367417961359024, -0.006224527955055237, 0.0590878389775753, 0.01084353867918253, 0.07229796051979065, -0.021459627896547318, -0.05305597186088562, 0.006720830220729113, -0.05211807042360306, -0.009503421373665333, 0.005380851216614246, 0.03534762188792229, 0.09027429670095444, -0.02263515442609787, 0.03522256761789322, -0.017929155379533768, 0.013659263029694557, -0.026374345645308495, 0.026213109493255615, -0.07337217032909393, -0.09535231441259384, 0.020604552701115608, -0.018170475959777832, 0.01355691533535719, 0.00584765849635005, 0.01685130037367344, -0.030915215611457825, 0.008676506578922272, -0.011021580547094345, -0.02667425572872162, -0.05933406203985214, 0.007044398691505194, -0.0036512487567961216, -0.00037681966205127537, -0.0082586370408535, -0.05596975237131119, -0.0702495351433754, 0.02214241772890091, 0.0379498265683651, 0.03508947044610977, 0.056007493287324905, 0.0316796749830246, -0.01867304928600788, -0.008706439286470413, -0.019667796790599823, 0.03597121685743332, 0.008289028890430927, 0.016498304903507233, 0.007685369811952114, 0.1306978315114975, 0.024141013622283936, -0.044357217848300934, 0.03158997744321823, 0.005080366972833872, -0.021698446944355965, -0.03831865265965462, -0.00020436204795259982, 0.031028997153043747, 0.03176923841238022, 0.005448414012789726, 0.01811935193836689, -0.03876262903213501, 0.04146646708250046, 0.008537148125469685, 0.0769025906920433, -0.03658369183540344, -0.034912109375, 0.06982829421758652, 0.002920574741438031, -0.023569859564304352, -0.014301147311925888, 0.01712626777589321, -0.0013673355570062995, 0.007099722512066364, -0.007951243780553341, 0.001365038100630045, -0.061560116708278656, 0.004366301465779543, 0.014290041290223598, 0.03729790449142456, -0.0019836584106087685, 0.02559557743370533, -0.0006397610413841903, -0.014493881724774837, -0.014602556824684143, 0.014165012165904045, 0.02357025258243084, -0.026040980592370033, 0.03394589573144913, 0.05439028888940811, 0.004220609553158283, -0.003946371842175722, -0.06687135249376297, -0.0061074187979102135, -0.025097930803894997, -0.028117036446928978, -0.10851281136274338, -5.872676471844052e-33, -0.02172466181218624, -0.03393716365098953, 0.049469225108623505, -0.013776556588709354, -0.05262535810470581, -0.04375838488340378, -0.049677591770887375, 0.0075398157350718975, -0.012566198594868183, 0.03172524273395538, -0.02656947448849678, 0.022991111502051353, 0.001849491847679019, 0.030788742005825043, 0.04637855291366577, -0.03763679787516594, 0.024377943947911263, -0.04470943287014961, 0.008677574805915356, 0.012514122761785984, 0.034688860177993774, 0.002045189030468464, -0.004136961884796619, -0.10179593414068222, 0.024582142010331154, -0.013544597662985325, -0.030181054025888443, 0.02486724592745304, -0.006255215499550104, 0.050631798803806305, -0.01671144738793373, -0.013257387094199657, 0.019657369703054428, 0.0020360853523015976, 0.00033525857725180686, 0.022705884650349617, -0.02033601701259613, -0.05139816179871559, 0.018062718212604523, 0.01626887172460556, -0.039762821048498154, -0.0012806614395231009, -0.019594339653849602, -0.03358805552124977, -0.016710301861166954, 0.060148563235998154, 0.023325493559241295, 0.02142435498535633, 0.01907236874103546, -0.008838153444230556, -0.064593106508255, 0.002589137526229024, -0.027974385768175125, -0.017438583076000214, -0.008909551426768303, 0.022748690098524094, -0.003000041702762246, -0.02966885082423687, -0.02495935745537281, 0.04765124246478081, -0.014719675295054913, -0.03623819723725319, 0.04342905431985855, 0.04391903430223465, -0.002259155036881566, 0.04859065264463425, 0.005621132906526327, -0.00545874098315835, -0.03227178379893303, 0.0015298724174499512, -0.009921186603605747, 0.041356299072504044, 0.011646699160337448, 0.05391446501016617, -0.029680870473384857, 0.028631769120693207, -0.03347519785165787, 0.013242009095847607, 0.037583112716674805, 0.044491712003946304, 0.013368691317737103, 0.012396321631968021, -0.028680995106697083, -0.004328046925365925, -0.010572545230388641, -0.008091786876320839, -0.01929105445742607, -0.05448673665523529, 0.025171974673867226, 0.012092222459614277, 0.0063785044476389885, -0.07276870310306549, 0.024920813739299774, -0.03041014075279236, 0.011634263209998608, 0.00977748166769743, -0.03267211467027664, 0.011193309910595417, -0.008521928451955318, 0.005096599459648132, -0.06965237110853195, 0.012611351907253265, 0.04956652596592903, -0.002252963837236166, 0.003992460202425718, 0.02745959162712097, -0.05947055295109749, 0.013913178816437721, -0.01653609424829483, -0.006303898058831692, 0.002970290370285511, 0.012771327048540115, -0.03529450297355652, 0.04948751628398895, -0.021594226360321045, -0.0246152151376009, -0.05136164277791977, 0.07302819937467575, -0.012527230195701122, -0.024751225486397743, -0.055089134722948074, -0.04003095254302025, 0.01973237842321396, 0.012786072678864002, -0.06449008733034134, 0.02407955937087536, -0.031969234347343445, 0.015230445191264153, 0.008034773170948029, -0.02938472293317318, 0.016605600714683533, 0.011701326817274094, 2.741347202572797e-07, -0.01976940408349037, 0.03748326376080513, -0.004094304516911507, 0.048978306353092194, 0.006079190876334906, 0.06346834450960159, -0.009626670740544796, 0.04764368385076523, 0.012501576915383339, 9.179151675198227e-05, 0.03633350133895874, -0.009565617889165878, 0.011149412952363491, -0.0093704704195261, -0.09118390828371048, -0.038009412586688995, -0.04129531979560852, -0.023778388276696205, -0.033390242606401443, 0.013108243234455585, 0.09404613077640533, 0.06946972012519836, 0.017719140276312828, 0.0025750950444489717, 0.0033791139721870422, 0.017967352643609047, 0.01992866024374962, -0.01449368242174387, -0.008883552625775337, 0.006816822104156017, 0.056036245077848434, -0.01692074164748192, -0.01816185750067234, -0.003152927616611123, -0.0012186175445094705, 0.03510098531842232, -0.036028992384672165, 0.08373552560806274, 0.0034919297322630882, -0.04876506328582764, 0.0030159105081111193, 0.01178805623203516, 0.029489928856492043, -0.03457288816571236, 0.030672326683998108, -0.01872103661298752, -0.03136911615729332, -0.004852386191487312, 0.011828761547803879, -0.007405125070363283, 0.01101896446198225, -0.02738095261156559, -0.020278047770261765, -0.020922381430864334, 0.003929768688976765, -0.01584082469344139, 0.022162845358252525, -0.06939606368541718, 0.015797069296240807, -0.050366997718811035, -0.04632456228137016, -0.023654894903302193, -0.0328998938202858, -0.003392221638932824, 0.03221495449542999, -0.03428885340690613, -0.011996890418231487, 2.295397920755258e-34, 0.022767459973692894, -0.006679482292383909, -0.022979695349931717, 0.04329482093453407, 0.02675953321158886, 0.023855965584516525, 0.03153839334845543, 0.02349986881017685, 0.06686192750930786, -0.10059232264757156, -0.034122418612241745]

['Julius Kunze', 'Louis Kirsch', 'Ilia Kurenkov', 'Andreas Krug', 'Jens Johannsmeier', 'Sebastian Stober']

1706.00290v1

End-to-end training of automated speech recognition (ASR) systems requires massive data and compute resources. We explore transfer learning based on model adaptation as an approach for training ASR models under constrained GPU memory, throughput and training data. We conduct several systematic experiments adapting a Wav2Letter convolutional neural network originally trained for English ASR to the German language. We show that this technique allows faster training on consumer-grade resources while requiring less training data in order to achieve the same accuracy, thereby lowering the cost of training ASR models in other languages. Model introspection revealed that small adaptations to the network's weights were sufficient for good performance, especially for inner layers.

Transfer Learning for Speech Recognition on a Budget

http://arxiv.org/pdf/1706.00290v1

Title Transfer Learning Speech Recognition Budget Summary Endtoend training automated speech recognition ASR system requires massive data compute resource explore transfer learning based model adaptation approach training ASR model constrained GPU memory throughput training data conduct several systematic experiment adapting Wav2Letter convolutional neural network originally trained English ASR German language show technique allows faster training consumergrade resource requiring le training data order achieve accuracy thereby lowering cost training ASR model language Model introspection revealed small adaptation network weight sufficient good performance especially inner layer Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0016755897086113691, 0.05258483067154884, 0.018963608890771866, 0.055986594408750534, 0.007710160221904516, 0.02001683972775936, 0.020336255431175232, -0.012822264805436134, -0.012132210657000542, -0.04293149709701538, -0.052866131067276, 0.009552624076604843, 0.01511545479297638, 0.04265570268034935, 0.003736619371920824, -0.0619448721408844, 0.02879670448601246, -0.06268973648548126, 0.012504782527685165, -0.024022482335567474, 0.016340406611561775, 0.004718300886452198, -0.03330305963754654, 0.004178602714091539, -0.000572175020352006, 0.04881681129336357, 0.011079044081270695, 0.003983153961598873, 0.016942277550697327, -0.007615449372678995, -0.0006461124285124242, -0.00766100874170661, 0.041615091264247894, 0.033691730350255966, 2.0862526071141474e-06, -0.042189691215753555, -0.06136531010270119, -0.006654837168753147, -0.03543034568428993, -0.01854456216096878, 0.05103171989321709, -0.015948696061968803, -0.034376710653305054, 0.060481246560811996, -0.009097459726035595, -0.007109276484698057, 0.0669168084859848, 0.04283619299530983, 0.017998825758695602, 0.06969252228736877, -0.030510038137435913, -0.03184144198894501, 0.01648487150669098, 0.011566162109375, -0.062338605523109436, -0.09819754213094711, 0.02535232901573181, -0.000794346327893436, -0.01868136040866375, -0.04036758840084076, -0.03404882922768593, 0.04389575868844986, -0.010175894014537334, -0.048191700130701065, -0.022923048585653305, -0.02815709076821804, -0.042547911405563354, -0.00886473711580038, -0.037484996020793915, 0.022578220814466476, 0.0016201352700591087, -0.019122837111353874, 0.007768918760120869, -0.015464930795133114, -0.03011508472263813, -0.0016419454477727413, -0.037186309695243835, -0.0032675645779818296, 0.012626790441572666, 0.020538371056318283, 0.0010459694312885404, 0.009769903495907784, 0.004609567578881979, 0.0009371432824991643, -0.03189656510949135, 0.005873951595276594, 0.009229159913957119, 0.0019734143279492855, 0.05131520330905914, 0.009128185920417309, 0.014442221261560917, -0.0023390264250338078, 0.06063031405210495, -0.004779350478202105, 0.00038148852763697505, 0.02056039497256279, -0.04869799315929413, -0.07639074325561523, -0.031717803329229355, -0.0431339405477047, 0.06255465000867844, 0.012231939472258091, -0.019939426332712173, 0.016823990270495415, -0.03656674921512604, 0.04741940647363663, 0.010242702439427376, -0.012117772363126278, -0.04791461303830147, -0.027118656784296036, -0.04444451630115509, 0.023468036204576492, -0.08001935482025146, 0.021365173161029816, -0.018108906224370003, -0.05761662498116493, -0.025607671588659286, 0.00310503994114697, 0.0022473300341516733, -0.05443340539932251, 0.051519665867090225, -0.007776839192956686, -0.007393718231469393, 0.007503180764615536, 0.032885387539863586, 0.07937870919704437, 0.047234319150447845, 0.05364891514182091, -0.026262281462550163, -0.0739276185631752, 0.03616856038570404, 0.026967111974954605, 0.04996185749769211, -0.0018213755683973432, 0.01571671850979328, 0.06055188551545143, -0.008649786934256554, 0.001390520017594099, -0.05030839517712593, 0.08644773066043854, -0.002944140462204814, -0.011862669140100479, 0.009937855415046215, -0.007232354953885078, 0.02071881853044033, 0.00287112919613719, 0.005189053248614073, -0.028447892516851425, -0.0010513309389352798, -0.004957397468388081, -0.023628223687410355, 0.06449360400438309, -0.05394531041383743, -0.005160641856491566, 0.0731675773859024, -0.03297773748636246, 0.010020926594734192, 0.039538171142339706, 0.05768905580043793, -0.015272061340510845, -0.01892821118235588, -0.08086463063955307, -0.03359229862689972, 0.03872087597846985, -0.02220837026834488, 0.00170717213768512, -0.02344503067433834, -0.02746361494064331, 0.019478537142276764, 0.01120765134692192, 0.06501996517181396, 0.06926142424345016, 0.02832084149122238, 0.001292200293391943, 0.03146735951304436, 0.03987540677189827, 0.04615949094295502, 0.01308075524866581, -0.00083546171663329, 0.010283232666552067, -0.0012602882925421, -0.05680086091160774, -0.0019651977345347404, 0.005490455776453018, -0.03018532320857048, -0.032532066106796265, -0.01512621808797121, -0.007182053290307522, -0.004477126058191061, -0.006785803008824587, 0.003718574298545718, 0.004268840420991182, 0.0034494788851588964, 0.020358186215162277, 0.06933030486106873, 0.023685786873102188, -0.04341984540224075, 0.004544560331851244, 0.02375902608036995, -0.017261669039726257, 0.00941407959908247, -0.06795820593833923, -0.004882500506937504, 0.008900396525859833, 0.0077461670152843, -0.0339181050658226, -0.028588097542524338, -0.009642277844250202, -0.012850064784288406, 0.014844219200313091, 0.012544450350105762, 0.0060821883380413055, 0.03466019406914711, -0.08355961740016937, 0.008996100164949894, 0.050677619874477386, -0.020742440596222878, 0.06742390245199203, -0.04119529202580452, 0.03739102557301521, 0.015160809271037579, 0.0314873531460762, -0.011338681913912296, 0.009106352925300598, 0.003205063985660672, -0.04119878634810448, 0.060438454151153564, 0.008535291068255901, 0.07499666512012482, 0.024791328236460686, 0.007627773564308882, -0.03867428004741669, 0.022855276241898537, -0.03134308382868767, 0.02005472406744957, 0.0148704769089818, -0.06339365988969803, 0.006216865032911301, 0.04343714192509651, 0.034053169190883636, 0.09134962409734726, 0.042793676257133484, -0.012429492548108101, -0.0810827761888504, 0.04228639602661133, -0.02695300057530403, 0.0645354688167572, -0.01703687012195587, 0.07210397720336914, 0.05279291048645973, 0.07140601426362991, 0.0035292431712150574, -0.015617645345628262, 0.0669458732008934, -0.04273458570241928, -0.021382683888077736, 0.02177010476589203, 0.015317409299314022, -0.04845985770225525, 0.0020069151651114225, 0.04097424075007439, -0.03459884598851204, 0.01651868037879467, -0.004890548996627331, -0.011310800909996033, -0.014643242582678795, 0.01924072578549385, -0.05073556676506996, -0.009149701334536076, 0.0025258874520659447, 0.031541209667921066, -0.006239400710910559, 0.03337264433503151, 0.004364462569355965, -0.04881739616394043, -0.012352443300187588, 0.025762612000107765, -0.007946579717099667, -0.013436933048069477, -0.019903572276234627, -0.0079162223264575, -0.0074020614847540855, -0.018663380295038223, -0.008269958198070526, 0.014119095169007778, 0.011157366447150707, -0.025425804778933525, -0.07431146502494812, -0.0654015839099884, 0.009358655661344528, 0.03317493200302124, 0.048324890434741974, 0.012537090107798576, -0.009734420105814934, -0.025122033432126045, 0.01668422855436802, -0.005778172519057989, 0.011925007216632366, 0.009951593354344368, -0.010194240137934685, 0.004425876773893833, 0.006592912133783102, -0.019689084962010384, 0.0010545398108661175, 0.032044991850852966, -0.004234383348375559, -0.004275488667190075, 0.021543165668845177, -0.043827302753925323, 0.028582116588950157, -0.0048500546254217625, 0.0346917025744915, -0.019568953663110733, -0.02052576094865799, -0.04353178292512894, -0.017753323540091515, -0.038427840918302536, -0.00608453992754221, -0.018975937739014626, -0.020209452137351036, 0.01129803154617548, -0.013963496312499046, -0.037296224385499954, -0.055369965732097626, -0.019926050677895546, -0.07628698647022247, -0.07293578237295151, -0.010981310158967972, 0.010623808950185776, -0.0045862337574362755, 0.016371097415685654, -0.019488366320729256, -0.03726470097899437, 0.015006981790065765, -0.006497313734143972, 0.004218426067382097, -0.03788450360298157, 0.0075545706786215305, -0.05043720453977585, 0.034713275730609894, -0.06181572005152702, -0.024554060772061348, -0.02707265503704548, 0.053320467472076416, -0.05259907990694046, 0.03651761636137962, 0.0018598065944388509, -0.02617952600121498, -0.0016880132025107741, 0.03546423837542534, 0.016899432986974716, 0.10255619883537292, 0.029558751732110977, 0.02079237625002861, -0.03543597832322121, 0.04786815494298935, 0.0619988888502121, 0.04403496906161308, -0.02868659421801567, 0.0234433114528656, 0.01620888151228428, -0.01154534611850977, 0.012806568294763565, 0.0008350115385837853, -0.09047646820545197, 0.007895451039075851, 0.053005196154117584, -0.017744699493050575, 0.011834952980279922, 0.0077944849617779255, 0.03990809619426727, -0.06095089763402939, 0.030639145523309708, 0.04168695956468582, -0.01883607730269432, -0.04939521476626396, -0.021080337464809418, -0.02348407171666622, -0.027278319001197815, -0.009258575737476349, 0.013585527427494526, -0.005184789653867483, -0.01634504646062851, 0.04178594797849655, 0.02980421856045723, 0.017485788092017174, 0.006200496107339859, -0.04125720635056496, -0.09846409410238266, 0.02647116594016552, -0.006979102734476328, -0.059066180139780045, -0.033214814960956573, -0.06134926527738571, 0.000285103713395074, -0.017616668716073036, 0.055822115391492844, -0.009896441362798214, -0.019904030486941338, -0.041547663509845734, 0.05714663863182068, -0.06714503467082977, -0.028031757101416588, -0.01549039501696825, 0.0009049047948792577, 0.08438996225595474, 0.0728902593255043, 0.023801200091838837, -0.03683796525001526, -0.019970564171671867, 0.019200868904590607, -0.03232854604721069, 0.02005649171769619, -0.05111647769808769, 0.03042534366250038, 0.02858445607125759, -0.013578908517956734, 0.014213252812623978, 0.03912621736526489, -0.03440291807055473, -0.002370256232097745, 0.042699333280324936, 0.026352345943450928, 0.016979238018393517, -0.04013221710920334, 0.011535701341927052, -0.01672682911157608, 0.029310686513781548, 0.024410905316472054, -0.011129582300782204, -0.021763300523161888, 0.008221633732318878, 0.01580667309463024, 0.006193993613123894, -0.01982945390045643, 0.0026551673654466867, 0.02877202257514, -0.02023274637758732, -0.0552031584084034, -0.037185125052928925, 0.02704191766679287, 0.012886889278888702, 0.05401473492383957, 0.06048787385225296, 0.046080633997917175, 0.012866630218923092, 0.028130222111940384, -0.0442749485373497, -0.015115419402718544, -0.017860576510429382, 0.037895575165748596, -0.06487729400396347, -0.02488102950155735, 0.014811260625720024, -0.05997488275170326, 0.004580333363264799, -0.05290065333247185, 0.0007584142149426043, -0.03402397781610489, 0.02174624241888523, 0.004105225671082735, 0.005459867417812347, 0.014320611022412777, -0.0415852852165699, -0.05852479115128517, 0.03551466017961502, -0.018971996381878853, -0.03633857145905495, 0.01063353568315506, 0.057744286954402924, 0.00874835904687643, -0.0272090844810009, 0.011560945771634579, -0.01905912347137928, 0.05055232718586922, 0.018271038308739662, -0.025705240666866302, 0.0008273341809399426, -0.04046660289168358, -0.0064349183812737465, 0.04582091048359871, 0.022626668214797974, -0.004568409640341997, -0.01897546462714672, -0.05270232632756233, 0.03301352262496948, 0.002177401212975383, 0.07910443842411041, -0.06440893560647964, -0.0012991413241252303, 0.02622208185493946, 0.026887673884630203, -0.013280692510306835, -0.02863270230591297, 0.007984723895788193, -0.09598096460103989, 0.016812866553664207, 0.11473365128040314, 0.0359744168817997, 0.05369479954242706, 0.02674182318150997, 0.01321974117308855, 0.0008454827475361526, -0.003147185780107975, 0.0891696885228157, 0.035729896277189255, -0.016100026667118073, 0.005204245448112488, -0.004269384779036045, 0.007545543368905783, 0.01852072775363922, 0.023949066177010536, 0.017544355243444443, -0.03419295325875282, -0.043342649936676025, 0.04560566693544388, 0.006231233477592468, -0.042239584028720856, 0.07287105172872543, 0.021142978221178055, 0.035848360508680344, -0.05921795964241028, 0.03683173656463623, -0.034901637583971024, 0.04082056134939194, 0.021249093115329742, -0.009686029516160488, -0.0018475877586752176, 0.06056267395615578, 0.0055024330504238605, 0.010581761598587036, 0.04814870283007622, -0.004891838878393173, 0.03065555728971958, -0.035695794969797134, -0.01635129377245903, -0.011402691714465618, -0.030498499050736427, -0.028639327734708786, 0.03688006475567818, 0.03889244794845581, -0.07018980383872986, -0.02441704273223877, -0.07065971940755844, 0.03611895442008972, -0.04258135333657265, -0.006778777111321688, -0.02693329006433487, -0.02726968750357628, 0.014458278194069862, -0.002995482413098216, -0.022634411230683327, -0.002669393550604582, -0.012224128469824791, 0.014698795042932034, -6.3712175850232e-33, -0.025002028793096542, 0.0410197488963604, 0.02477513998746872, -0.028209367766976357, -0.04304072633385658, 0.0036263668444007635, -0.018913300707936287, -0.003719592234119773, -0.031553786247968674, -0.022723332047462463, -0.03114834427833557, -0.03850875422358513, 0.0478968508541584, 0.02234065718948841, -0.003507432760670781, 0.024657675996422768, 0.0604601614177227, -0.009079224430024624, 0.020077314227819443, -0.010610034689307213, 0.03535349667072296, 0.08051726222038269, 0.07881700247526169, -0.08668790757656097, -0.0949995219707489, 0.06253521889448166, 0.016320187598466873, -0.04569847509264946, 0.041600871831178665, -0.01520642638206482, 0.007960768416523933, 0.044570229947566986, 0.018653657287359238, -0.015986725687980652, -0.006809184327721596, 0.034880224615335464, -0.06873884797096252, 0.00764393201097846, -0.01721157692372799, 0.09283304214477539, 0.013276060111820698, -0.03643028438091278, 0.030551904812455177, 0.009001566097140312, -0.02825593762099743, 0.013583648018538952, 0.02117319218814373, -0.05882188677787781, -0.029522597789764404, -0.009572755545377731, -0.05936285853385925, 0.04428765922784805, -0.00972905382514, 0.01056759711354971, 0.06733617186546326, 0.02100246213376522, -0.0471939817070961, -0.04522846266627312, -0.04282240569591522, 0.022235486656427383, 0.00494106812402606, 0.057930927723646164, 0.04116851091384888, 0.03551812097430229, -0.020771272480487823, -0.021299967542290688, 0.03965179994702339, -0.09328479319810867, 0.04251856356859207, -0.04621326923370361, 0.04010878503322601, 0.03270967677235603, 0.0196874737739563, -0.0023945423308759928, 0.06273066252470016, -0.062117110937833786, -0.031880151480436325, -0.032998327165842056, 0.00966551061719656, 0.004931746982038021, -0.001475629978813231, 0.04116201400756836, -0.03533061966300011, -0.0027520544826984406, -0.023648187518119812, -0.008975546807050705, -0.014838963747024536, -0.04015638679265976, 0.07109688967466354, -0.015254223719239235, -0.013828945346176624, -0.004989790264517069, 0.04717949405312538, -0.0567597858607769, 0.02021726220846176, -0.03682894632220268, 0.015406463295221329, -0.021963326260447502, -0.013531447388231754, 0.01151900552213192, -0.06644049286842346, -0.055954158306121826, 0.016190074384212494, 0.033187370747327805, 0.018876351416110992, -0.02457437850534916, 0.004822628106921911, 0.06995268166065216, -0.04323432222008705, -0.018121041357517242, -0.0018353185150772333, 0.023019932210445404, 0.030206535011529922, 0.07423517853021622, -0.011101169511675835, -0.04489000514149666, 0.004349926020950079, 0.017498083412647247, -0.0161608774214983, -0.01795877330005169, -0.007944369688630104, -0.02648928202688694, 0.03472164645791054, 0.019825706258416176, -0.10111688822507858, 0.00862344540655613, -0.00618003960698843, 0.011183306574821472, 0.029541486874222755, -0.01109693106263876, -0.017983512952923775, 0.019230516627430916, 2.7844964733958477e-07, -0.014380956068634987, 0.03580878674983978, -0.013501932844519615, -0.04563535377383232, -0.03672415018081665, -0.020735548809170723, 0.007534799166023731, 0.012229414656758308, 0.01531823631376028, 0.08131774514913559, 0.0009193434962071478, -0.005007319152355194, 0.08140626549720764, 0.015447397716343403, -0.06396211683750153, -0.06908097863197327, -0.05970649793744087, 0.050965942442417145, 0.02039610594511032, 0.05138074979186058, 0.010686974041163921, 0.09838810563087463, -0.0020872363820672035, -0.060956452041864395, 0.02683156356215477, -0.014055207371711731, -0.022474706172943115, -0.01939385198056698, 0.06317213922739029, -0.0009086806094273925, -0.006531869526952505, -0.01614692062139511, -0.042548201978206635, 0.02815777249634266, -0.040963150560855865, 0.05931580066680908, 0.03352493792772293, 0.012549174018204212, -0.06547701358795166, -0.010531972162425518, 0.023270392790436745, 0.04530494287610054, 0.010139946825802326, -0.010190923698246479, 0.04279176890850067, 0.008276606909930706, -0.036385878920555115, -0.06394321471452713, -0.041169483214616776, -0.0082227298989892, -0.029660791158676147, 0.010606744326651096, 0.04458250477910042, -0.0035114993806928396, 0.022040309384465218, -0.02086521126329899, -0.06993798911571503, -0.039926815778017044, 0.03450290486216545, -0.007463653571903706, -0.020923614501953125, -0.01097989920526743, -0.03076469898223877, -0.008670531213283539, 0.00587054155766964, 0.009043097496032715, 0.04452260211110115, 1.9830849133648637e-34, -0.010228632017970085, -0.019919604063034058, 0.008966321125626564, 0.010138769634068012, -0.006306642200797796, -0.029738055542111397, 0.01845344342291355, 0.05385586991906166, -0.0330350436270237, -0.0700848326086998, -0.04484691098332405]

['Matt Shannon']

1706.02776v1

State-level minimum Bayes risk (sMBR) training has become the de facto standard for sequence-level training of speech recognition acoustic models. It has an elegant formulation using the expectation semiring, and gives large improvements in word error rate (WER) over models trained solely using cross-entropy (CE) or connectionist temporal classification (CTC). sMBR training optimizes the expected number of frames at which the reference and hypothesized acoustic states differ. It may be preferable to optimize the expected WER, but WER does not interact well with the expectation semiring, and previous approaches based on computing expected WER exactly involve expanding the lattices used during training. In this paper we show how to perform optimization of the expected WER by sampling paths from the lattices used during conventional sMBR training. The gradient of the expected WER is itself an expectation, and so may be approximated using Monte Carlo sampling. We show experimentally that optimizing WER during acoustic model training gives 5% relative improvement in WER over a well-tuned sMBR baseline on a 2-channel query recognition task (Google Home).

Optimizing expected word error rate via sampling for speech recognition

http://arxiv.org/pdf/1706.02776v1

Title Optimizing expected word error rate via sampling speech recognition Summary Statelevel minimum Bayes risk sMBR training become de facto standard sequencelevel training speech recognition acoustic model elegant formulation using expectation semiring give large improvement word error rate WER model trained solely using crossentropy CE connectionist temporal classification CTC sMBR training optimizes expected number frame reference hypothesized acoustic state differ may preferable optimize expected WER WER interact well expectation semiring previous approach based computing expected WER exactly involve expanding lattice used training paper show perform optimization expected WER sampling path lattice used conventional sMBR training gradient expected WER expectation may approximated using Monte Carlo sampling show experimentally optimizing WER acoustic model training give 5 relative improvement WER welltuned sMBR baseline 2channel query recognition task Google Home Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0015462484443560243, 0.019713643938302994, 0.03889480233192444, 0.007201068103313446, -0.020102335140109062, -0.019838565960526466, 0.021725941449403763, -0.027281509712338448, -0.018865812569856644, -0.038721613585948944, -0.04394925385713577, -0.04947885125875473, 0.07006166875362396, 0.01906268671154976, -0.0026919839438050985, -0.07812347263097763, 0.011305534280836582, -0.05294278264045715, -0.008717389777302742, -0.01057430263608694, 0.013679270632565022, 0.010645647533237934, -0.06394362449645996, 0.02649129554629326, -0.010193330235779285, 0.057244252413511276, -0.0203765407204628, 0.01099068857729435, -0.01566801778972149, -0.0653262510895729, 0.007517563179135323, 0.04974003881216049, 0.04483652487397194, 0.008501688949763775, 2.3858133317844477e-06, -0.01248624175786972, -0.009959431365132332, -0.011251273564994335, -0.040126245468854904, -0.01357279159128666, 0.03636937588453293, -0.009774608537554741, -0.024064088240265846, 0.07294361293315887, 0.02160353772342205, -0.024194959551095963, 0.07243391871452332, 0.03498021885752678, -0.024648014456033707, 0.053304508328437805, -0.0029814857989549637, -0.026745997369289398, 0.015623502433300018, -0.02331545203924179, 0.008020862936973572, -0.052361324429512024, -0.009952324442565441, -0.006245684809982777, -0.007907708175480366, -0.03024759329855442, -0.056960392743349075, 0.03359677270054817, -0.030033469200134277, 0.003560418263077736, 0.00602690689265728, 0.056388624012470245, 0.012499404139816761, -0.007901418022811413, -0.05154400318861008, 0.06727562844753265, 0.03203839436173439, 0.0032554392237216234, 0.008381649851799011, 0.0018300834344699979, -0.053528085350990295, 0.018439562991261482, 0.021333817392587662, 0.0024367119185626507, -0.014886457473039627, 0.010364631190896034, -0.033560797572135925, 0.01226996909826994, -0.004294190090149641, -0.012968819588422775, -0.006753654684871435, 0.0321565605700016, -0.0018482651794329286, -0.05923796445131302, 0.025041036307811737, -0.045928146690130234, 0.04821581393480301, -0.039042167365550995, 0.05077187344431877, -0.012640860863029957, -0.005637648981064558, 0.025473320856690407, -0.06246703118085861, -0.08141062408685684, -0.006317750550806522, 0.000636893033515662, 0.0026646433398127556, 0.03360139578580856, 0.022103656083345413, 0.02792239375412464, 0.02886987291276455, 0.0065277270041406155, 0.019661948084831238, -0.0051262155175209045, -0.017383567988872528, 0.03450346738100052, -0.03917887061834335, 0.02338232845067978, -0.040671635419130325, 0.010780345648527145, -0.02446121536195278, -0.024690773338079453, -0.07035216689109802, -0.03336382284760475, 0.02609405666589737, -0.026159584522247314, 0.0367296002805233, 0.007468583527952433, -0.0357096865773201, -0.021458733826875687, -0.0007322566234506667, 0.015770647674798965, 0.03283242881298065, 0.0533900260925293, -0.024993257597088814, -0.06125884875655174, -0.007906985469162464, 0.0038901439402252436, 0.05140300840139389, -0.026712149381637573, 0.003956513479351997, 0.035465508699417114, 0.009329666383564472, -0.05266530439257622, -0.04770376905798912, 0.005032678134739399, -0.039025530219078064, 0.006461278069764376, -0.01744809001684189, -0.08114712685346603, 0.03195822611451149, -0.023861514404416084, -0.02335292659699917, 0.024042105302214622, 0.018858125433325768, -0.021150976419448853, -0.0017628808273002505, 0.05780660733580589, -0.025286490097641945, -0.012856724672019482, 0.09857285767793655, 0.003002976533025503, 0.07073099166154861, 0.06785484403371811, 0.0733318030834198, -0.027089644223451614, 0.039135340601205826, -0.005438751075416803, -0.01898418366909027, 0.05525710806250572, -0.014250602573156357, -0.0005517083336599171, -0.02477111481130123, -0.045332182198762894, 0.011551628820598125, 0.04817723482847214, 0.08600657433271408, 0.07708750665187836, -0.0502144992351532, -0.009015115909278393, 0.052957262843847275, 0.07084949314594269, 0.004045271314680576, -0.03264271467924118, 0.013203419744968414, 0.02305394969880581, 0.01663743145763874, -0.030634701251983643, 0.00716918520629406, 0.013215375132858753, 0.010337496176362038, 0.0077662393450737, 0.05904151871800423, -0.02283065766096115, -0.008385945111513138, -0.03525933250784874, -0.016900034621357918, -0.032353419810533524, -0.012163924984633923, 0.021020079031586647, 0.09063966572284698, -0.023819126188755035, -0.06022227182984352, 0.06166095286607742, 0.02356383390724659, -0.03768474981188774, 0.010678771883249283, -0.034293077886104584, 0.026252692565321922, 0.010109061375260353, 0.02814246155321598, -0.04080212488770485, 0.012908338569104671, -0.025582266971468925, -0.040911585092544556, 0.044206470251083374, 0.049052268266677856, -0.0057189129292964935, 0.058371830731630325, -0.07002192735671997, -0.03465845808386803, 0.07409258186817169, -0.019739743322134018, 0.022360000759363174, -0.017871301621198654, 0.027314575389027596, 0.032189447432756424, -0.032454635947942734, -0.019702153280377388, 0.02587130106985569, 0.015527872368693352, -0.032950934022665024, -0.014616509899497032, 0.01989813707768917, 0.0690380334854126, 0.02459787204861641, -0.029855061322450638, 0.009694335982203484, 0.008800879120826721, -0.02401505596935749, -0.014538413845002651, 0.0023653595708310604, -0.04023280367255211, -0.07595093548297882, 0.03293735533952713, -0.006621980108320713, 0.037218011915683746, 0.020622065290808678, 0.0058153714053332806, -0.07370439916849136, 0.016012007370591164, -0.04283823072910309, 0.0519021600484848, -0.05865853279829025, 0.04301745817065239, 0.017729032784700394, -0.006385230924934149, -0.014299938455224037, 0.00016141777450684458, -0.0027207364328205585, -0.0109748849645257, -0.020948637276887894, -0.019048722460865974, -0.008956839330494404, -0.08779305219650269, -0.02976585365831852, 0.04561008885502815, 0.002855521161109209, 0.01685725711286068, 0.006548708770424128, 0.01707427389919758, -0.06055821478366852, -0.008547148667275906, -0.07660022377967834, -0.021304046735167503, -0.011055049486458302, 0.057727012783288956, -0.0036371357273310423, 0.015422665514051914, -0.014832157641649246, -0.01833229511976242, -0.0005372439045459032, -0.02422594651579857, -0.01244516484439373, -0.031430263072252274, -0.04087855666875839, -0.021662432700395584, -0.03780638054013252, -0.05245208367705345, 0.016713982447981834, -0.014221140183508396, 0.00850575603544712, -0.0028988244011998177, -0.05118013173341751, -0.040720392018556595, 0.03174971789121628, 0.014106165617704391, 0.04095100983977318, 0.03548160195350647, -0.004832373932003975, -0.0011443935800343752, -0.036466315388679504, 0.006624277681112289, 0.0162500012665987, 0.03926704451441765, -0.012591390870511532, -0.012268953956663609, 0.01323619019240141, -0.04513853043317795, 0.01247453037649393, 0.015340014360845089, 0.03964401036500931, -0.018667683005332947, -0.031738150864839554, -0.017852405086159706, 0.0764261931180954, 0.058241765946149826, 0.06345221400260925, 0.0060746632516384125, -0.022606531158089638, -0.024957049638032913, -0.06869827955961227, -0.022528216242790222, -0.048570770770311356, -0.03183405473828316, -0.002728387713432312, -0.02569359540939331, -0.025255808606743813, 0.03520258888602257, -0.06000770255923271, -0.016730502247810364, -0.05068729445338249, -0.013530165888369083, 0.024886542931199074, 0.016358857974410057, -0.04078272730112076, 0.02300143986940384, -0.025604531168937683, -0.08834705501794815, -0.014966134913265705, -0.047102876007556915, 0.043777283281087875, -0.04774594306945801, 0.007563100662082434, -0.044142212718725204, 0.03205154091119766, -0.023935694247484207, -0.025694232434034348, -0.01669715903699398, 0.011296323500573635, -0.04565155878663063, -2.3240434529725462e-05, -0.009906726889312267, 0.016773514449596405, -0.012174597941339016, 0.045502737164497375, 0.02633499540388584, 0.06828905642032623, -0.014416541904211044, -0.024038584902882576, -0.0011069024913012981, 0.08875385671854019, 0.03425248712301254, 0.0389687642455101, -0.003019882831722498, -0.0008734301081858575, 0.026781242340803146, 0.033494334667921066, 0.11343283206224442, 0.0376790314912796, -0.04231816157698631, -0.003818739205598831, 0.06045382097363472, -0.030398042872548103, -0.03118930384516716, 0.04384868964552879, 0.0504738874733448, -0.04189884662628174, -0.011847198009490967, 0.10861852020025253, 0.009409798309206963, -0.02383790723979473, -0.039601169526576996, -0.018235450610518456, -0.0066608586348593235, -0.029961049556732178, 0.00155581661965698, -0.0026026663836091757, -0.03854990378022194, 0.036664873361587524, 0.08102946728467941, -0.005124062765389681, -0.0010897531174123287, 0.001583472010679543, -0.10128273814916611, 0.026433506980538368, 0.012206746265292168, -0.023983046412467957, -0.04294252023100853, -0.06785105168819427, 0.003968527540564537, -0.015492820180952549, 0.050443194806575775, 0.052234821021556854, -0.003372883191332221, -0.017173754051327705, 0.07689215242862701, -0.06648238003253937, -0.05131202191114426, 0.004951323848217726, -0.06787210702896118, 0.054244332015514374, 0.05439723655581474, 0.019943447783589363, -0.043742503970861435, 0.0029047674033790827, 0.007560608442872763, -0.04027823358774185, -0.01172160729765892, -0.017836034297943115, 0.05316437408328056, -0.01674247719347477, -0.0009309605229645967, 0.012862669304013252, 0.034290678799152374, 0.00381804839707911, 0.026805946603417397, 0.03198499232530594, 0.032468754798173904, -0.03483698144555092, 0.04413531720638275, -0.005720924586057663, 0.040407296270132065, 0.02872232161462307, 0.015455065295100212, 0.0060940333642065525, -0.0010079147759824991, -0.011185086332261562, 0.01034671999514103, 0.05129382386803627, -0.031172864139080048, 0.0037103674840182066, -0.016966626048088074, -0.018497632816433907, -0.024014875292778015, -0.06335635483264923, -0.07252384722232819, -0.0205805916339159, 0.07423215359449387, 0.005919772200286388, 0.01558717805892229, 0.0392569936811924, 0.05059976130723953, -0.00039344868855550885, -0.04568817839026451, -0.005730090197175741, 0.05444822087883949, -0.049015387892723083, 0.0031592505984008312, 0.019981887191534042, -0.02507692202925682, -0.0291608776897192, -0.005611706990748644, -0.022073708474636078, -0.05714689940214157, 0.014580548740923405, 0.009501629509031773, 0.017765622586011887, 0.038362618535757065, -0.03110293671488762, -0.07182570546865463, 0.09158213436603546, 0.00343292742036283, 0.010176099836826324, 0.037990979850292206, 0.05949237197637558, 0.02502238191664219, -0.03425149992108345, 0.00040468265069648623, -0.0362703762948513, 0.0042772297747433186, -0.007057898677885532, 0.037348274141550064, -0.02596995234489441, -0.045220185071229935, -0.00067089160438627, 0.022015852853655815, 0.05754765868186951, -0.0011552644427865744, 0.029013346880674362, -0.06499560922384262, 0.058972932398319244, 0.008093597367405891, 0.04600052535533905, -0.02853791043162346, 0.035837188363075256, 0.0029010209254920483, -1.2620053894352168e-05, -0.030370661988854408, -0.017271606251597404, -0.0320887416601181, -0.04824654012918472, 0.03757598623633385, 0.08463049679994583, 0.02610284648835659, 0.008445913903415203, -0.006244555115699768, -0.03788631409406662, -0.04625077173113823, -0.0011199928121641278, 0.050835441797971725, 0.029227150604128838, -0.0176030695438385, 0.04546578601002693, -0.03471815213561058, -0.021868186071515083, -0.0015280573861673474, -0.014638031832873821, -0.020616212859749794, -0.005948444362729788, -0.03639582172036171, 0.05668260157108307, 0.03916456550359726, -0.043052755296230316, 0.023130742833018303, 0.009309782646596432, 0.009561251848936081, -0.03877760469913483, 0.027604326605796814, -0.04608626663684845, 0.05726313963532448, 0.0630967915058136, 0.012477862648665905, 0.002610940020531416, 0.013565121218562126, 0.05989405885338783, 0.01879287138581276, 0.041379719972610474, 0.000331432354869321, -0.012834747321903706, -0.016329068690538406, -0.03645888715982437, 0.011273504234850407, -0.013745860196650028, -0.05684357136487961, -0.01292779203504324, -0.018147505819797516, -0.06477682292461395, 0.05039918050169945, 0.035017333924770355, 0.05101241171360016, -0.01856008917093277, 0.034680742770433426, 0.052607011049985886, -0.03834271430969238, 0.047650087624788284, -0.04213711991906166, -0.04129330441355705, 0.02840712107717991, 0.0035917237401008606, -0.033372558653354645, -6.349567183132961e-33, -0.035061225295066833, 0.0027963833417743444, -0.005386694800108671, -0.029924064874649048, -0.05010378360748291, 0.03043675236403942, 0.00436229445040226, 0.00918886810541153, 0.019226158037781715, 0.0012248328421264887, -0.046863533556461334, -0.016002697870135307, 0.04740166664123535, -0.0004309812211431563, 0.010378659702837467, -0.014905346557497978, 0.03733406960964203, -0.041845161467790604, -0.01647602953016758, -0.03804744780063629, 0.07474324107170105, 0.06867895275354385, 0.07711958140134811, -0.01065760012716055, -0.005608389154076576, 0.04471636191010475, -0.012450074777007103, -0.04152835160493851, 0.06344761699438095, 0.05714593827724457, -0.00966458860784769, 0.01224554143846035, -0.03835706412792206, -0.0367903970181942, 0.002305326983332634, -0.014500021003186703, -0.08624117821455002, -0.0016090775607153773, -0.027693049982190132, 0.031894367188215256, -0.029005661606788635, 0.04013912379741669, 0.05563947558403015, 0.029742320999503136, -0.06279996782541275, 0.0008680849568918347, 0.015085703693330288, -0.025025909766554832, -0.07568252831697464, -0.06220552325248718, -0.0060285599902272224, 0.05115247145295143, 0.0005294423317536712, -0.006280119996517897, 0.04838016629219055, 0.006464836653321981, -0.023943964391946793, -0.042861368507146835, -0.05201750993728638, 0.046677231788635254, 0.003591044107452035, 0.039766665548086166, 0.008870410732924938, 0.018950169906020164, 0.010487068444490433, 0.01702655479311943, 0.06458482891321182, -0.062359925359487534, 0.06597837060689926, -0.03090600110590458, 0.031888581812381744, -0.017712842673063278, -0.0016362793976441026, 0.015756413340568542, 0.027841132134199142, -0.0235553327947855, -0.04886080324649811, 0.008119906298816204, 0.0526810847222805, 0.04895982891321182, 0.0160333551466465, 0.004877857398241758, -0.0745941773056984, -0.0014504879945889115, -0.07257352024316788, -0.026664974167943, -0.018384728580713272, 0.008043643087148666, 0.014427064917981625, 0.057811278849840164, 0.010388145223259926, -0.05222098156809807, 0.02825181558728218, 0.01834527775645256, 0.013441200368106365, -0.04839739948511124, 0.04077606275677681, -0.02537078782916069, -0.02581251971423626, 0.005764365661889315, -0.03506596013903618, -0.015252400189638138, 0.029039135202765465, 0.02144463360309601, 0.006107543595135212, -0.024548159912228584, -0.011028130538761616, 0.04932159185409546, -0.06376869231462479, 0.008904954418540001, -0.004410941619426012, -0.019673284143209457, 0.012208066880702972, 0.031427618116140366, 0.04155411571264267, -0.06386212259531021, -0.003309349063783884, 0.02440583147108555, -0.002810090547427535, -0.005623615346848965, -0.008352283388376236, -0.0013423050986602902, -0.008391606621444225, 0.06714940816164017, -0.04763933643698692, 0.018636994063854218, -0.006122595630586147, -0.059575267136096954, 0.030303189530968666, -0.04132700338959694, -0.016806507483124733, 0.020310672000050545, 3.072888716815214e-07, -0.02328748069703579, -0.0006940842140465975, -0.01307755708694458, -0.007903285324573517, 0.0031358038540929556, 0.020971475169062614, -0.004412422887980938, 0.005688969511538744, -0.004796765744686127, 0.04154810309410095, 0.06113676354289055, -0.03973986953496933, 0.04362218827009201, 0.010437222197651863, -0.08512698113918304, -0.031475573778152466, -0.07591459900140762, 0.059687308967113495, 0.027088558301329613, 0.009077509865164757, 0.025921717286109924, 0.07686138153076172, -0.008741440251469612, -0.043642308562994, -0.0034416834823787212, -0.01004924438893795, 0.0376410186290741, -0.0008677381556481123, 0.008397037163376808, -0.001693996600806713, 0.024480417370796204, 0.004846610594540834, -0.0030160893220454454, 0.01091192290186882, -0.06333740055561066, 0.027590561658143997, 0.03304105997085571, 0.020803911611437798, -0.027644159272313118, -0.039093319326639175, 0.05327530950307846, 0.03877600282430649, -0.011978860944509506, 0.004933950025588274, 0.0400860421359539, -0.017033366486430168, 0.00250694015994668, -0.002009341260418296, -0.043016839772462845, 0.012952465564012527, 0.006985488813370466, -0.013144717551767826, -0.0014433973701670766, -0.02992984652519226, -0.004748607520014048, -0.011167692020535469, 0.0007420435431413352, -0.0338134840130806, 0.040474191308021545, 0.0171233918517828, -0.015963692218065262, -0.07324641942977905, 0.0076852538622915745, 0.013447536155581474, 0.01293996348977089, -0.05260239541530609, -0.027631942182779312, 3.0001485692239714e-34, 0.027632765471935272, -0.006277342326939106, -0.010412423871457577, 0.02633676864206791, 0.025620240718126297, -0.01986592635512352, 0.025783345103263855, -0.0307773444801569, 0.004558452870696783, -0.08931747078895569, -0.048931784927845]

['Artem M. Grachev', 'Dmitry I. Ignatov', 'Andrey V. Savchenko']

1708.05963v1

In this paper, we consider several compression techniques for the language modeling problem based on recurrent neural networks (RNNs). It is known that conventional RNNs, e.g, LSTM-based networks in language modeling, are characterized with either high space complexity or substantial inference time. This problem is especially crucial for mobile applications, in which the constant interaction with the remote server is inappropriate. By using the Penn Treebank (PTB) dataset we compare pruning, quantization, low-rank factorization, tensor train decomposition for LSTM networks in terms of model size and suitability for fast inference.

Neural Networks Compression for Language Modeling

http://arxiv.org/pdf/1708.05963v1

Title Neural Networks Compression Language Modeling Summary paper consider several compression technique language modeling problem based recurrent neural network RNNs known conventional RNNs eg LSTMbased network language modeling characterized either high space complexity substantial inference time problem especially crucial mobile application constant interaction remote server inappropriate using Penn Treebank PTB dataset compare pruning quantization lowrank factorization tensor train decomposition LSTM network term model size suitability fast inference Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.022581350058317184, 0.021247537806630135, -0.0034962582867592573, 0.019048819318413734, -0.03415098786354065, -0.01466596033424139, -0.003558417782187462, 0.054771434515714645, -0.08111077547073364, -0.0035942259710282087, 0.018638819456100464, -0.05355372279882431, 0.038730550557374954, 0.00589417852461338, 0.020290054380893707, -0.022094888612627983, 0.003585127415135503, 0.013218661770224571, 0.013220613822340965, 0.039579126983881, 0.017094727605581284, 0.0022021837066859007, 0.06148086488246918, 0.05073787271976471, -0.010984301567077637, -0.005424903240054846, -0.01719883643090725, 0.010327215306460857, -0.08964850008487701, -0.02833780273795128, -0.004882241599261761, 0.03598074987530708, 0.0548059418797493, 0.0490507148206234, 2.0910056264256127e-06, 0.004494668450206518, -0.01696779392659664, -0.02677122876048088, -0.025888249278068542, 0.03450561314821243, 0.0765821784734726, -0.02133052796125412, -0.012670600786805153, 0.0408741720020771, -0.037088651210069656, -0.05631916970014572, 0.06440932303667068, 0.03738301619887352, 0.055709049105644226, 0.04093195125460625, 0.0018942481838166714, -0.04079939424991608, -0.01448721345514059, -0.05065833777189255, -0.025774706155061722, -0.030909167602658272, 0.008039284497499466, -0.01563120447099209, -0.010015003383159637, 0.002184481592848897, -0.028245020657777786, 0.0005962903960607946, 0.029242122545838356, -0.0005868217558600008, -0.04372462257742882, -0.0067620351910591125, -0.014648484997451305, -0.007012663409113884, 0.0045679062604904175, 0.03460775315761566, -0.03744261711835861, -0.039862748235464096, -0.008009999990463257, 0.03774435073137283, -0.03980736434459686, -0.04767182841897011, -0.049887239933013916, 0.04460868611931801, 0.005260167643427849, 0.0327020138502121, -0.02396530471742153, 0.03520433232188225, 0.03395858407020569, -0.015200462192296982, -0.009885750710964203, -0.0031061565969139338, 0.0055181654170155525, -0.028319736942648888, -0.05682208389043808, -0.05185023322701454, 0.029906367883086205, -0.057256799191236496, 0.03951376676559448, 0.020982196554541588, 0.04690275713801384, 0.011848260648548603, -0.035226110368967056, -0.0748957023024559, 0.020606236532330513, -0.06751047074794769, 0.030986091122031212, 0.012748814187943935, 0.01320943608880043, -0.012167245149612427, -0.04642479494214058, 0.06903331726789474, -0.022092873230576515, -0.03153679147362709, -0.025829358026385307, -0.006567828822880983, -0.033537186682224274, -0.017092986032366753, -0.03574364259839058, 0.05383094772696495, -0.015822406858205795, -0.018778854981064796, -0.07526849955320358, -0.019345853477716446, 0.05268718674778938, -0.028153318911790848, 0.04862424358725548, 0.03580988571047783, -0.026858000084757805, -0.008892489597201347, 0.0006618527695536613, 0.027830863371491432, 0.005465696100145578, 0.01039023045450449, -0.012496518902480602, -0.04353949800133705, 0.003871372202411294, 0.04036321863532066, -0.00040971877751871943, 0.029368607327342033, -0.011285927146673203, 0.030884305015206337, 0.02223191224038601, 0.02369285747408867, -0.029825083911418915, 0.00997507106512785, 0.0073218257166445255, -0.012398558668792248, -0.02451455406844616, -0.07051689922809601, 0.044661980122327805, -0.05091700330376625, -0.03692632168531418, -0.03171263635158539, 0.0036157916765660048, 0.03005489520728588, -0.07250266522169113, 0.02256433293223381, -0.013245759531855583, 0.011383330449461937, 0.06049763038754463, 0.014303985983133316, 0.08921609818935394, -0.0013060475466772914, 0.0681583508849144, 0.036717191338539124, 0.010037488304078579, -0.047655876725912094, 0.008380158804357052, 0.03523961082100868, 0.029148481786251068, -0.03397654369473457, -0.07115360349416733, -0.03813007473945618, -0.005323413293808699, 0.03528279438614845, 0.02529180608689785, 0.09425599128007889, -0.027486255392432213, -0.046656474471092224, 0.026440344750881195, 0.09227417409420013, 0.0737517699599266, 0.09886322170495987, 0.041546110063791275, 0.01796446554362774, 0.001182839274406433, -0.01452756766229868, -0.004506729543209076, 0.04525962471961975, -0.03418326377868652, 0.0038196593523025513, 0.02093343995511532, 0.022459356114268303, -0.018572375178337097, -0.042574815452098846, -0.023466207087039948, -0.04653385281562805, 0.04229789227247238, -0.0463227815926075, 0.030589547008275986, 0.006674131378531456, -0.038343384861946106, 0.0217840988188982, -0.008299371227622032, -0.040024179965257645, -0.015148738399147987, -0.03099983185529709, -0.02594965137541294, 0.015510023571550846, 0.029727138578891754, 0.04564677178859711, -0.012628089636564255, -0.02879144996404648, -0.03638365492224693, 0.012007678858935833, -0.012148557230830193, 0.004920461680740118, 0.011206110939383507, -0.10453566908836365, 0.011297429911792278, 0.04480975866317749, 0.004485151264816523, 0.03170072287321091, -0.042101942002773285, 0.030943268910050392, 0.04451252520084381, 0.00806858018040657, -0.04830373078584671, 0.016224276274442673, -0.012580393813550472, -0.015182329341769218, 0.04252475127577782, 0.006220618262887001, 0.019161807373166084, -0.00040418459684588015, 0.01594032533466816, 0.0082244873046875, 0.038060128688812256, -0.049029190093278885, 0.001020359224639833, -0.019075259566307068, -0.061547599732875824, -0.04402117803692818, 0.03262181207537651, -0.009004887193441391, 0.07305421680212021, 0.06712034344673157, -0.029070816934108734, -0.056756678968667984, 0.09479141235351562, -0.0518396720290184, 0.05355425179004669, -0.04727768525481224, 0.022720254957675934, -0.012720559723675251, 0.028180856257677078, 0.002323856810107827, 0.021230852231383324, -0.019396163523197174, 0.04886303469538689, 0.026242967694997787, -0.0026253792457282543, 0.02495584823191166, -0.032572075724601746, -0.043987613171339035, 0.04074127599596977, -0.04218083247542381, -0.0021496193949133158, 0.023538028821349144, 0.019547512754797935, 0.03462783247232437, -0.019730204716324806, -0.042699068784713745, 0.019307224079966545, 0.012707737274467945, 0.017314542084932327, 0.01633540540933609, 0.03937043622136116, 0.0102107934653759, -0.03647701442241669, -0.045263368636369705, 0.007594844792038202, 0.009373528882861137, -0.0035189553163945675, 0.023953508585691452, 0.015225651673972607, -0.011333931237459183, -0.03216797858476639, -0.06283369660377502, 0.009362095966935158, 0.08287779986858368, -0.03297607600688934, -0.06546139717102051, -0.006898136343806982, 0.028262978419661522, -0.0193022470921278, 0.029832378029823303, 0.016790468245744705, -0.10929218679666519, -0.02584207057952881, -0.025824779644608498, 0.0333353690803051, 0.02150009758770466, 0.016837874427437782, -0.010317748412489891, 0.044236570596694946, 0.00549938902258873, -0.028440168127417564, -0.013642859645187855, -0.025977997109293938, -0.02114706300199032, 4.295993494451977e-05, -0.08577162772417068, -0.0012757621007040143, 0.10963015258312225, 0.027659883722662926, 0.005971758626401424, -0.03802873194217682, -0.0466579906642437, -0.04146932065486908, 0.017328619956970215, -0.021907152608036995, -0.03392995893955231, -0.003903951495885849, 0.03383859246969223, 0.008683309890329838, -0.028635667636990547, 0.05996023118495941, -0.052148036658763885, 0.00015773731865920126, -0.03702149540185928, -0.05680348351597786, -0.03399033471941948, 0.02214829996228218, 0.0017592397052794695, 0.03436936065554619, 0.015092599205672741, -0.025264354422688484, -0.0164230577647686, -0.0012032401282340288, 0.006138223689049482, -0.06447669118642807, -0.012609140016138554, 0.0030002507846802473, -0.028659267351031303, -0.04843594878911972, 0.004649028182029724, 0.017124051228165627, -0.026651427149772644, 0.029046380892395973, -0.004527008160948753, 0.04523654654622078, -0.008169084787368774, 0.02293328382074833, 0.08504319936037064, -0.020280878990888596, 0.03574972599744797, -0.007744462229311466, 0.015797896310687065, 0.01856895722448826, 0.036339178681373596, 0.01540745235979557, 0.005746133159846067, 0.014265332370996475, 0.04118088260293007, 0.025793379172682762, 0.014430740848183632, -0.004881764762103558, 0.05469295382499695, -0.07775262743234634, 0.013172122649848461, 0.010087787173688412, 0.0008771902066655457, -0.04577736556529999, 0.06350015103816986, 0.002054287353530526, -0.07026804983615875, 0.002348227659240365, 0.10563774406909943, 0.023037783801555634, -0.06363245099782944, -0.021968606859445572, 0.0011974613880738616, 0.01590311899781227, 0.008080385625362396, 0.04450955614447594, -0.018778931349515915, 0.015531781129539013, -0.007632031105458736, -0.007242468651384115, -0.01620776392519474, -0.03807245194911957, -0.027576910331845284, -0.08064933866262436, 0.004356385208666325, 0.011295663192868233, 0.0024080886505544186, -0.014194185845553875, -0.036610182374715805, -0.013249747455120087, 0.008111387491226196, -0.021001577377319336, 0.013459600508213043, 0.028931526467204094, -0.021305032074451447, 0.050045743584632874, -0.10713134706020355, -0.02240561693906784, -0.012847700156271458, -0.02309688739478588, 0.04974750429391861, 0.05294876545667648, 0.04990184307098389, -0.023484285920858383, -0.03302094712853432, -0.0009039448923431337, 0.014998233877122402, 0.01263116579502821, -0.013704346492886543, -0.02530728653073311, 0.05056942254304886, 0.004023073706775904, 0.003762866137549281, 0.020816458389163017, -0.01587904989719391, 0.04143483191728592, -0.03617052733898163, 0.06199418380856514, 0.014495360665023327, -0.029019281268119812, -0.05907575786113739, 0.018936607986688614, -0.00338752381503582, 0.050377257168293, 0.045506030321121216, -0.026633713394403458, -0.044772885739803314, 0.010183303616940975, 0.019354047253727913, -0.03129104524850845, -0.014309684745967388, 0.007023160345852375, 0.019472014158964157, -0.05436522513628006, -0.07952563464641571, -0.015161137096583843, -0.03137972578406334, -0.001194256474263966, 0.01490348856896162, 0.03649812936782837, 0.027912834659218788, 0.01606830395758152, -0.06435572355985641, -0.05297341197729111, 0.020501267164945602, -0.018477903679013252, -0.052886225283145905, 0.05144476518034935, 0.032776303589344025, -0.013397415168583393, 0.014032133854925632, -0.030473310500383377, -0.10032229125499725, -0.01091702003031969, -0.021353086456656456, 0.0164907518774271, 0.01928703300654888, 0.02674749866127968, -0.028081851080060005, -0.07044769078493118, 0.005233917851001024, 0.008968674577772617, -0.052031874656677246, 0.02501044236123562, 0.012376120314002037, -0.024902531877160072, 0.012936496175825596, 0.02650461159646511, -0.017321063205599785, 0.045159321278333664, -0.017882004380226135, 0.007724374067038298, -0.017973093315958977, -0.04815477132797241, 0.034878190606832504, -0.01955632120370865, 0.036907363682985306, 0.0242750383913517, -0.022857576608657837, 0.026258349418640137, 0.024426294490695, -0.018567895516753197, 0.02871960774064064, -0.04242931306362152, 0.01379441563040018, 0.05820102244615555, 0.032131459563970566, 0.016731036826968193, -0.047821082174777985, 0.041600096970796585, -0.030605977401137352, 0.0465710274875164, 0.03568275272846222, -0.01261822134256363, 0.016215888783335686, 0.011371731758117676, 0.04189957305788994, -0.02761431224644184, -0.034861836582422256, -0.007998197339475155, 0.014704748056828976, -0.06394340097904205, 0.02853645756840706, -0.006830907426774502, 0.027115076780319214, -0.019268399104475975, 0.04179217666387558, 0.009256902150809765, 0.015796395018696785, -0.03796079382300377, 0.0012744227424263954, 0.041798513382673264, -0.01352567970752716, -0.03757283836603165, -0.017115723341703415, 0.04000236839056015, -0.025834335014224052, 0.037587396800518036, -0.012399007566273212, 0.010343332774937153, 0.027911271899938583, -0.004731448367238045, -0.038428790867328644, 0.003710245480760932, 0.06355410814285278, 0.05937216058373451, 0.00022390132653526962, 0.014023098163306713, -0.015216216444969177, -0.004927934613078833, 0.023940786719322205, -0.033950548619031906, 0.03349023312330246, -0.01677130162715912, -0.013969910331070423, -0.02616395801305771, -0.049850914627313614, 0.014834165573120117, 0.01983295939862728, 0.04773065820336342, -0.015223943628370762, 0.037768468260765076, 0.03531602397561073, 0.027989020571112633, 0.057047538459300995, -0.0031845641788095236, 0.0025652700569480658, -0.0035700772423297167, -0.03365866094827652, -0.04742471128702164, -5.836396675415845e-33, -0.01694769784808159, 0.01877453923225403, 0.004489873070269823, -0.03853980451822281, -0.0371769554913044, 0.013269628398120403, -0.019862350076436996, -0.04499733820557594, -0.031551726162433624, -0.03223137557506561, -0.04278775304555893, 0.01581806130707264, 0.001718787825666368, 0.04124220460653305, 0.020779114216566086, 0.04011215269565582, 0.038770999759435654, -0.02333648130297661, 0.004169850144535303, 0.022053785622119904, 0.01720569282770157, 0.03093024156987667, 0.04830675572156906, -0.02589874155819416, -0.04767029359936714, -0.028565851971507072, 0.02916231006383896, -0.00019398587755858898, 0.0641542375087738, 0.04710065573453903, -0.05001506209373474, -0.0026540416292846203, 0.018083810806274414, -0.06990933418273926, -0.024735920131206512, 0.05366401746869087, -0.053337130695581436, -0.0565442331135273, -0.0048291501589119434, -0.004195744171738625, -0.023633019998669624, -0.016393033787608147, 0.07116078585386276, 0.005166939459741116, -0.027598828077316284, 0.04525918513536453, 0.010998369194567204, -0.039175305515527725, -0.06979820132255554, -0.059565432369709015, 0.012582085095345974, 0.008871805854141712, 0.00013683747965842485, -0.017032643780112267, 0.04584638774394989, 0.015084340237081051, -0.07562385499477386, 0.021577097475528717, -0.08461736887693405, 0.024861756712198257, -0.02635687217116356, 0.09383434057235718, 0.03809909150004387, -0.02667582593858242, 0.029641199856996536, -0.004974379204213619, -0.0008797892951406538, -0.021631421521306038, -0.04310160130262375, 0.03718201071023941, 0.0239112488925457, 0.01305512897670269, 0.07681813836097717, 0.0359463170170784, 0.0949237048625946, -0.05985068157315254, -0.05480573698878288, 0.013522886671125889, 0.05652110278606415, 0.03337010368704796, 0.026743771508336067, 0.016236858442425728, -0.01780976913869381, -0.04571453854441643, -1.1248754162807018e-05, -0.017277762293815613, -0.005538540426641703, -0.08851908147335052, 0.01603567972779274, -0.004706916864961386, 0.01888551376760006, -0.009631340391933918, 0.025875605642795563, -0.05709163472056389, 0.015394110232591629, 0.010525067336857319, 0.008614443242549896, 0.022503679618239403, 0.012429129332304, 0.03295261785387993, -0.03848373144865036, -0.003932117484509945, -0.01253791619092226, 0.0146463792771101, 0.006074951495975256, 0.004539114888757467, 0.008430114947259426, 0.02800038456916809, -0.03602233901619911, -0.019207913428544998, 0.0040480331517755985, -0.006504470948129892, 0.0012560932664200664, 0.014458025805652142, 0.024897320196032524, -0.026415575295686722, 0.012148777022957802, 0.03624831885099411, 0.010998079553246498, -0.018517788499593735, 0.012190375477075577, -0.032301779836416245, 0.06361688673496246, 0.032187558710575104, -0.05302197113633156, -0.014606038108468056, -0.06907013058662415, 0.027669725939631462, 0.06032506749033928, -0.018960006535053253, -0.03409285098314285, 0.0565507598221302, 2.680615125427721e-07, -0.03318820148706436, 0.02229139767587185, 0.033801138401031494, -0.06367570161819458, 0.04649069905281067, -0.01566503755748272, 0.000931460119318217, 0.03255384787917137, 0.0030437877867370844, -0.011563966982066631, 0.015428618527948856, -0.04433745518326759, 0.042742371559143066, -0.015315861441195011, -0.09575474262237549, -0.0008978894329629838, -0.11041229218244553, 0.02024705335497856, -0.014784694649279118, 0.004193621687591076, 0.06692684441804886, 0.14125949144363403, 0.018959229812026024, -0.020232001319527626, -0.010604253038764, 0.00852904748171568, 0.002598609309643507, -0.010058345273137093, 0.008530896157026291, 0.016668623313307762, 0.012273135595023632, 0.023457583039999008, -0.03804219886660576, -0.040094394236803055, -0.02032395824790001, 0.016305629163980484, 0.002446066355332732, 0.03234996646642685, -0.004487968049943447, 0.0009476528503000736, 0.04328656196594238, -0.03682338446378708, -0.04412338137626648, -0.02514537237584591, 0.022313088178634644, 0.0008715054136700928, -0.04094672575592995, -0.039324671030044556, 0.031145652756094933, -0.006387081928551197, -0.005295401439070702, -0.02071094885468483, 0.03236458823084831, -0.0016991231823340058, 0.008256565779447556, -0.010963575914502144, 0.0013919556513428688, -0.06333205103874207, -0.001304725999943912, 0.011065720580518246, -0.005200211890041828, 0.017769353464245796, -0.054216817021369934, 0.013973535969853401, 0.08625645935535431, 0.0029139206744730473, 0.004195644520223141, 2.643037288452747e-34, -0.01341797225177288, -0.034547921270132065, 0.018225766718387604, 0.03701427951455116, -0.020391248166561127, -0.023690320551395416, 0.012813452631235123, 0.04721080884337425, -0.014541602693498135, -0.08029874414205551, -0.0413142591714859]

['Mostafa Dehghani', 'Aliaksei Severyn', 'Sascha Rothe', 'Jaap Kamps']

1711.00313v2

Training deep neural networks requires massive amounts of training data, but for many tasks only limited labeled data is available. This makes weak supervision attractive, using weak or noisy signals like the output of heuristic methods or user click-through data for training. In a semi-supervised setting, we can use a large set of data with weak labels to pretrain a neural network and then fine-tune the parameters with a small amount of data with true labels. This feels intuitively sub-optimal as these two independent stages leave the model unaware about the varying label quality. What if we could somehow inform the model about the label quality? In this paper, we propose a semi-supervised learning method where we train two neural networks in a multi-task fashion: a "target network" and a "confidence network". The target network is optimized to perform a given task and is trained using a large set of unlabeled data that are weakly annotated. We propose to weight the gradient updates to the target network using the scores provided by the second confidence network, which is trained on a small amount of supervised data. Thus we avoid that the weight updates computed from noisy labels harm the quality of the target network model. We evaluate our learning strategy on two different tasks: document ranking and sentiment classification. The results demonstrate that our approach not only enhances the performance compared to the baselines but also speeds up the learning process from weak labels.

Avoiding Your Teacher's Mistakes: Training Neural Networks with Controlled Weak Supervision

http://arxiv.org/pdf/1711.00313v2

Title Avoiding Teachers Mistakes Training Neural Networks Controlled Weak Supervision Summary Training deep neural network requires massive amount training data many task limited labeled data available make weak supervision attractive using weak noisy signal like output heuristic method user clickthrough data training semisupervised setting use large set data weak label pretrain neural network finetune parameter small amount data true label feel intuitively suboptimal two independent stage leave model unaware varying label quality could somehow inform model label quality paper propose semisupervised learning method train two neural network multitask fashion target network confidence network target network optimized perform given task trained using large set unlabeled data weakly annotated propose weight gradient update target network using score provided second confidence network trained small amount supervised data Thus avoid weight update computed noisy label harm quality target network model evaluate learning strategy two different task document ranking sentiment classification result demonstrate approach enhances performance compared baseline also speed learning process weak label Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0369996540248394, 0.051004763692617416, -0.01590188406407833, 0.018436508253216743, 0.024910999462008476, -0.00912522617727518, 0.03938376158475876, -0.03585285693407059, -0.0014833923196420074, -0.022313877940177917, -0.08250012993812561, 0.011987103149294853, -0.038493309170007706, 0.03639517351984978, 0.018426405265927315, -0.04620170220732689, 0.012392123229801655, 0.012526016682386398, -0.0037661066744476557, 0.012311195954680443, 0.025882776826620102, -0.008457926101982594, 0.010752295143902302, 0.006734846625477076, -0.030959030613303185, -0.020588954910635948, 0.009665812365710735, -0.008365322835743427, -0.007727289572358131, -0.04260287806391716, 0.08182572573423386, 0.012586911208927631, 0.004291946534067392, 0.04527318477630615, 2.3124730432755314e-06, -0.006693228147923946, -0.021118970587849617, -0.03359931707382202, 0.025638271123170853, -0.0069784969091415405, 0.03810672461986542, -0.01435944251716137, -0.0045525021851062775, -0.012589051388204098, -0.03914444148540497, -0.042107321321964264, 0.029997194185853004, 0.116112619638443, 0.05932565778493881, 0.02344602160155773, -0.009494652040302753, -0.027185920625925064, -0.019819296896457672, -0.036938928067684174, 0.03584481030702591, -0.060773126780986786, 0.013769861310720444, 0.006954933982342482, -0.03693277761340141, 0.02522670477628708, -0.013463151641190052, 0.03557595610618591, 0.02530500665307045, -0.06270089745521545, 0.038461003452539444, 0.028970664367079735, -0.02456723526120186, -0.01498476229608059, -0.015683790668845177, 0.06490243226289749, -0.030588766559958458, 0.019798966124653816, -0.010475888848304749, 0.005446593277156353, -0.0019673246424645185, -0.04302467033267021, -0.008966583758592606, -0.018015675246715546, 0.01203183550387621, 0.025653669610619545, -0.044932957738637924, 0.052260298281908035, 0.01646837592124939, 0.014734516851603985, 0.040297675877809525, 0.018438955768942833, -0.030274277552962303, -0.03883860632777214, 0.04651344567537308, 0.02925078384578228, -0.003773848991841078, -0.016959644854068756, 0.023898642510175705, 0.00636874046176672, -0.014014695771038532, -0.013693779706954956, -0.023653516545891762, -0.07185905426740646, 0.011110302992165089, -0.0774315819144249, 0.009179729036986828, -0.04932360723614693, -0.06713610887527466, 0.01906122826039791, -0.026253826916217804, 0.006652308627963066, 0.0011156826512888074, 0.02906021662056446, -0.0105201480910182, 0.027846937999129295, -0.073516346514225, -0.0011097830720245838, -0.01056278869509697, 0.07566499710083008, 0.030879732221364975, -0.011669047176837921, -0.08547739684581757, -0.013975240290164948, -0.07083547860383987, -0.0019324489403516054, 0.01594950444996357, 0.05668618530035019, -0.012734257616102695, 0.0458647795021534, -0.0010986027773469687, 0.028637198731303215, -0.020198745653033257, 0.06960871815681458, -0.025916699320077896, 0.03867581486701965, 0.03513107821345329, 0.03577343747019768, 0.008451986126601696, 0.03067254275083542, 0.05005411431193352, 0.07520720362663269, -0.0020788146648555994, 0.028697196394205093, -0.10701420158147812, -0.03688589110970497, -0.0353628471493721, -0.04065244644880295, -0.020855175331234932, -0.05365017428994179, -0.01001004409044981, -0.05006953701376915, -0.008287248201668262, 0.024758312851190567, 0.002684131497517228, -0.005953919608145952, -0.03441686928272247, 0.0614917166531086, -0.02817528322339058, -0.03174992650747299, 0.03771191090345383, 0.024453915655612946, 0.003074048087000847, 0.029605256393551826, -0.0019070091657340527, 0.03310564532876015, 0.03173971176147461, 0.022691814228892326, -0.005043486598879099, -0.02762419357895851, 0.01831968128681183, -0.024359162896871567, 0.006988614797592163, -0.05073440447449684, 0.004243351053446531, 0.00748974084854126, 0.0036255216691643, 0.05728376656770706, -0.0015767961740493774, 0.018240420147776604, 0.0539788156747818, 0.00042967344052158296, 0.035566817969083786, 0.009234578348696232, 0.013607658445835114, -0.005956243723630905, 0.010803581215441227, 0.007074010092765093, 0.016582442447543144, 0.019228285178542137, -0.0310463048517704, -0.052491459995508194, -0.02487923763692379, -0.026247121393680573, -0.06512054800987244, -0.08223925530910492, 0.017606394365429878, -0.04944073036313057, -0.020512713119387627, -0.007629688363522291, 0.10315164923667908, 0.06053629890084267, 0.002440929412841797, -0.03962630033493042, 0.031209884211421013, 0.026368802413344383, -0.018811941146850586, -0.04654490575194359, 0.004603435751050711, 0.021151645109057426, -0.039836835116147995, -0.04376301169395447, -0.017154179513454437, -0.03764426335692406, 0.04138603433966637, -0.01800614222884178, 0.029906852170825005, -0.013727809302508831, 0.005537097342312336, -0.05476278439164162, -0.010969862341880798, -0.003696192055940628, 0.024286726489663124, 0.012739329598844051, -0.06891797482967377, 0.019714701920747757, 0.02363353967666626, 0.00614260183647275, -0.07049442082643509, 0.02939555235207081, 0.03728361055254936, -0.02277391217648983, 0.038218554109334946, 0.03077622316777706, 0.013027718290686607, 0.04294809699058533, 0.012654036283493042, -0.008198217488825321, 0.022497307509183884, -0.0224353838711977, -0.07608859986066818, -0.043363239616155624, -0.04094468057155609, -0.012156672775745392, 0.013289539143443108, -0.025602487847208977, -0.005563365761190653, 0.027788681909441948, -0.010651243850588799, -0.050715330988168716, -0.008434866555035114, -0.016207994893193245, -0.0335090272128582, -0.004505657125264406, -0.015508784912526608, 0.006296922918409109, -0.019073285162448883, -0.0546087808907032, 0.03667442873120308, 0.026680216193199158, 0.011060715653002262, -0.009119552560150623, -0.024595526978373528, 0.017224425449967384, 0.00377078028395772, -0.054872360080480576, -0.014182692393660545, -0.04052573814988136, 0.00841254461556673, 0.0004754005349241197, 0.07417932897806168, -0.018075525760650635, -0.014564220793545246, -0.02682580053806305, -0.0030318177305161953, -0.008819849230349064, -0.027410928159952164, -0.011701521463692188, -0.011525426991283894, 0.04850785806775093, -0.02972586639225483, -0.054259564727544785, 0.03634013235569, 0.0019718462135642767, -0.0019098682096228004, 0.03800693899393082, 0.04180070385336876, 0.033236902207136154, -0.02135501615703106, -0.012558629736304283, -0.011551673524081707, 0.0050869351252913475, 0.07654815912246704, -0.062377121299505234, -0.057926785200834274, 0.04545001685619354, -0.009442194364964962, 0.03927163779735565, 0.033040110021829605, -0.05447911098599434, -0.019275318831205368, -0.011696908622980118, -0.003519886638969183, 0.0295664444565773, -0.03380264714360237, 0.022985046729445457, 0.036338623613119125, 0.06041954457759857, -0.015871305018663406, 1.6599096852587536e-06, -0.029364028945565224, -0.029020311310887337, 0.005650304723531008, 0.029326094314455986, -0.03330274298787117, 0.018815770745277405, 0.03731665387749672, -0.007239153143018484, -0.012042009271681309, 0.004775638226419687, -0.038996294140815735, -0.008704074658453465, -0.03282983601093292, -0.01096786092966795, 0.0439266636967659, 0.0022122834343463182, 0.0016885572113096714, -0.011783069930970669, 0.06217380240559578, 0.05841599404811859, 0.006640109233558178, -0.0321352556347847, -0.061355240643024445, -0.0032465497497469187, -0.0004126144922338426, -0.01571088470518589, 0.026612740010023117, 0.01578160934150219, -0.020273247733712196, -0.034704070538282394, -0.0037026782520115376, 0.013067297637462616, -0.00560417165979743, -0.02728964574635029, -0.011995538137853146, 0.010882179252803326, -0.007428057957440615, -0.05094750598073006, -0.034877583384513855, 0.013568799942731857, -0.017776260152459145, 0.0017588638002052903, 0.022016014903783798, 0.008110887371003628, 0.002296752529218793, 0.00262126955203712, -0.01076608058065176, 0.04488331452012062, -0.040808577090501785, -0.028963861986994743, 0.013279899023473263, 0.0075646196492016315, 0.03152255713939667, -0.06877664476633072, -0.029909798875451088, -0.03244652599096298, 0.008608369156718254, 0.050767723470926285, 0.016660096123814583, 0.010209239087998867, -0.06661636382341385, 0.013043572194874287, 0.009254551492631435, 0.015232439152896404, -0.005327718798071146, -0.019688181579113007, 0.036713313311338425, -0.056355636566877365, -0.0030339264776557684, 0.07255706936120987, -0.0021857405081391335, -0.08502974361181259, -0.021262167021632195, 0.0006249557482078671, -0.016743630170822144, 0.03661040961742401, 0.016717683523893356, -0.014730041846632957, -0.020974131301045418, -0.055673472583293915, 0.040636904537677765, -0.014430204406380653, -0.027487797662615776, 0.025641992688179016, -0.06702873110771179, -0.011752763763070107, -0.006322776433080435, -0.028299320489168167, -0.015176471322774887, -0.05654622241854668, -0.0129824448376894, -0.020857058465480804, -0.009876838885247707, -0.024049745872616768, 0.04413141682744026, -0.013144598342478275, 0.06760452687740326, -0.032896049320697784, -0.03886048123240471, 0.011357733979821205, -0.05885285139083862, 0.0408710278570652, 0.04459896311163902, 0.028788862749934196, -0.061594460159540176, -0.02176310122013092, 0.0742080956697464, 0.005119961686432362, -0.0027560540474951267, -0.015560923144221306, 0.12600693106651306, -0.015457907691597939, -0.027996718883514404, -0.012889246456325054, 0.049032069742679596, -0.03915023058652878, 0.05226537212729454, 0.02364845760166645, 0.06439922004938126, -0.013371537439525127, -0.011940456926822662, -0.03893067687749863, 0.010792591609060764, 0.04613818600773811, 0.01564640924334526, -0.016994807869195938, -0.10040295124053955, -0.0013530560536310077, 0.024409094825387, -0.00666756322607398, -0.025721115991473198, -0.029826568439602852, 0.043348025530576706, -0.0287872813642025, -0.053694047033786774, -0.06399877369403839, -0.038790713995695114, 0.02165338397026062, 0.03965504467487335, 0.027416210621595383, 0.01970447413623333, 0.03646253049373627, 0.012788641266524792, -0.029092522338032722, -0.010076325386762619, 0.037488654255867004, -0.0060635581612586975, -0.047432880848646164, -0.014934527687728405, 0.06050964444875717, 0.017080998048186302, -0.016620252281427383, -0.053490281105041504, -0.03785015270113945, -0.0360933393239975, -0.011566097848117352, 0.07721255719661713, 0.011163303628563881, -0.006813072599470615, -0.02952631749212742, -0.06456059217453003, 0.0028639137744903564, 0.04048581048846245, -0.0369296632707119, -0.04761046916246414, 0.06413589417934418, -0.025478683412075043, 0.0032173192594200373, 0.024167299270629883, -0.02777727134525776, 0.08858834952116013, 0.04394753277301788, -0.04782255366444588, -0.015681250020861626, 0.01789293810725212, 0.005088816396892071, -0.01888449676334858, 0.08075584471225739, 0.010472705587744713, -0.019122647121548653, -0.046270448714494705, 0.00427383603528142, 0.003382208291441202, -0.025769680738449097, -0.049486760050058365, 0.038790397346019745, 0.04015884920954704, 0.04106082394719124, -0.013452949933707714, -0.027264423668384552, 0.05797817185521126, 0.034056324511766434, -0.03337622433900833, 0.03795495629310608, -0.007616863120347261, 0.03399332985281944, -0.022005030885338783, 0.0254968274384737, -0.020931653678417206, -0.021351173520088196, 0.06712129712104797, 0.006495026405900717, 0.002564689377322793, -0.008131749927997589, 0.053209446370601654, 0.02136395312845707, -0.02953195571899414, 0.015686357393860817, -0.02757607400417328, -0.02321307361125946, -0.045369699597358704, 0.028922272846102715, 0.029849082231521606, -0.03667141869664192, -0.013102555647492409, 0.01425850111991167, -0.0014759674668312073, -0.019085092470049858, 0.01721208356320858, -0.00479950150474906, 0.017697572708129883, 0.02208533138036728, -0.007886428385972977, 0.010845663025975227, 0.024552110582590103, 0.06609465181827545, 0.008771984837949276, 0.005513988900929689, -0.02160787209868431, -0.05361173674464226, -0.03461573272943497, 0.06023922935128212, 0.027396028861403465, 0.04051317274570465, -0.0035684523172676563, 0.011369899846613407, 0.04098347947001457, -0.02020229399204254, 0.03404304012656212, 0.0002299732732353732, 0.051224470138549805, 0.00425424799323082, 0.06204396113753319, 0.029065001755952835, -0.0015291082672774792, 0.02971254289150238, -0.03150365501642227, -0.036592498421669006, 0.07110337913036346, -0.008909313008189201, -0.036652807146310806, -6.256999207057614e-33, 0.024653766304254532, -0.019948426634073257, -0.0423407144844532, -0.002391337649896741, -0.009252957999706268, 0.04939240962266922, -0.01841919682919979, 0.01381626445800066, 0.003583062207326293, 0.05172913894057274, 0.0045279753394424915, 0.012612792663276196, 0.012118350714445114, 0.04435408115386963, 0.07175958901643753, -0.014015454798936844, 0.06267543882131577, -0.007862013764679432, 0.05950825288891792, 0.04377933591604233, 0.046121202409267426, 0.054957885295152664, 0.05851542204618454, -0.14137466251850128, 0.011796019971370697, 0.03515424206852913, -0.03323778510093689, -0.022896233946084976, -0.012846116907894611, 0.03254427760839462, 0.0012083582114428282, 0.07375690340995789, 0.014306504279375076, -0.0303456112742424, -0.009114667773246765, 0.018952086567878723, -0.05047415941953659, -0.03942161053419113, -0.08485650271177292, 0.014029072597622871, -0.05450937896966934, 0.013134550303220749, 0.06762567907571793, 0.009277320466935635, -0.004640017636120319, 0.027820345014333725, 0.08191563189029694, -0.023020636290311813, 0.0025527977850288153, -0.08104044944047928, -0.03437039256095886, 0.008727737702429295, 0.0015808859607204795, 0.006952540948987007, 0.005210782401263714, 0.0508430078625679, -0.039643581956624985, -0.018144072964787483, -0.08602701127529144, -0.011578112840652466, -0.038095224648714066, 0.05009804293513298, -0.020353473722934723, 0.05251896753907204, -0.03504922613501549, 0.0415940061211586, 0.04292736575007439, 0.052917126566171646, 0.010123144835233688, -0.016231916844844818, 0.009544935077428818, 0.05021122470498085, 0.09157930314540863, -0.008567565120756626, 0.0450189970433712, -0.05543248727917671, -0.10101386904716492, -0.010096407495439053, 0.021977515891194344, -0.0054274979047477245, -0.009739191271364689, 0.01497429609298706, -0.04185450077056885, -0.022906888276338577, 0.024989953264594078, -0.03529273346066475, -0.016352452337741852, 0.00036074526724405587, 0.0019033256685361266, 0.006824183743447065, -0.0007773366523906589, 0.0112351318821311, -0.018062438815832138, -0.05832711607217789, -0.016725344583392143, -0.040058013051748276, 0.011032930575311184, 0.029883552342653275, 0.007490161340683699, -0.039645716547966, -0.04314505308866501, -0.045114025473594666, -0.018836617469787598, 0.04112786054611206, 0.020798496901988983, 0.012325149029493332, 0.10261532664299011, 0.00014010563609190285, -0.022229308262467384, -0.04668176546692848, 0.012780346907675266, -0.02996327541768551, 0.04483649134635925, 0.04657803475856781, 0.0010651361662894487, -0.03670192137360573, -0.021051621064543724, 0.09360045939683914, 0.03481731936335564, 0.014524901285767555, -0.02882535569369793, -0.021156083792448044, 0.019299563020467758, -0.008220904506742954, -0.056873682886362076, -0.04139140248298645, -0.03989033028483391, 0.00142531783785671, 0.021672209724783897, -0.09761868417263031, 0.008876911364495754, -0.004090414382517338, 2.926313698026206e-07, -0.010251548141241074, 0.00441390136256814, -0.027549467980861664, -0.05687590688467026, 0.013930496759712696, 0.039759427309036255, -0.002887803828343749, 0.013618126511573792, -0.022729652002453804, -0.020729705691337585, 0.020776649937033653, -0.03965920954942703, 0.009708352386951447, 0.017752630636096, -0.0880122259259224, -0.04752526059746742, -0.021679367870092392, 0.013184878043830395, -0.02057631127536297, 0.02680019661784172, 0.0770961195230484, 0.09243576973676682, 0.04340720549225807, -0.020842500030994415, 0.03974854573607445, -0.00806318037211895, 0.017894461750984192, 0.026515984907746315, 0.04140080139040947, 0.0003277922223787755, 0.06818897277116776, 0.01869918592274189, -0.028849445283412933, 0.02292761392891407, -0.05223098024725914, -0.017905941233038902, 0.042137790471315384, 0.03145797550678253, -0.02085605077445507, 0.016092197969555855, 0.04081752896308899, 0.04706607386469841, 0.02877475880086422, 0.03699133172631264, 0.0578981414437294, -0.07428653538227081, -0.04405249282717705, -0.0033501875586807728, 0.013582101091742516, -0.020397989079356194, 0.04150315746665001, -0.004391801543533802, -0.012324359267950058, -0.010652601718902588, 0.01457726489752531, -0.014079906046390533, -0.05484485253691673, -0.043125201016664505, 0.03018295392394066, 0.024935107678174973, -0.009565564803779125, -0.015677740797400475, -0.004928086884319782, 0.02645326405763626, 0.04334764555096626, -0.04608500003814697, -0.003915536217391491, 2.7814797580883998e-34, 0.03399225324392319, -0.022117387503385544, 0.02945743314921856, -0.03364235907793045, -0.031420618295669556, 0.013920820318162441, -0.03768264874815941, -0.01202020887285471, 0.006737182382494211, -0.0022811724338680506, -0.04817378520965576]

['Christopher Tegho', 'Paweł Budzianowski', 'Milica Gašić']

1711.11486v1

In statistical dialogue management, the dialogue manager learns a policy that maps a belief state to an action for the system to perform. Efficient exploration is key to successful policy optimisation. Current deep reinforcement learning methods are very promising but rely on epsilon-greedy exploration, thus subjecting the user to a random choice of action during learning. Alternative approaches such as Gaussian Process SARSA (GPSARSA) estimate uncertainties and are sample efficient, leading to better user experience, but on the expense of a greater computational complexity. This paper examines approaches to extract uncertainty estimates from deep Q-networks (DQN) in the context of dialogue management. We perform an extensive benchmark of deep Bayesian methods to extract uncertainty estimates, namely Bayes-By-Backprop, dropout, its concrete variation, bootstrapped ensemble and alpha-divergences, combining it with DQN algorithm.

Uncertainty Estimates for Efficient Neural Network-based Dialogue Policy Optimisation

http://arxiv.org/pdf/1711.11486v1

Title Uncertainty Estimates Efficient Neural Networkbased Dialogue Policy Optimisation Summary statistical dialogue management dialogue manager learns policy map belief state action system perform Efficient exploration key successful policy optimisation Current deep reinforcement learning method promising rely epsilongreedy exploration thus subjecting user random choice action learning Alternative approach Gaussian Process SARSA GPSARSA estimate uncertainty sample efficient leading better user experience expense greater computational complexity paper examines approach extract uncertainty estimate deep Qnetworks DQN context dialogue management perform extensive benchmark deep Bayesian method extract uncertainty estimate namely BayesByBackprop dropout concrete variation bootstrapped ensemble alphadivergences combining DQN algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.05407075583934784, 0.06020825356245041, -0.009871243499219418, 0.03316120430827141, 0.0015843056607991457, 0.0019181536044925451, 0.0073473891243338585, -0.03800572082400322, -0.016431016847491264, -0.02771364524960518, -0.04231969267129898, -0.051028646528720856, -0.0011075044749304652, 0.08347871154546738, -0.044833336025476456, -0.08134806156158447, 0.02201448567211628, -0.029774153605103493, 0.04486776143312454, 0.010178077034652233, 0.018234770745038986, -0.03252845257520676, -0.034668147563934326, 0.059269484132528305, -0.021406546235084534, 0.002589664189144969, -0.05957464128732681, -0.009385771118104458, 0.04188510775566101, -0.03847125917673111, 0.017447099089622498, 0.029917119070887566, 0.02294842153787613, 0.06192905083298683, 2.155288029825897e-06, -0.04795944690704346, 0.002387936692684889, -0.030432038009166718, -0.020344983786344528, -0.015380270779132843, 0.020213518291711807, 0.06467534601688385, -0.01656038872897625, 0.04880882799625397, -0.036073338240385056, -0.0036643838975578547, 0.05241804197430611, 0.06185917556285858, 0.04337142035365105, 0.03707434609532356, -0.008634197525680065, -0.0381915345788002, -0.017733542248606682, -0.003136176848784089, 0.01182015985250473, -0.1338985562324524, 0.021968714892864227, -0.006285456474870443, 0.00047749356599524617, -0.008203728124499321, -0.011960742063820362, 0.002754020970314741, -0.0011932133929803967, -0.04420742020010948, -0.05696169659495354, 0.018556509166955948, 0.039404336363077164, -0.005730177741497755, -0.042705319821834564, 0.0864771232008934, 0.02993650548160076, 0.06666417419910431, 0.01614668034017086, -0.017510615289211273, 0.013909979723393917, -0.002576475962996483, -0.022800790145993233, 0.0014999457634985447, -0.027689261361956596, -0.022202856838703156, -0.025316886603832245, 0.04189938306808472, 0.006279019173234701, 0.022166362032294273, -0.029186157509684563, 0.06503665447235107, -0.046767134219408035, -0.017503516748547554, 0.021016987040638924, -0.01712474599480629, 0.0070469919592142105, -0.08083762973546982, 0.004511674866080284, 0.03675950691103935, -0.1011107861995697, 0.028459470719099045, -0.013808215968310833, 0.006833655759692192, 0.0011956787202507257, -0.03348008915781975, -0.001530683832243085, 0.04107934609055519, 0.0238958653062582, 0.042232412844896317, 0.043781526386737823, 0.04585722088813782, 0.002205208409577608, -0.015849478542804718, 0.014400162734091282, 0.022641774266958237, -0.03139277920126915, -0.004212120547890663, -0.06802202016115189, 0.012301219627261162, -0.06086048483848572, -0.06399133801460266, -0.03475486859679222, 0.025955701246857643, -0.013989345170557499, 0.0378151498734951, 0.006042892578989267, 0.05216611176729202, -0.042873531579971313, 0.011639932170510292, -0.08538839966058731, 0.010581455193459988, -0.05484841391444206, 0.036497607827186584, 0.039087601006031036, -0.016892313957214355, 0.023544419556856155, 0.015727845951914787, 0.008026105351746082, 0.018983107060194016, -0.029073160141706467, 0.09461786597967148, -0.0064003076404333115, 0.034339237958192825, -0.03421195223927498, 0.010411441326141357, -0.020732497796416283, -0.050696954131126404, -0.04328220337629318, -0.059439193457365036, 0.004612920340150595, -0.03875424340367317, -0.04893220216035843, 0.00381838739849627, 0.0019706322345882654, 0.013517682440578938, 0.003921848721802235, 0.07409144192934036, -0.0029674784746021032, -0.018877744674682617, 0.08594299107789993, 0.012979308143258095, -0.0056401765905320644, 0.06114484369754791, 0.05535353347659111, 0.028374185785651207, 0.00841845665127039, 0.016264712437987328, 0.031803786754608154, -0.008363811299204826, -0.02469010464847088, 0.005559537559747696, 0.019155239686369896, -6.651256626355462e-06, -0.021211016923189163, 0.05080348253250122, -0.022652920335531235, 0.05244310572743416, -0.056522395461797714, 0.006137780379503965, 0.026597199961543083, 0.05675576254725456, -0.019401991739869118, -0.029684681445360184, 0.021883662790060043, 0.038011424243450165, 0.00620601000264287, -0.025623464956879616, -0.010929357260465622, 0.02987203374505043, 0.0478697270154953, -0.03450436890125275, 0.02189616486430168, -0.005141785368323326, -0.014594413340091705, -0.07638020813465118, 0.022365497425198555, 0.010679331608116627, 0.03254476189613342, 0.01757862977683544, 0.02966710552573204, -0.03193551301956177, -0.06856800615787506, -0.03318709507584572, -0.011556415818631649, 0.030011573806405067, -0.04731994867324829, -0.04550107195973396, 0.026721881702542305, 0.031367916613817215, 0.009965585544705391, -0.025352617725729942, -0.06262996792793274, -0.05450311675667763, -0.024196729063987732, 0.02477419748902321, 0.06155485287308693, -0.03409995883703232, 0.021611925214529037, -0.053335852921009064, -0.055816683918237686, -0.014126947149634361, -0.0014551350614055991, 0.07236656546592712, -0.012254118919372559, 0.009849902242422104, 0.013225674629211426, 0.07712707668542862, 0.0074648503214120865, -0.002954116091132164, 0.023386001586914062, -0.05805784836411476, 0.02962506376206875, 0.006020249333232641, 0.0651969462633133, 0.01158254686743021, 0.007950283586978912, -0.005938301794230938, 0.00495212571695447, 0.043080225586891174, -0.024578161537647247, 0.008125300519168377, -0.0669061616063118, -0.050772007554769516, 0.02883768454194069, 0.026731671765446663, 0.021651851013302803, -0.04695432633161545, -0.055463965982198715, -0.07063229382038116, -0.0036245964001864195, -0.014021510258316994, 0.006656484678387642, -0.0068753804080188274, 0.01116153597831726, 0.018348002806305885, -0.016042934730648994, -0.044191885739564896, 0.05036742240190506, -0.008836583234369755, -0.014140342362225056, 0.05279213562607765, 0.048274748027324677, 0.052114129066467285, -0.07781398296356201, 0.00786984246224165, 0.015516816638410091, -0.03463627025485039, 0.00023742210760246962, 0.02695363759994507, 0.0322369784116745, -0.026845658197999, 0.011491723358631134, -0.06908000260591507, 0.005185355432331562, -0.02123829908668995, -0.009330840781331062, -0.001969901379197836, 0.04072015732526779, -0.012867282144725323, -0.03677750751376152, -0.030436914414167404, 0.003432217985391617, 0.057498857378959656, -0.007907687686383724, 0.031549230217933655, 0.0902995616197586, -0.014186236076056957, -0.04922115057706833, 0.01594076119363308, -0.0007069386774674058, -0.008379071019589901, 0.011557999067008495, -0.04559788480401039, -0.029351014643907547, 0.0008697118028067052, -0.03774990886449814, 0.031353648751974106, -0.02081860415637493, -0.054873690009117126, 0.020258130505681038, 0.00690464349463582, 0.007134438492357731, 0.02781488001346588, 0.020396050065755844, 0.03155906870961189, -0.001375242369249463, -0.013051680289208889, -0.05630732327699661, 0.0706176832318306, -0.009376768954098225, -0.02342848666012287, -0.04505646228790283, 0.027929844334721565, 0.023121628910303116, 0.037989601492881775, 0.013325568288564682, 0.05017922446131706, -0.046438366174697876, 0.06029953807592392, 0.015436431393027306, -0.025391152128577232, -0.03530940040946007, -0.01416189968585968, -0.04280320182442665, 0.0639209970831871, -0.015023634769022465, -0.007986732758581638, 0.07206433266401291, 0.02611072175204754, -0.01919683627784252, -0.06137221306562424, -0.05439450219273567, 0.004833105485886335, 0.02131194807589054, -0.0448799692094326, 0.021290408447384834, -0.016120590269565582, -0.06424333155155182, -0.04977865517139435, -0.07080139219760895, 0.035508349537849426, -0.039032645523548126, -0.006213563494384289, -0.026024019345641136, 0.013238626532256603, -0.010855752974748611, -0.02490532584488392, -0.07782910764217377, 0.006846804171800613, -0.05394323542714119, -0.025463659316301346, 0.029293345287442207, -0.045683205127716064, 0.006455524358898401, 0.019320283085107803, 0.01333552785217762, 0.062440771609544754, -0.01405467838048935, -0.008648322895169258, -0.007776487618684769, 0.0033897433895617723, 0.033803507685661316, 0.03188888728618622, 0.016866443678736687, 0.015358220785856247, 0.07525475323200226, 0.02244066819548607, 4.026756141684018e-05, -0.012483636848628521, -0.011002269573509693, -0.029017698019742966, 0.012791534885764122, -0.018315792083740234, 0.014746113680303097, 0.06774916499853134, 0.06524346768856049, -0.06268571317195892, 0.0003224750398658216, 0.07858332246541977, 0.029304753988981247, -0.027906669303774834, -0.02986449934542179, -0.03372403234243393, -0.006672572810202837, -0.006106087937951088, 0.03668056055903435, -0.06315358728170395, -0.01815326139330864, 0.010153199546039104, 0.055843353271484375, -0.0026694899424910545, -0.03763525187969208, 0.009114588610827923, -0.08091963827610016, 0.04085883870720863, -0.0362887941300869, -0.038868729025125504, -0.006869620177894831, -0.009432479739189148, 0.0025717569515109062, -0.01526557095348835, 0.039951350539922714, 0.025275591760873795, 0.04979421943426132, -0.024720562621951103, 0.02236846648156643, 0.005486579611897469, -0.021265001967549324, -0.006802584510296583, -0.039756227284669876, 0.05019386112689972, 0.07525813579559326, 0.05576199293136597, 0.01892668940126896, 0.01055714301764965, -0.013775959610939026, 0.000785754295065999, -0.003541636746376753, -0.024121558293700218, 0.04242661967873573, 0.004806335084140301, -0.005051786545664072, 0.004503603558987379, 0.04230356588959694, 0.0050746300257742405, 0.00900535099208355, 0.03174502030014992, -0.0046905879862606525, -0.05599414184689522, -0.0021215174347162247, -0.026304779574275017, 0.05458865687251091, 0.06140579283237457, 0.029458170756697655, -0.012383168563246727, -0.012421231716871262, -0.05721752718091011, -0.0541653037071228, -0.015603059902787209, -0.06353715807199478, 0.035289466381073, -0.006859574932605028, 0.017085595056414604, -0.014145846478641033, -0.08282829821109772, -0.041554249823093414, -0.014873906970024109, 0.05823171138763428, -0.012505861930549145, -0.024124594405293465, 0.015138371847569942, 0.05654270946979523, 0.03561966121196747, -0.04253513738512993, 0.03102250210940838, 0.026113875210285187, -0.053136520087718964, 0.04492156580090523, 0.027288300916552544, -0.0019437894225120544, -0.015180238522589207, -0.011737003922462463, -0.036724723875522614, -0.05830046162009239, -0.025919001549482346, 0.07498887926340103, 0.010122054256498814, 0.027408747002482414, -0.016440218314528465, -0.019720565527677536, 0.008685389533638954, -0.001051893224939704, 0.013809546828269958, -0.06419499218463898, 0.05406525358557701, 0.10567585378885269, -0.03943398967385292, 0.011824431829154491, -0.05190814658999443, 0.003312483662739396, -0.030395271256566048, 0.01782059296965599, -0.06287525594234467, -0.09558925777673721, -0.009128957986831665, -0.04622029885649681, 0.025863228365778923, 0.016302580013871193, -0.014058129861950874, -0.023203687742352486, 0.024048760533332825, -0.015524715185165405, -0.03120529279112816, -0.0444510281085968, 0.01983417198061943, 0.012759910896420479, -0.028142644092440605, 0.021896669641137123, -0.017765898257493973, 0.003366007236763835, -0.017122484743595123, 0.022074950858950615, 0.03744935616850853, 0.05654534697532654, -0.0014731789706274867, 0.002323780208826065, -0.0028280618134886026, 0.002504911972209811, 0.037045832723379135, 0.050671692937612534, 0.03794585168361664, 0.03204429894685745, 0.08239653706550598, 0.017136206850409508, -0.03768669441342354, 0.041301291435956955, -0.0017878065118566155, -0.06827482581138611, -0.09282809495925903, -0.015895944088697433, 0.053453970700502396, 0.03775629773736, 0.00800847914069891, -0.04772495478391647, -0.043341461569070816, 0.020546341314911842, 0.013093533925712109, 0.024445494636893272, 0.006652931682765484, 0.0055147018283605576, 0.05732497572898865, 0.025288745760917664, -0.019470613449811935, -0.005175275728106499, 0.04542667046189308, 0.03076585754752159, 0.027552345767617226, -0.013196557760238647, -0.0428476482629776, -0.043756574392318726, -0.021955516189336777, -0.00047038300544954836, 0.07884382456541061, -0.004061819985508919, 0.007412991486489773, 0.012367517687380314, -0.016305189579725266, -0.016998399049043655, 0.033531446009874344, 0.018080798909068108, -0.01827346161007881, 0.053119536489248276, 0.013159103691577911, 0.012124642729759216, 0.010299677029252052, -0.03708791732788086, 0.00012099971354473382, -0.009206155315041542, -0.01644328236579895, -0.06300754100084305, -5.714239302478393e-33, -0.013703590258955956, -0.035241130739450455, 0.02036726288497448, -0.027307860553264618, -0.03188450261950493, -0.042572930455207825, -0.013831091113388538, 0.004295183811336756, -0.007126686628907919, 0.02103017084300518, -0.01922115497291088, 0.007815188728272915, 0.019612258300185204, 0.017757492139935493, 0.010757614858448505, -0.023491591215133667, 0.044688984751701355, -0.002890191040933132, -0.020405994728207588, 0.021477527916431427, 0.0421900749206543, 0.02985921874642372, 0.02410099282860756, -0.06296855211257935, -0.0024727710988372564, 0.041040677577257156, -0.008254677057266235, 0.04681277647614479, 0.005411036778241396, 0.03571474179625511, 0.00173748133238405, -0.02121841162443161, -0.01355821918696165, -0.06814803928136826, -0.01185337733477354, 0.0095316581428051, -0.023368868976831436, -0.05145242065191269, -0.029172617942094803, 0.040710948407649994, -0.00676006218418479, 0.009771528653800488, 0.029653165489435196, 0.016471300274133682, -0.008102912455797195, 0.04615255817770958, 0.003412544261664152, 0.017555763944983482, -0.012970095500349998, -0.04615109786391258, -0.02810044214129448, 0.03686083108186722, -0.031434305012226105, -0.05068487673997879, -0.0126486262306571, 0.04688644036650658, -0.009652111679315567, -0.02932547591626644, -0.022050682455301285, 0.010447434149682522, -1.1706308214343153e-05, -0.016833309084177017, 0.04425986856222153, 0.08032394200563431, 0.03875621780753136, 0.024629035964608192, -0.01034941989928484, 0.022926917299628258, -0.0414600670337677, -0.031698599457740784, -0.026982944458723068, 0.0457279346883297, 0.010112457908689976, 0.0593290850520134, 0.0172690711915493, -0.00879316870123148, -0.04658913612365723, 0.04399201273918152, 0.033642224967479706, 0.06707262247800827, -0.008103299885988235, 0.03684931993484497, -0.04555583745241165, -0.02094506472349167, -0.03752543032169342, 0.01928253471851349, 0.0010699130361899734, -0.04149562492966652, 0.021251754835247993, 0.0017310804687440395, -0.0005332315340638161, -0.02819601073861122, 0.05820631608366966, -0.042569153010845184, -0.013602061197161674, 0.006791359279304743, 0.0123532023280859, 0.015925467014312744, -0.002814035164192319, 0.0014532003551721573, -0.04694654047489166, -0.024736514315009117, 0.024286866188049316, 0.024386463686823845, -0.023467738181352615, 0.002349721034988761, -0.04550487920641899, -0.013506008312106133, -0.025650765746831894, 0.021756919100880623, 0.00816416833549738, 0.04172559827566147, -0.006345090456306934, 0.06819365173578262, -0.016820667311549187, -0.059176716953516006, -0.010646247304975986, 0.08171812444925308, -0.000500394613482058, -0.011789204552769661, -0.028278805315494537, -0.06476327776908875, 0.007176490500569344, -0.004514757078140974, -0.05315340682864189, 0.0009403825388289988, -0.046411775052547455, -0.021424459293484688, -0.02288075163960457, -0.028936251997947693, 0.005263661500066519, 0.017124345526099205, 2.701425785289757e-07, -0.05681880563497543, 0.023183362558484077, 0.028180647641420364, 0.03728737682104111, 0.03138502314686775, 0.05236726999282837, 0.020154964178800583, -0.0005346656544134021, 0.021061971783638, -0.01506071351468563, 0.04196798801422119, 0.0076410965994000435, 0.009650490246713161, 0.024358151480555534, -0.08586374670267105, -0.0934922844171524, -0.09561291337013245, 0.004836175125092268, -0.04056457057595253, -0.005300164222717285, 0.03456515446305275, 0.07341203093528748, 0.000582622888032347, 0.01276434026658535, 0.04342062398791313, 0.010240674018859863, 0.008031535893678665, -0.0070123253390192986, 0.000367295608157292, 0.039789218455553055, 0.041760653257369995, 0.020133694633841515, -0.007905314676463604, -0.026348713785409927, -0.011002839542925358, 0.05112146586179733, -0.040020160377025604, 0.051758602261543274, 0.015421093441545963, -0.04475945606827736, 0.0023630871437489986, -0.011042219586670399, 0.053181469440460205, -0.040049176663160324, 0.023773737251758575, -0.06607628613710403, -0.009986469522118568, -0.024298114702105522, 0.025532692670822144, -0.04338829591870308, 0.05111522227525711, -0.02457064390182495, -0.007517443038523197, -0.03419351950287819, -0.017819225788116455, 0.00234787305817008, 0.0232340507209301, -0.05548647418618202, 0.019439583644270897, -0.002526122611016035, -0.02716663107275963, -0.029599405825138092, -0.03489339351654053, -0.0417182631790638, 0.011354727670550346, -0.006564308889210224, -0.000427962833782658, 2.1809123474136004e-34, 0.016397038474678993, -0.021604642271995544, -0.030978402122855186, 0.008196922019124031, 0.02946346066892147, 0.03401442989706993, 0.02990240976214409, 0.018696876242756844, 0.0933266282081604, -0.047619592398405075, -0.026923030614852905]

['Yuanhang Su', 'Yuzhong Huang', 'C. -C. Jay Kuo']

1803.01686v1

In this work, we investigate the memory capability of recurrent neural networks (RNNs), where this capability is defined as a function that maps an element in a sequence to the current output. We first analyze the system function of a recurrent neural network (RNN) cell, and provide analytical results for three RNNs. They are the simple recurrent neural network (SRN), the long short-term memory (LSTM), and the gated recurrent unit (GRU). Based on the analysis, we propose a new design to extend the memory length of a cell, and call it the extended long short-term memory (ELSTM). Next, we present a dependent bidirectional recurrent neural network (DBRNN) for the sequence-in-sequence-out (SISO) problem, which is more robust to previous erroneous predictions. Extensive experiments are carried out on different language tasks to demonstrate the superiority of our proposed ELSTM and DBRNN solutions.

On Extended Long Short-term Memory and Dependent Bidirectional Recurrent Neural Network

http://arxiv.org/pdf/1803.01686v1

Title Extended Long Shortterm Memory Dependent Bidirectional Recurrent Neural Network Summary work investigate memory capability recurrent neural network RNNs capability defined function map element sequence current output first analyze system function recurrent neural network RNN cell provide analytical result three RNNs simple recurrent neural network SRN long shortterm memory LSTM gated recurrent unit GRU Based analysis propose new design extend memory length cell call extended long shortterm memory ELSTM Next present dependent bidirectional recurrent neural network DBRNN sequenceinsequenceout SISO problem robust previous erroneous prediction Extensive experiment carried different language task demonstrate superiority proposed ELSTM DBRNN solution Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.016818039119243622, -0.02590359002351761, -0.006911926437169313, 0.06631135195493698, -0.03752010688185692, -0.009794680401682854, 0.015172813087701797, -0.020624857395887375, 0.007288065273314714, -0.04691636934876442, -0.024906670674681664, -0.0552426353096962, 0.013229344971477985, 0.04268839582800865, 0.03988541290163994, -0.038731399923563004, 0.045732345432043076, -0.021083125844597816, 0.005962254945188761, 0.010295047424733639, 0.028445320203900337, -0.02583756111562252, -0.025989918038249016, 0.01354377530515194, 0.002198785776272416, 0.007744948845356703, -0.008347125723958015, -0.01998036913573742, -0.011340659111738205, -0.0671202763915062, 0.03770194575190544, 0.04645608365535736, 0.01918407715857029, 0.031184513121843338, 2.2406093194149435e-06, -0.010875990614295006, 0.005751776043325663, -0.038022879511117935, 0.002339951228350401, -0.006053747609257698, 0.006648492068052292, 0.018732260912656784, -0.010043520480394363, 0.040089771151542664, -0.03602830320596695, -0.029036754742264748, 0.043377798050642014, 0.06883702427148819, 0.012819978408515453, 0.07563204318284988, -0.004245278425514698, -0.06420767307281494, 0.049201976507902145, -0.04172694310545921, 0.027950789779424667, -0.03590002655982971, 0.0209218617528677, -0.06068357080221176, 0.010807332582771778, 0.004401241894811392, -0.02505476400256157, 0.04105985164642334, 0.03700633347034454, 0.023160314187407494, -0.010944775305688381, 0.01851891539990902, -0.01520262099802494, 0.005215892568230629, 0.010857246816158295, 0.06979481130838394, -0.04419129714369774, -0.009497184306383133, -0.009602366015315056, 0.003975427243858576, -0.033893708139657974, -0.05085932835936546, -0.037759929895401, 0.007292083464562893, -0.011795698665082455, 0.010921797715127468, -0.005408325232565403, 0.018719982355833054, 0.031624436378479004, 0.01795017533004284, -0.027590148150920868, 0.007377763744443655, 0.01263141818344593, -0.046532176434993744, -0.04406777396798134, -0.028863202780485153, 0.006048445124179125, -0.05342601239681244, 0.025012372061610222, 0.05597100406885147, 0.0012535561108961701, 0.0319359116256237, -0.0011112963547930121, -0.1176631897687912, 0.030393162742257118, -0.05657840147614479, 0.03609533980488777, 0.015508360229432583, -0.024272194132208824, -0.01159337442368269, -0.048623982816934586, 0.04697089642286301, -0.028267662972211838, -0.007599911652505398, 0.012484312988817692, -0.0034407435450702906, -0.017258750274777412, -0.01658310741186142, 0.010951580479741096, 0.05404863879084587, -0.0002723348152358085, -0.004819036461412907, -0.06725913286209106, -0.029643338173627853, -0.009162897244095802, -0.002646425971761346, 0.042879942804574966, 0.0421624481678009, -0.0279019046574831, -0.003678326727822423, -0.024690069258213043, 0.025685839354991913, -0.026741797104477882, -0.003578373696655035, -0.018507156521081924, -0.012501775287091732, 0.012641724199056625, 0.04441871494054794, 0.007538421545177698, -0.014502521604299545, -0.035143014043569565, 0.09067351371049881, 0.005295546259731054, -0.03137645870447159, -0.07758889347314835, 0.0006619777996093035, -0.005353468935936689, -0.06838846206665039, 0.031007027253508568, -0.06789654493331909, 0.0032870688010007143, -0.006972471252083778, -0.04566316679120064, 0.0010394385317340493, 0.025029802694916725, 0.042665742337703705, 0.026446053758263588, 0.06383340060710907, -0.004210823215544224, -0.05434543639421463, 0.025732696056365967, 0.017195412889122963, 0.036201056092977524, 0.017913568764925003, 0.04627081751823425, 0.04525025188922882, -0.00643888907507062, -0.038448672741651535, 0.03277071565389633, 0.009664398618042469, 0.028392283245921135, -0.0408901609480381, -0.023276494815945625, -0.015217985957860947, 0.029938768595457077, 0.042679909616708755, -0.0008939390536397696, 0.06580130010843277, 0.013723556883633137, -0.018975861370563507, 0.03229700028896332, 0.04349799454212189, 0.05567149445414543, 0.06342039257287979, 0.018964216113090515, -0.02321287803351879, -0.007193210069090128, 0.021344535052776337, -0.024499649181962013, 0.0711250975728035, -0.03295831382274628, 0.0026399397756904364, -0.01266008522361517, -0.01360241323709488, -0.02395136095583439, -0.013751668855547905, -0.0037136857863515615, -0.03726491704583168, 0.04182642325758934, -0.03239240124821663, 0.041813094168901443, 0.004870516248047352, -0.06674835085868835, 0.053256429731845856, -0.018359089270234108, -0.04201102256774902, -0.016470350325107574, -0.024505609646439552, 0.010279634967446327, -0.00809092354029417, 0.00316572654992342, -0.04692477360367775, -0.06614675372838974, -0.0011261157924309373, -0.03156840056180954, 0.05110221356153488, 0.01210647914558649, 0.03698759898543358, -0.02057673968374729, -0.08176250755786896, 0.018766561523079872, 0.03724377602338791, -0.040359653532505035, 0.061762794852256775, -0.023965252563357353, 0.040080081671476364, 0.035381216555833817, 0.03402415290474892, -0.041091300547122955, 0.0017917683580890298, -0.04797403886914253, -0.009086040779948235, -0.002830483950674534, 0.041294533759355545, 0.014171998016536236, 0.017918121069669724, 0.04011600837111473, 0.022821540012955666, 0.05246121808886528, -0.05028847977519035, -0.019649021327495575, -0.02692762203514576, -0.12360244989395142, -0.08160058408975601, 0.032148897647857666, 0.03445113077759743, 0.01513866800814867, 0.031117286533117294, -0.008961331099271774, -0.0900629460811615, 0.06527438014745712, -0.037645887583494186, 0.03646630048751831, -0.040567658841609955, 0.022842705249786377, 0.05115344002842903, 0.03683168813586235, -0.012366989627480507, 0.02411971427500248, -0.029572220519185066, 0.0469014011323452, 0.016150811687111855, 0.021454663947224617, 0.021450811997056007, -0.044257327914237976, -0.06109999492764473, 0.04685518145561218, -0.011824473738670349, -0.003443309338763356, -0.008830574341118336, -0.0173181165009737, -0.040211137384176254, -0.0266738124191761, -0.019663548097014427, 0.0021841234993189573, -0.004439972806721926, 0.02568906918168068, -0.0007332112290896475, 0.006738454103469849, 0.033986613154411316, -0.02434539422392845, -0.05789690837264061, 0.03187539055943489, -0.006764527875930071, -0.005450645461678505, 0.021108530461788177, 0.025756578892469406, -0.009332106448709965, -0.03137501701712608, -0.03509785607457161, -0.008347065187990665, 0.017690397799015045, -0.008342278189957142, -0.05425423011183739, -0.043513745069503784, 0.03417660668492317, -0.0014348728582262993, 0.06973767280578613, -0.006774003151804209, -0.08380510658025742, -0.00921128410845995, -0.041149020195007324, 0.06385571509599686, 0.004507432691752911, 0.02745760791003704, -0.058112844824790955, -0.005395285319536924, -0.03177972137928009, 0.0019313199445605278, 0.018919512629508972, -0.0047296383418142796, 0.045293450355529785, 0.01622839644551277, 0.03173651173710823, -0.06079784035682678, 0.03671026602387428, 0.003639959031715989, 0.023903977125883102, -0.016135631129145622, -0.0032974297646433115, 0.016256581991910934, -0.004507868550717831, 0.005322795361280441, -0.011507549323141575, -0.04211697354912758, -0.0022478471510112286, -0.006625851150602102, -0.009449873119592667, 0.027042100206017494, -0.013466470874845982, 0.003211778588593006, -0.04632243886590004, -0.01740712858736515, -0.03496700897812843, 0.049512267112731934, 0.029629558324813843, -0.009970040060579777, -0.03633585199713707, -0.06258789449930191, -0.0400763563811779, -0.01788288913667202, -0.05302325263619423, -0.049875225871801376, 0.050959404557943344, -0.004359401762485504, 0.004228945821523666, -0.05016842484474182, -0.022137576714158058, -0.03656970337033272, 0.035783179104328156, 0.03189002722501755, 0.016737090423703194, 0.02267957665026188, -0.024237563833594322, 0.0018640334019437432, 0.03324226289987564, 0.02427823282778263, 0.044056765735149384, -0.033017631620168686, 0.034768544137477875, -0.002856906969100237, 0.0569717176258564, 0.01584944874048233, 0.0018325831042602658, -0.0028551719151437283, 0.0478726364672184, 0.024808190762996674, 0.036179475486278534, -0.024866551160812378, -0.024574846029281616, -0.0896029844880104, -0.009510309435427189, 0.00903809443116188, -0.027664776891469955, -0.028813302516937256, 0.0075907399877905846, -0.0009677807101979852, -0.11390464007854462, 5.774989858764457e-06, 0.0707421600818634, 0.0007384293130598962, -0.08007727563381195, -0.04184355586767197, -0.012873205356299877, -0.019070258364081383, 0.015576387755572796, 0.00846042949706316, -0.020579280331730843, -0.020498719066381454, -0.02050657384097576, 0.0032431520521640778, 0.0026908202562481165, -0.057525645941495895, -0.01945316046476364, -0.10715854912996292, -0.00374428927898407, -0.02129220962524414, -0.0741107314825058, -0.0483342669904232, 0.013652537018060684, -0.012430994771420956, 0.028079569339752197, 0.015900613740086555, 0.051649387925863266, -0.002448451239615679, -0.025067441165447235, 0.048258911818265915, -0.10346833616495132, 0.002689818385988474, 0.03047422133386135, -0.06128727272152901, 0.011505943723022938, 0.052791912108659744, 0.03877023980021477, -0.03316568210721016, -0.018936365842819214, 0.019026875495910645, -0.021721087396144867, 0.02983948215842247, -0.006474874913692474, 0.02921505831182003, 0.004000393208116293, -0.031683556735515594, -0.0174708254635334, 0.025036267936229706, -0.04859710484743118, 0.016903361305594444, -0.006930527277290821, 0.0820196196436882, -0.011450870893895626, 0.006269536446779966, -0.03690961003303528, -0.016850166022777557, 0.030837101861834526, 0.02313905768096447, 0.027618078514933586, -0.0178102795034647, -0.05589396879076958, 0.008071871474385262, 0.004963659215718508, -0.10387004166841507, 0.021299533545970917, -0.019616624340415, 0.003340291092172265, -0.019599778577685356, -0.09078077971935272, -0.07843270152807236, 0.007322346791625023, 0.04305947199463844, 0.018893541768193245, 0.04545212537050247, 0.04120215028524399, -0.010052159428596497, -0.03516559302806854, -0.03306372091174126, 0.02330382913351059, 0.03893198445439339, -0.06714029610157013, 0.02853253111243248, 0.038198746740818024, -0.02172335609793663, 0.02474299818277359, -0.008976486511528492, -0.07828045636415482, -0.03599970042705536, 0.02582990564405918, 0.031536344438791275, 0.0029448543209582567, 0.007461529225111008, -0.00024837974342517555, -0.05032257363200188, 0.00272571062669158, 0.0013593359617516398, -0.01346543524414301, -0.016772208735346794, 0.058993373066186905, 0.03238402307033539, -0.0016580276424065232, 0.017231127247214317, 0.008125540800392628, 0.04285842552781105, 0.02102174051105976, 0.02286461926996708, -0.00037917535519227386, 0.004177205730229616, -0.018700124695897102, 0.020441068336367607, 0.057507362216711044, 0.016774578019976616, 0.017198780551552773, -0.04412059113383293, 0.051058635115623474, 0.002854312304407358, 0.024536965414881706, -0.01142985187470913, 0.033757615834474564, 0.017182232812047005, -0.005979582201689482, -0.021095195785164833, -0.04798269271850586, 0.037580396980047226, -0.08996642380952835, 0.015476901084184647, 0.06912459433078766, -0.0041478294879198074, 0.007733546197414398, 0.002706141909584403, 0.03688238933682442, -0.03553662449121475, 0.0033560222946107388, 0.014340746216475964, 0.0458773709833622, -0.03836061805486679, 0.06846442073583603, 0.016834599897265434, 0.009677850641310215, -0.0009518140577711165, 0.016629453748464584, 0.012696729972958565, 0.007206337992101908, -0.02395537868142128, 0.011836168356239796, 0.06499514728784561, -0.02845972403883934, -0.0049985540099442005, 0.002294886391609907, 0.031194234266877174, -0.02951200306415558, 0.04237731918692589, -0.0455511137843132, 0.026647672057151794, 0.030147366225719452, 0.013280809856951237, -0.011789451353251934, 0.008818931877613068, 0.05752053111791611, 0.0034666829742491245, 0.02197089232504368, 0.030375583097338676, 0.002565269824117422, -0.005299773067235947, -0.015467831864953041, 0.04785270616412163, 0.006691137328743935, -0.022602060809731483, 0.0007360278395935893, 0.01200748048722744, -0.08167356252670288, 0.05033833533525467, 0.012089882977306843, 0.047042809426784515, -0.015675587579607964, 0.04792144149541855, 0.007086657918989658, 0.017180761322379112, 0.03945234790444374, -0.01279173418879509, 0.03954199329018593, 0.035762153565883636, -0.0022608519066125154, -0.046721626073122025, -6.5152163776829e-33, -0.011387438513338566, -0.029858633875846863, 0.023664098232984543, -0.013925566338002682, -0.014081384055316448, -0.0018943216418847442, -0.028970330953598022, -0.002697837073355913, -0.015265018679201603, -0.020201565697789192, -0.02738732099533081, 0.017553268000483513, 0.006787015590816736, 0.04867193102836609, 0.05857250094413757, -0.030465882271528244, 0.010077190585434437, 0.01964441128075123, 0.060757361352443695, 0.00575144262984395, 0.09927202016115189, 0.06891824305057526, 0.09583083540201187, -0.014728723093867302, -0.021865010261535645, -0.02376638911664486, 0.03587888926267624, -0.008159376680850983, -0.009122319519519806, 0.025515727698802948, -0.034184448421001434, 0.019598733633756638, 0.034825630486011505, -0.08637437224388123, -0.024672122672200203, 0.004282323177903891, -0.05694390460848808, -0.07543687522411346, -0.009045078419148922, 0.005787340458482504, -0.059228379279375076, 0.009079936891794205, 0.0812612995505333, 0.00788008514791727, -0.002810870995745063, 0.04916775971651077, 0.016814332455396652, -0.006192198023200035, -0.01422309223562479, 0.004875399637967348, -0.06531711667776108, 0.02176937460899353, 0.026495909318327904, 0.01023774966597557, 0.03378726541996002, -0.014882713556289673, -0.017462264746427536, -0.017374662682414055, -0.12483904510736465, -0.025542737916111946, -0.008668524213135242, 0.08763585239648819, 0.033503275364637375, 0.05244245380163193, -0.013072885572910309, 0.009648802690207958, 0.05388358607888222, 0.005005684681236744, 0.007428376469761133, 0.027359873056411743, 0.0005599696305580437, 0.013810470700263977, 0.10157200694084167, -0.00020696190767921507, 0.10957082360982895, -0.021224040538072586, -0.029963558539748192, -0.008780945092439651, 0.029418017715215683, 0.07567638903856277, 0.03534300625324249, -0.0022712924983352423, -0.023314466699957848, -0.008535654284060001, 0.018110090866684914, 0.0545252300798893, -0.0456453301012516, -0.061161551624536514, 0.05178095027804375, -0.008055632002651691, 0.024678479880094528, 0.027605218812823296, 0.00801297090947628, -0.008919605053961277, 0.04499901086091995, 0.0044196718372404575, 0.01456885039806366, 0.002860523061826825, -0.010001691058278084, 0.00080628483556211, -0.05268023908138275, -0.009858429431915283, 0.0016716265818104148, 0.023970840498805046, -0.004690992645919323, 0.011748434975743294, 0.04094500467181206, 0.004908654373139143, -0.02144201658666134, -0.02799179032444954, -0.01871652342379093, 0.0009014041279442608, 0.019633909687399864, 0.037765201181173325, 0.01504435669630766, -0.01724856160581112, -0.009882413782179356, 0.07721451669931412, -0.0021072307135909796, -0.018810974434018135, -0.00458745751529932, -0.06082897633314133, 0.048094239085912704, 0.022665424272418022, -0.02865350805222988, -0.009920655749738216, -0.04642549529671669, 0.03030136600136757, -0.012933402322232723, -0.046660564839839935, 0.013957604765892029, 0.04992101714015007, 2.9935196721453394e-07, 0.01047891192138195, 0.006486530881375074, 0.03503445163369179, -0.004185506608337164, -0.004879904445260763, -0.020627710968255997, -0.019673429429531097, 0.02429596707224846, -0.0023631411604583263, 0.019636178389191628, 0.015414630062878132, -0.009906308725476265, -0.0032998232636600733, -0.007193587254732847, -0.0962439626455307, -0.038326844573020935, -0.08423792570829391, 0.04402674362063408, 0.0045456658117473125, 0.037043407559394836, 0.08311934769153595, 0.08314052224159241, 0.006668125744909048, -0.02222314104437828, -0.00699204346165061, -0.002628898248076439, 0.009022763930261135, 0.020277855917811394, 0.011335530318319798, -0.015445119701325893, 0.03161357343196869, 0.0358540378510952, -0.03781361132860184, -0.007071972358971834, -0.028966376557946205, 0.02864910662174225, 0.008689332753419876, -0.03583689406514168, -0.013648402877151966, -0.06357687711715698, 0.04360758513212204, -0.009394763968884945, -0.0056511275470256805, 0.007803583983331919, 0.03189966455101967, -0.03169088438153267, -0.04161608964204788, 0.019564617425203323, 0.0028665063437074423, 0.02116275206208229, 0.004565894603729248, -0.012796365655958652, 0.009652111679315567, -0.022981738671660423, -0.010865380987524986, -0.04584665223956108, -0.02860046923160553, -0.09049706161022186, 0.014062351547181606, 0.02264087088406086, -0.039204955101013184, -0.0069297365844249725, -0.07508254051208496, 0.0005036233924329281, 0.04678814858198166, -0.055863168090581894, -0.030595870688557625, 2.569908912450879e-34, 0.0069054290652275085, -0.011668136343359947, -0.029132211580872536, 0.022530779242515564, -0.0028448179364204407, -0.009798893705010414, -0.03577689453959465, 0.019774150103330612, 0.0032880306243896484, -0.07688524574041367, -0.08746539056301117]

['Lin Ma', 'Zhengdong Lu', 'Hang Li']

1506.00333v2

In this paper, we propose to employ the convolutional neural network (CNN) for the image question answering (QA). Our proposed CNN provides an end-to-end framework with convolutional architectures for learning not only the image and question representations, but also their inter-modal interactions to produce the answer. More specifically, our model consists of three CNNs: one image CNN to encode the image content, one sentence CNN to compose the words of the question, and one multimodal convolution layer to learn their joint representation for the classification in the space of candidate answer words. We demonstrate the efficacy of our proposed model on the DAQUAR and COCO-QA datasets, which are two benchmark datasets for the image QA, with the performances significantly outperforming the state-of-the-art.

Learning to Answer Questions From Image Using Convolutional Neural Network

http://arxiv.org/pdf/1506.00333v2

Title Learning Answer Questions Image Using Convolutional Neural Network Summary paper propose employ convolutional neural network CNN image question answering QA proposed CNN provides endtoend framework convolutional architecture learning image question representation also intermodal interaction produce answer specifically model consists three CNNs one image CNN encode image content one sentence CNN compose word question one multimodal convolution layer learn joint representation classification space candidate answer word demonstrate efficacy proposed model DAQUAR COCOQA datasets two benchmark datasets image QA performance significantly outperforming stateoftheart Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0839354544878006, 0.060329996049404144, -0.008508297614753246, 0.08565450459718704, -0.015195291489362717, 0.00968173984438181, 0.025598539039492607, 0.0436222068965435, 0.002900107530876994, -0.03461875766515732, 0.015335976146161556, 0.011785490438342094, -0.03949568793177605, 0.04100176692008972, 0.018722284585237503, -0.07422883063554764, 0.019836727529764175, 0.014088167808949947, -0.013008960522711277, 0.003645141376182437, 0.05339130014181137, 0.010049746371805668, -0.0043484484776854515, 0.0311543308198452, -0.036088865250349045, -0.030255844816565514, -0.031989794224500656, 0.024876495823264122, -0.02507687546312809, -0.029603807255625725, 0.03655320405960083, 0.06747065484523773, 0.009530245326459408, 0.023104345425963402, 1.8592101014291984e-06, 0.00043618734343908727, -0.008483218960464, -0.0227177944034338, 0.013042286038398743, -0.03424197807908058, 0.024311399087309837, 0.009003126993775368, 0.029484691098332405, 0.01940760761499405, -0.06467737257480621, 0.02956545725464821, 0.03304649516940117, 0.08970840275287628, 0.056049272418022156, 0.02947291173040867, -0.01944112963974476, -0.0552050955593586, 0.04541819915175438, 0.0032902159728109837, 0.02731337584555149, -0.002553466707468033, -0.023139627650380135, 0.007861643098294735, -0.0008991082431748509, 0.021654900163412094, -0.03336944803595543, 0.07741685211658478, 0.0237121619284153, -0.017158376052975655, 0.002222706563770771, 0.0338909886777401, 0.0010787112405523658, -0.03551783785223961, -0.008168218657374382, 0.12456773221492767, -0.027773752808570862, 0.006971739698201418, -0.0485740527510643, -0.005251074209809303, 0.02249765582382679, 0.03270600736141205, -0.0481049008667469, -0.002446969272568822, -0.026997091248631477, 0.00022821234597358853, -0.04076627269387245, 0.001567893661558628, -0.029876982793211937, 0.0305886622518301, -0.008174681104719639, -0.034038398414850235, 0.022000690922141075, -0.006525122094899416, -0.016157228499650955, 0.0086280582472682, 0.003801950952038169, -0.055162861943244934, 0.026893137022852898, 0.03640388697385788, 0.02718442678451538, 0.019285893067717552, -0.03659096360206604, -0.08559620380401611, 0.03813431039452553, -0.048449013382196426, -0.002375252079218626, -0.011127649806439877, -0.046819690614938736, 0.030207952484488487, -0.02334265224635601, 0.04149133712053299, 0.014508452266454697, 0.04168850928544998, -0.06437555700540543, -0.009612093679606915, -0.016602547839283943, -0.032999638468027115, -0.03432484343647957, 0.057915642857551575, -0.05387286841869354, -0.05486192926764488, -0.01989063248038292, 0.0018753474578261375, 0.04813966527581215, 0.00458936532959342, -0.0086525222286582, 0.07204221934080124, 0.004945067688822746, 0.02131194807589054, -0.0321994423866272, 0.03036256693303585, -0.0392327718436718, 0.0290820449590683, 0.019794346764683723, -0.014786683954298496, 0.03075583465397358, -0.003662586910650134, 0.05711231753230095, -0.003804170060902834, 0.03565211594104767, 0.03884058818221092, -0.015178199857473373, -0.06780700385570526, 0.032503604888916016, -0.032413214445114136, -0.022129852324724197, -0.013001617975533009, 0.0021244569215923548, -0.06320508569478989, 0.04918256774544716, -0.016210174188017845, 0.0009905964834615588, 0.022783562541007996, 0.016978485509753227, 0.06952540576457977, -0.034347232431173325, 0.09394580870866776, -0.02725636586546898, -0.01299060508608818, 0.08341464400291443, 0.011769680306315422, 0.10017946362495422, 0.021964577957987785, 0.002991848159581423, 0.02565883658826351, 0.0492933951318264, -0.0023246142081916332, 0.03688453510403633, 0.009941563941538334, 0.012000129558146, -0.033491458743810654, 0.013777841813862324, 0.04957158491015434, 0.01274866797029972, 0.039675161242485046, -0.0373644195497036, 0.08053187280893326, 0.015929704532027245, -0.04533299058675766, 0.0651605874300003, 0.07595445215702057, -0.008791593834757805, 0.02221478335559368, -0.04520116373896599, 0.025960421189665794, 0.046087365597486496, -0.012765550054609776, -0.036277998238801956, 0.08316420018672943, -0.020473530516028404, -0.017280392348766327, -0.0062992628663778305, -0.0029922369867563248, -0.051867708563804626, -0.03102586604654789, -0.002147887833416462, -0.00958607904613018, -0.010446145199239254, 0.018331531435251236, 0.008225020952522755, 0.028026944026350975, -0.06071985885500908, -0.012826747260987759, -0.01044066995382309, -0.03297530859708786, -0.01159591879695654, -0.045224085450172424, 0.034196801483631134, -0.0016600160161033273, 0.023343943059444427, -0.01581669971346855, -0.0131771769374609, -0.022481955587863922, 0.02264365926384926, 0.045890700072050095, -0.006007700227200985, -0.006732659880071878, -0.0036415765061974525, -0.03339538723230362, -0.025691207498311996, -0.012935741804540157, -0.03998227044939995, -0.021321536973118782, -0.00022958558110985905, 0.013938091695308685, 0.017429867759346962, 0.03682519868016243, -0.026566382497549057, 0.04615448787808418, 0.07048486173152924, -0.026653731241822243, 0.006705437786877155, 0.037605978548526764, -0.018604207783937454, 0.03014383465051651, -0.015705544501543045, 0.01860073022544384, 0.019748719409108162, -0.036240577697753906, -0.056322794407606125, 0.004035004414618015, -0.05243704468011856, -0.07232746481895447, 0.003516930853947997, -0.07882830500602722, 0.03651629760861397, 0.0553988479077816, -0.03331845998764038, -0.028222443535923958, -0.024959146976470947, -0.027157101780176163, -0.007815184071660042, -0.051444150507450104, -0.01861729472875595, 0.03049914538860321, 0.02839108742773533, -0.06048114225268364, 0.037958912551403046, -0.028707774356007576, 0.016892164945602417, -0.06103535741567612, 0.008501704782247543, 0.005325670354068279, -0.01881636120378971, -0.025466809049248695, 0.015655040740966797, -0.02423439919948578, 0.02135797217488289, 0.01547201257199049, 0.027758227661252022, -0.03976908326148987, 0.00048616487765684724, -0.09219668060541153, -0.04567229375243187, -0.011442006565630436, -0.019013328477740288, 0.020752521231770515, 0.04352576285600662, 0.0016988562420010567, -0.06751948595046997, -0.07512617111206055, 0.03397093340754509, 0.03764178603887558, 0.024238551035523415, 0.06735827773809433, 0.0061360797844827175, 0.05748765170574188, -0.04428718984127045, -0.0333947017788887, 0.004342320840805769, 0.04993045702576637, 0.03388768061995506, -0.02448030188679695, 0.000917287019547075, -0.05600966513156891, -0.039322737604379654, 0.02988964319229126, 0.03659364953637123, -0.05191633105278015, -0.002075999276712537, -0.034950073808431625, 0.02508341521024704, 0.05790559947490692, 0.03537894785404205, 0.007425275165587664, -0.023240337148308754, 0.02942170575261116, -0.011779059655964375, 0.01830194517970085, -0.022412247955799103, -0.03911055251955986, 0.029745562002062798, -0.01912776567041874, -0.006706574931740761, 0.009945864789187908, 0.017891069874167442, -0.0034089493565261364, -0.017039114609360695, 0.03197720646858215, -0.05058472603559494, -0.009456157684326172, -0.10563588887453079, 0.021652385592460632, 0.01523546315729618, 0.034424252808094025, -0.02623729407787323, -0.043547123670578, 0.03191894292831421, -0.006260765716433525, -0.006633728742599487, -0.0497099794447422, -0.030427096411585808, -0.03857798874378204, 0.08356133103370667, 0.011769718490540981, 0.032785288989543915, 0.006466996390372515, -0.004529645200818777, -0.04656578227877617, -0.010196875780820847, -0.018995197489857674, -0.03382521867752075, 0.021023882552981377, -0.011205365881323814, 0.01087051909416914, -0.03814837709069252, -0.03790059685707092, -0.041857581585645676, -0.05933714285492897, -0.012407328002154827, -0.011749627999961376, -0.027722163125872612, 0.008037850260734558, 0.027527449652552605, -0.011605879291892052, 0.014043319970369339, 0.002734265523031354, -0.04213371127843857, -0.007605247665196657, -0.008654940873384476, 0.13216152787208557, 0.08209912478923798, 0.024155108258128166, -0.009044944308698177, -0.016080765053629875, 0.0302013847976923, 0.050497278571128845, -0.0026462518144398928, 0.02238951064646244, -0.008578606881201267, 0.005570264998823404, 0.014473110437393188, 0.0015108144143596292, -0.0016421449836343527, 0.005522279534488916, 0.05443521589040756, -0.02469000779092312, 0.0011755675077438354, 0.0568682998418808, 0.056043174117803574, -0.057625070214271545, -0.015144461765885353, 0.021235628053545952, -0.051870375871658325, 0.023042110726237297, 0.04161176458001137, -0.0644298791885376, -0.018346140161156654, -0.04472033306956291, -0.021000657230615616, 0.013375695794820786, 0.006381423678249121, -0.0020551274064928293, -0.04473726823925972, 0.008765012957155704, -0.05140778049826622, -0.04590017348527908, -0.009762334637343884, -0.004259962122887373, -0.023187268525362015, 0.0379805825650692, -0.009500320069491863, 0.014610161073505878, 0.006907692179083824, -0.013937171548604965, -0.0054764277301728725, 0.03183841332793236, 0.05044729635119438, -0.0017122284043580294, -0.040324367582798004, -0.014646747149527073, 0.05749806761741638, 0.04487119987607002, -0.03432111069560051, -0.016624363139271736, 0.00813012570142746, -0.05617957562208176, 0.00995398685336113, -0.014542888849973679, 0.09700250625610352, -0.024333560839295387, -0.005179501138627529, -0.048386815935373306, 0.039996493607759476, -0.011652962304651737, 0.037406086921691895, 0.03888597711920738, 0.008891577832400799, 0.0019885720685124397, 0.024984627962112427, -0.09163075685501099, 0.017352789640426636, 0.03416110575199127, 0.02057611756026745, 0.016945797950029373, -0.055911168456077576, -0.04744629189372063, -0.01902216114103794, -0.014551784843206406, -0.05667345970869064, -0.0006088941008783877, 0.007924810983240604, 0.0072358339093625546, 0.04461913928389549, -0.08387305587530136, -0.04581436887383461, -0.010226131416857243, -0.001040034694597125, -0.006771761458367109, -0.0054305060766637325, -0.004256696440279484, 0.028157591819763184, -0.060899872332811356, -0.01708700694143772, 0.018502864986658096, 0.028398603200912476, -0.03904563933610916, 0.017554042860865593, 0.04613557457923889, -0.05057917535305023, -0.028079096227884293, -0.024670401588082314, -0.08178926259279251, -0.003365089651197195, -0.020075885578989983, 0.03783980756998062, -0.0007684684242121875, -0.02662145346403122, -0.01239051390439272, -0.06527303904294968, 0.02316918596625328, -0.0026448096614331007, -0.0023934750352054834, -0.033551935106515884, -0.024802902713418007, 0.013073469512164593, -0.005761460401117802, 0.023694045841693878, -0.03293788433074951, 0.03639571741223335, 0.0011598820565268397, -0.016946978867053986, -0.03073209896683693, -0.03494594991207123, 0.013919634744524956, 0.0034821692388504744, -0.004887070041149855, 0.030125431716442108, -0.018104854971170425, -0.022909998893737793, 0.04832979664206505, -0.012875785119831562, -0.010820762254297733, -0.034421466290950775, 0.008185326121747494, 0.010119220241904259, -0.005719585809856653, -0.004515987820923328, -0.020974023267626762, 0.007444879971444607, 0.028482526540756226, -0.013495794497430325, 0.015183686278760433, 0.017649587243795395, -0.018231749534606934, -0.03252759948372841, 0.0007389992242679, -0.020283827558159828, 0.02892894670367241, 3.1512145142187364e-06, 0.0293534304946661, 0.009889787994325161, 0.06125859171152115, -0.005672478582710028, -0.051720693707466125, -0.021421749144792557, 0.031958676874637604, -0.04066375643014908, -0.012753603048622608, -0.04483070597052574, 0.07399602234363556, 0.0488547682762146, -0.029196269810199738, -0.05202515050768852, 0.03591388463973999, -0.007062367629259825, 0.021388869732618332, 0.0422733873128891, -0.020782699808478355, -0.03289564326405525, 0.09554451704025269, 0.00137185154017061, 0.022029245272278786, -0.03132244572043419, 0.012394820339977741, -0.003363646799698472, -0.018926572054624557, 0.036092840135097504, -0.0127440569922328, -0.04644768685102463, 0.03422701358795166, 0.004031997174024582, 0.046168021857738495, -0.003683803603053093, 0.06821849197149277, 0.006325230002403259, -0.03251397982239723, -0.011077499948441982, 0.017282571643590927, 0.017358211800456047, 0.028370464220643044, 0.0361732542514801, 0.048200592398643494, 0.03913740813732147, -0.03464899957180023, -0.04124495014548302, 0.026935948058962822, -0.0575096495449543, -0.03138810768723488, -0.0010778959840536118, -6.175319247406758e-33, -0.021740257740020752, -0.0217380840331316, 0.0022964049130678177, 0.003385755931958556, -0.029324769973754883, 0.036576781421899796, -0.011403057724237442, 0.011228051967918873, -0.05727948993444443, -0.00794376153498888, -0.026408841833472252, -0.008005684241652489, 0.010947078466415405, 0.05011630803346634, -0.004389354959130287, -0.034408606588840485, -0.016877440735697746, -0.04059717059135437, 0.032107364386320114, 0.0354900062084198, 0.010806899517774582, 0.03871454671025276, 0.047696709632873535, -0.028746597468852997, 0.0036344900727272034, -0.02879585139453411, 0.0023132534697651863, 0.007850746624171734, 0.0006090628448873758, 0.043643347918987274, -0.03316539525985718, 0.02604476734995842, 0.035781048238277435, 0.010554501786828041, -0.00422538910061121, 0.059820111840963364, -0.09908483177423477, -0.025904688984155655, -0.03408098220825195, 0.02192217856645584, -0.10311945527791977, 0.020329674705863, 0.03680984675884247, -0.03315718099474907, 0.04201488569378853, -0.01724894903600216, 0.07592473924160004, 0.0011010572779923677, 0.014455702155828476, -0.013471987098455429, -0.06227331608533859, -0.010617769323289394, 0.0007157520740292966, -0.0037720082327723503, 0.006648520473390818, 0.05579245835542679, 0.03441562503576279, 0.021080201491713524, -0.03625791519880295, -0.0008602172019891441, 0.010151160880923271, 0.030138948932290077, 0.04825747013092041, 0.03395893797278404, -0.04055581986904144, 0.04683035984635353, 0.0037253343034535646, -0.028691867366433144, 0.0012511066161096096, 0.01633165031671524, 0.02611471153795719, 0.04272692650556564, 0.1195162981748581, 0.027377508580684662, 0.018403129652142525, -0.008823496289551258, -0.06463528424501419, 0.011430192738771439, 0.0010582447284832597, 0.00524019543081522, -0.0034911148250102997, -0.013845419511198997, -0.01905752159655094, 0.050553854554891586, -0.025251582264900208, 0.03250452131032944, -0.06016961485147476, -0.021527254953980446, 0.01401119027286768, 0.0016205012798309326, -0.03159716725349426, 0.03941468149423599, 0.05424440652132034, -0.025656167417764664, -0.002921193605288863, -0.013511509634554386, 0.023553205654025078, 0.025308934971690178, 0.0004342977190390229, 0.010603731498122215, -0.039476215839385986, 0.02984180487692356, 0.0073875542730093, -0.0022760045249015093, -0.03500550240278244, -0.001172287855297327, 0.028800353407859802, -0.026896322146058083, -0.047735076397657394, -0.02896939404308796, 0.006898256950080395, -0.010298267006874084, 0.004150455817580223, 0.030620208010077477, -0.02832464873790741, 0.02568928152322769, -0.05174929276108742, -0.006901993881911039, 0.013883651234209538, -0.014464360661804676, -0.04971732199192047, -0.06479404121637344, 0.03488988056778908, 0.03023863397538662, -0.04828180745244026, 0.0006067603244446218, -0.05927096679806709, -0.004364554304629564, 0.01922546699643135, -0.09073641151189804, -0.007337545044720173, 0.06236924231052399, 2.2749311767711333e-07, 0.05129089951515198, 0.00936020165681839, 0.014485198073089123, 0.034879762679338455, -0.014481405727565289, 0.00241857604123652, 0.042865339666604996, 0.050421394407749176, 0.010796856135129929, 0.021274227648973465, 0.010221075266599655, 0.025646988302469254, 0.014298498630523682, 0.01762085221707821, -0.08673514425754547, -0.027798835188150406, -0.046625006943941116, -0.009091365151107311, -0.046693239361047745, 0.015370875597000122, 0.12624478340148926, 0.0948980301618576, 0.020756803452968597, -0.028225742280483246, 0.0012552108382806182, -0.014278952963650227, 0.025504810735583305, 0.028317177668213844, 0.009343178942799568, -0.007243251893669367, -0.0037640875671058893, 0.0429597944021225, -0.006816544570028782, 0.017822131514549255, -0.0091454042121768, -0.02091161534190178, 0.0824703797698021, -0.00015244766836985946, -0.02278062514960766, -0.0510687381029129, -0.014042767696082592, 0.030758213251829147, -0.007594786584377289, -0.09661886841058731, 0.0956183597445488, -0.024448083713650703, -0.00408789049834013, -0.05301683768630028, -0.015069582499563694, -0.018288416787981987, 0.06066069006919861, -0.0375107079744339, -0.020744672045111656, 0.0017331840936094522, 0.040205687284469604, -0.04639314115047455, -0.0005908397724851966, -0.05809502676129341, -0.018901508301496506, 0.011197948828339577, -0.0018392254132777452, 0.01066336315125227, -0.05421385541558266, -0.056855980306863785, -0.02560650371015072, -0.039609748870134354, -0.05043074116110802, 1.72322616028688e-34, 0.013842007145285606, 0.0064780330285429955, 0.014841092750430107, 0.022266797721385956, -0.031470995396375656, -0.008843318559229374, 0.03096943348646164, -0.012088481336832047, 0.005262668710201979, -0.08879105001688004, -0.025439336895942688]

['Zichao Yang', 'Xiaodong He', 'Jianfeng Gao', 'Li Deng', 'Alex Smola']

1511.02274v2

This paper presents stacked attention networks (SANs) that learn to answer natural language questions from images. SANs use semantic representation of a question as query to search for the regions in an image that are related to the answer. We argue that image question answering (QA) often requires multiple steps of reasoning. Thus, we develop a multiple-layer SAN in which we query an image multiple times to infer the answer progressively. Experiments conducted on four image QA data sets demonstrate that the proposed SANs significantly outperform previous state-of-the-art approaches. The visualization of the attention layers illustrates the progress that the SAN locates the relevant visual clues that lead to the answer of the question layer-by-layer.

Stacked Attention Networks for Image Question Answering

http://arxiv.org/pdf/1511.02274v2

Title Stacked Attention Networks Image Question Answering Summary paper present stacked attention network SANs learn answer natural language question image SANs use semantic representation question query search region image related answer argue image question answering QA often requires multiple step reasoning Thus develop multiplelayer SAN query image multiple time infer answer progressively Experiments conducted four image QA data set demonstrate proposed SANs significantly outperform previous stateoftheart approach visualization attention layer illustrates progress SAN locates relevant visual clue lead answer question layerbylayer Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0011845617555081844, 0.009816315956413746, -0.022241875529289246, 0.03702593967318535, -0.0039842999540269375, -0.007120921742171049, 0.021945452317595482, -0.006195677910000086, 0.010406684130430222, -0.05124964937567711, -0.006271982099860907, 0.05718287080526352, -0.013278278522193432, 0.03345341607928276, 0.03317740187048912, -0.08056799322366714, 0.04781986400485039, -4.213759530102834e-05, -0.015528066083788872, 0.03273460268974304, 0.03095337562263012, -0.005264550447463989, 0.026428889483213425, 0.034501343965530396, 0.01775357499718666, -0.04795278608798981, -0.006918952334672213, -0.0011185093317180872, -0.010772420093417168, -0.0560055747628212, 0.009013289585709572, 0.06388378143310547, 0.05430677905678749, 0.010867835022509098, 2.222142484242795e-06, 0.017437251284718513, 0.03607190400362015, -0.02688777446746826, -0.01762385293841362, -0.0208533126860857, -0.03959483280777931, 0.013349466025829315, 0.038734208792448044, -0.001094247680157423, -0.08147275447845459, -0.03529273346066475, 0.025523805990815163, 0.06559053808450699, 0.09294513612985611, -0.007225257810205221, -0.006103930063545704, -0.03158335015177727, -0.0009761318797245622, 0.009579189121723175, 0.02595590427517891, -0.000987405888736248, -0.002632464747875929, 0.018713727593421936, 0.04649326205253601, 0.006320493295788765, -0.03283711150288582, 0.06771697103977203, 0.024290060624480247, -0.015125714242458344, 0.02446931041777134, 0.045754574239254, -0.02140280045568943, 0.020992768928408623, 0.006277649197727442, 0.0975208431482315, -0.0253197830170393, -0.01064049731940031, -0.07841271162033081, 0.0075826686806976795, -0.004388431552797556, 0.0017367199761793017, -0.05550942197442055, 0.024348527193069458, -0.030286947265267372, 0.006634251214563847, -0.005898888222873211, 0.011204282753169537, -0.0024105538614094257, 0.0011564514134079218, -0.004841628484427929, 0.011426758021116257, 0.0026988540776073933, -0.006084289867430925, -0.007331747096031904, 0.0206398107111454, -0.04177030920982361, -0.05200759693980217, 0.04417729750275612, 0.06075892969965935, -0.018202774226665497, 0.019423959776759148, -0.0046642073430120945, -0.08915896713733673, 0.005194990895688534, -0.05469135567545891, 0.010206366889178753, 0.009879347868263721, -0.06323803961277008, 0.05221272259950638, -0.006858350243419409, 0.020676398649811745, -0.002734885783866048, 0.02755163051187992, -0.04042188450694084, 0.02080126479268074, -0.020032266154885292, -0.037081144750118256, -0.060601331293582916, 0.039193492382764816, -0.05978004261851311, -0.04880475625395775, 0.0062729050405323505, 0.005347042344510555, -0.005151309538632631, -0.017342517152428627, 0.030401039868593216, 0.06676681339740753, 0.003043045988306403, 0.023182349279522896, -0.048767317086458206, 0.061585620045661926, -0.06896915286779404, 0.025949550792574883, 0.008569499477744102, -0.014375394210219383, 0.014123070985078812, 0.02059635892510414, 0.02203790470957756, -0.001280345139093697, 0.005664400290697813, 0.04300510883331299, -0.010309283621609211, -0.010192163288593292, -0.03951810672879219, -0.029844706878066063, 0.01573951356112957, -0.011017315089702606, 0.010100835002958775, -0.024574771523475647, 0.0182366743683815, -0.02942804992198944, -0.03972860425710678, 0.022519243881106377, 0.006518421228975058, 0.07751302421092987, -0.029422689229249954, 0.08292364329099655, -0.014482278376817703, -0.02418292686343193, 0.027166368439793587, 0.02926546521484852, 0.023966901004314423, 0.053020723164081573, -0.004593732766807079, 0.03223148733377457, 0.03385382890701294, -0.01366393081843853, -1.151084688899573e-05, -0.004074123688042164, -0.00921806413680315, -0.033106740564107895, -0.05933113396167755, 0.04960504546761513, -0.014911951497197151, 0.007660399656742811, -0.013077786192297935, 0.01702834852039814, -0.028882797807455063, -0.03484972193837166, 0.027379710227251053, 0.08267645537853241, 0.01383662223815918, 0.013651041314005852, 0.004899334162473679, -0.03775237128138542, 0.01323190052062273, 0.010688346810638905, -0.041222814470529556, 0.10049840062856674, -0.01265658438205719, -0.007012807298451662, -0.03392116725444794, 0.015496739186346531, -0.051177944988012314, -0.02585451863706112, 0.012001730501651764, 0.020075330510735512, -0.007556295022368431, 0.04290171340107918, 0.04933985322713852, 0.04039859399199486, -0.016564689576625824, 0.008364266715943813, 0.0005381142254918814, -0.02001531794667244, 0.0031601518858224154, -0.02727445773780346, 0.051988523453474045, 0.02971671335399151, 0.044933468103408813, -0.03853993862867355, -0.038186196237802505, -0.005081578157842159, 0.016962572932243347, 0.024734536185860634, -0.037082839757204056, 0.003947900142520666, -0.013071809895336628, -0.045395344495773315, -0.017668558284640312, -0.021135449409484863, -0.008653617464005947, -0.009604372084140778, -0.01729653961956501, 0.032651059329509735, -0.0019209322053939104, 0.026367634534835815, 0.017641089856624603, 0.058861538767814636, 0.05185258388519287, 0.014442246407270432, 0.0010506645776331425, 0.040142808109521866, -0.02003849670290947, 0.021177474409341812, 0.013571251183748245, 0.029953552410006523, 0.017041964456439018, -0.03132893890142441, -0.018211500719189644, -0.02670395001769066, -0.04478907585144043, -0.10156185179948807, -0.0010013715364038944, -0.09715506434440613, -0.02064356952905655, 0.026873821392655373, -0.0319904163479805, -0.007283262442797422, 0.021435828879475594, -0.01998671144247055, -0.029249044135212898, -0.04480673372745514, -0.009405821561813354, 0.04286298528313637, 0.035342372953891754, -0.05511850118637085, 0.08991320431232452, -0.030600547790527344, 0.02990066632628441, -0.023548340424895287, -9.051933739101514e-05, 0.03274736553430557, -0.033639777451753616, 0.022068317979574203, -0.013277941383421421, -0.03085767850279808, -0.018158361315727234, -0.02030114457011223, 0.025220314040780067, -0.06010405346751213, 0.01110484916716814, -0.05186477303504944, -0.0016939034685492516, -0.03120367042720318, -0.013676616363227367, 0.018710952252149582, 0.03134448826313019, 0.00715681491419673, -0.07074516266584396, -0.07756782323122025, 0.015331258997321129, 0.010362242348492146, 0.01848350465297699, 0.03619568049907684, 0.0033484480809420347, 0.061502259224653244, -0.028983457013964653, -0.03006320260465145, -0.010761330835521221, 0.05254088342189789, 0.014743599109351635, -0.02934807538986206, -0.016561320051550865, -0.018131690099835396, -0.04783809185028076, 0.05258160084486008, 0.02579006738960743, -0.017622387036681175, 0.028353217989206314, -0.07804317772388458, -0.010309030301868916, 0.08784002810716629, 0.018873896449804306, 0.01549975574016571, -0.0022701772395521402, 0.015277288854122162, -0.020221399143338203, 0.0487297885119915, -0.002966793719679117, 0.06459668278694153, 0.04987450689077377, -0.009418162517249584, -0.006639640312641859, 0.02756025642156601, 0.0058798398822546005, 0.004545069765299559, -0.012642580084502697, 0.01671871729195118, -0.004073458258062601, 0.0031440574675798416, -0.09092628955841064, 0.009223374538123608, 0.0357462540268898, 0.01143618393689394, -0.0539393313229084, -0.017085913568735123, 0.0707552433013916, 0.020526764914393425, -0.028098002076148987, -0.052167218178510666, -0.006132140289992094, -0.0484713613986969, 0.07008609175682068, 0.0013697476824745536, 0.013154669664800167, -0.003184580709785223, -0.01680729165673256, -0.0324874110519886, -0.04663826897740364, -0.00840380135923624, -0.012466316111385822, 0.04328605905175209, -0.005496460944414139, -0.0033447425812482834, -0.04850152134895325, -0.017595479264855385, -0.024844013154506683, -0.03840768709778786, -0.04256448149681091, -0.007724747993052006, -0.04954512417316437, 0.0034845599438995123, 0.004242379684001207, 0.0038213026709854603, 0.0222760122269392, 0.010609655641019344, -0.013169005513191223, -0.025491131469607353, 0.00425051199272275, 0.08209921419620514, 0.07129625231027603, 0.02914547175168991, 0.01783493533730507, -0.019514303654432297, 0.03683299571275711, 0.0634211003780365, 0.019488060846924782, -0.005631611682474613, -0.04306832700967789, 0.02927543967962265, 0.049042534083127975, -0.0030226539820432663, -0.014885229989886284, 0.00292049627751112, 0.04401809349656105, -0.0767013430595398, 0.006531465798616409, 0.06488253176212311, 0.05019697919487953, -0.04201922193169594, -0.006871198769658804, -0.017295226454734802, -0.03571435809135437, 0.04814014211297035, 0.055693503469228745, -0.06326601654291153, -0.04502878710627556, -0.05287180840969086, -0.021262548863887787, 0.018198605626821518, -0.00645184563472867, -0.0034339481499046087, -0.05878826975822449, 0.05358310416340828, -0.0411786325275898, -0.10005883872509003, -0.012998325750231743, -0.008414829149842262, 0.0003405556199140847, 0.04553060233592987, -0.014239826239645481, -0.009165778756141663, 0.015434111468493938, -0.01236503105610609, -0.014779843389987946, 0.006842011585831642, 0.06731733679771423, 0.03211197629570961, -0.06817758828401566, -0.007297070696949959, 0.012641296721994877, 0.02969789318740368, -0.011292415671050549, -0.10826396942138672, -0.012242177501320839, -0.03276514261960983, 0.021593092009425163, -0.028071574866771698, 0.0507751889526844, 0.0008645729976706207, -0.018523182719945908, -0.055855218321084976, 0.029511677101254463, -0.03853362426161766, 0.0069346241652965546, 0.019584771245718002, 0.08282279968261719, -0.03614426776766777, -0.02163573168218136, -0.084108367562294, 0.04648258909583092, 0.015152574516832829, -0.007732930593192577, 0.06922031193971634, -0.033067598938941956, -0.04781687632203102, -0.013500570319592953, -0.0036072824150323868, -0.0666888877749443, 0.015139799565076828, 0.05607910826802254, 0.010678024031221867, -0.0011342125944793224, -0.045827385038137436, -0.04045848548412323, 0.016183631494641304, 0.0632205680012703, -0.03063938580453396, 0.0025777905248105526, -0.0109817860648036, 0.02196599543094635, -0.0272391214966774, 0.01727631501853466, -0.009787279181182384, 0.03953320160508156, 0.017980260774493217, 0.03929780423641205, 0.004265506751835346, -0.01953067258000374, -0.024174734950065613, -0.06908975541591644, -0.04281274974346161, 0.004052688833326101, -0.02873462438583374, 0.05377940461039543, 0.005295430310070515, -0.0292433463037014, -0.048042695969343185, -0.05459392070770264, 0.036831896752119064, 0.0162772499024868, -0.024903617799282074, -0.05706225708127022, -0.017651308327913284, -0.0391492135822773, -0.0019221544498577714, 0.005921386647969484, 0.010004833340644836, 0.02697020210325718, -0.009726299904286861, 0.007619717624038458, -0.0347040593624115, -0.03884477540850639, -0.0063547128811478615, 0.001989742275327444, 0.02676328644156456, 0.049247439950704575, 0.022468550130724907, -0.010097155347466469, 0.030195903033018112, 0.003766145557165146, -0.02327585779130459, -0.01838829554617405, -0.0003887482453137636, -0.007093990687280893, -0.03353936970233917, -0.010848171077668667, -0.0178110022097826, -0.008454902097582817, 0.013141807168722153, -0.01693902350962162, 0.015782300382852554, 0.05586038529872894, 0.03464499115943909, -0.04110698774456978, 0.010598232038319111, -0.031324636191129684, 0.00010679417755454779, 0.0032109853345900774, 0.05133891850709915, -0.007084767334163189, 0.10731585323810577, 0.010214352048933506, -0.005084074102342129, -0.032209813594818115, 0.014690684154629707, -0.05079985037446022, -0.036775071173906326, -0.020756090059876442, 0.003165194997563958, 0.06331329792737961, -0.007883867248892784, -0.051624711602926254, 0.050756338983774185, -0.009383886121213436, 0.022490542382001877, 0.030578212812542915, -0.008967499248683453, -0.04028351977467537, 0.08564338833093643, 0.02037983573973179, 0.01621919497847557, -0.01582213118672371, 0.03630584478378296, -0.04213706776499748, 0.018061531707644463, 0.0333062969148159, -0.04084710404276848, -0.031130632385611534, -0.011495235376060009, 0.0020671430975198746, 0.04857528582215309, -0.009031890891492367, 0.04995495453476906, -0.02822314389050007, -0.06386863440275192, -0.016898496076464653, 0.0199178047478199, 0.005878125783056021, 0.04812284931540489, 0.04001059755682945, 0.017303885892033577, 0.06254202872514725, -0.02291109226644039, -0.017246607691049576, 0.035652220249176025, -0.05516400188207626, -0.025012657046318054, -0.019239498302340508, -6.565196928111925e-33, -0.030948150902986526, -0.0384298712015152, 0.04637030512094498, 0.007371261715888977, -0.04105249047279358, -0.006019520573318005, -0.04769649729132652, -0.015384255908429623, -0.055980272591114044, 0.016152437776327133, -0.040614377707242966, 0.011234498582780361, -0.016219912096858025, 0.04149402678012848, 0.007106482051312923, -0.03923468664288521, -0.009624642319977283, -0.001536295167170465, 0.02769499085843563, 0.023884495720267296, 0.05708931013941765, 0.011853639967739582, 0.05149480327963829, -0.024155268445611, -0.03827885910868645, 0.015121525153517723, -0.0025742321740835905, 0.015329818241298199, -0.023689216002821922, 0.043372105807065964, -0.017751531675457954, 0.013852724805474281, 0.02325558289885521, -0.015900079160928726, -0.025273283943533897, 0.05952782183885574, -0.07999199628829956, -0.07806990295648575, -0.010434173047542572, 0.03220885246992111, -0.10260389745235443, 0.014141634106636047, 0.01637883484363556, -0.0016304190503433347, 0.07436633110046387, -0.013531405478715897, 0.06865402311086655, -0.0004316176346037537, -0.03185876086354256, -0.002469568746164441, -0.0325399711728096, -0.005438924767076969, -0.022947590798139572, 0.0010279114358127117, -0.020761504769325256, 0.05723213031888008, 0.010196886956691742, 0.012066611088812351, -0.043874651193618774, 0.023715995252132416, 0.024698978289961815, 0.015056995674967766, 0.04508531093597412, 0.04380621016025543, 0.004797608125954866, 0.05183447524905205, 0.0036478149704635143, -0.027923818677663803, -0.026029985398054123, -0.014478589408099651, 0.033506155014038086, 0.04657388851046562, 0.09941565990447998, -0.014511817134916782, 0.015228328295052052, 0.015311616472899914, -0.100479856133461, -0.001102931215427816, -0.009770558215677738, 0.07167614996433258, -0.026806369423866272, -0.0064216130413115025, -0.002251560101285577, 0.00867255125194788, -0.022988909855484962, 0.011599118821322918, -0.056051675230264664, -0.012232618406414986, 0.028381941840052605, 0.02310522273182869, -0.005971219390630722, 0.07061117887496948, 0.04304760321974754, -0.021019350737333298, 0.03907462954521179, -0.025676079094409943, 0.03283093497157097, 0.006026087794452906, 0.032347649335861206, 0.017659053206443787, -0.05139264091849327, 0.022402122616767883, 0.017437860369682312, 0.0015060113510116935, -0.027797557413578033, 0.04058238863945007, 0.07612957805395126, -0.017175061628222466, -0.027159716933965683, -0.021291213110089302, -0.012763086706399918, -0.027029994875192642, 0.00476006930693984, 0.014573870226740837, 0.013916635885834694, -0.0006419125711545348, -0.05169295519590378, 0.04066872224211693, 0.008439438417553902, 0.02149420790374279, -0.016655636951327324, -0.03467324748635292, 0.027025312185287476, 0.026196489110589027, -0.01828388310968876, 0.013442019931972027, -0.08398605138063431, -0.004494879860430956, 0.019630229100584984, -0.09977979958057404, -0.011329117231070995, 0.07025135308504105, 2.659583913100505e-07, 0.04821034148335457, -0.012644191272556782, -0.004254376981407404, 0.02601628005504608, 0.03505131974816322, 0.026653079316020012, 0.002312583616003394, 0.013950200751423836, 0.009966081008315086, 0.03317657858133316, -0.01083727553486824, 0.03632860258221626, -4.8208512453129515e-05, 0.03776917606592178, -0.04019118472933769, -0.024282341822981834, -0.04103776067495346, -0.0007966298144310713, -0.028852099552750587, -0.036434344947338104, 0.10209646075963974, 0.09110179543495178, -0.004695145413279533, -0.018946370109915733, 0.014626918360590935, -0.04247280955314636, 0.033165764063596725, 0.05874091386795044, 0.03067750297486782, -0.026504816487431526, -0.004288894589990377, 0.04101044684648514, -0.029747502878308296, 0.0029418973717838526, -0.022947007790207863, -0.025718001648783684, 0.05673695728182793, 0.003611814696341753, -0.040254756808280945, -0.05194107070565224, -0.0006099533056840301, 0.003058869857341051, 0.023818571120500565, -0.06604371964931488, 0.08163677901029587, -0.04715617746114731, -0.011759338900446892, -0.035232063382864, -0.05289417877793312, -0.0067939781583845615, 0.04009663313627243, -0.0201913770288229, 0.007931637577712536, -0.013167360797524452, 0.01857004128396511, -0.053101420402526855, -0.01470012217760086, -0.09397771954536438, -0.018612835556268692, 0.005992715246975422, -0.01577325165271759, 0.03302683308720589, -0.05581476911902428, -0.024716772139072418, 0.030433200299739838, -0.037902772426605225, -0.055515822023153305, 2.327586721336115e-34, 0.007241746410727501, -0.013489734381437302, 0.021999990567564964, 0.03113812394440174, 0.004547945223748684, -0.025245219469070435, -0.01669337786734104, -0.031100934371352196, 0.040600743144750595, -0.08842460066080093, -0.019055292010307312]

['Jacob Andreas', 'Marcus Rohrbach', 'Trevor Darrell', 'Dan Klein']

1511.02799v4

Visual question answering is fundamentally compositional in nature---a question like "where is the dog?" shares substructure with questions like "what color is the dog?" and "where is the cat?" This paper seeks to simultaneously exploit the representational capacity of deep networks and the compositional linguistic structure of questions. We describe a procedure for constructing and learning *neural module networks*, which compose collections of jointly-trained neural "modules" into deep networks for question answering. Our approach decomposes questions into their linguistic substructures, and uses these structures to dynamically instantiate modular networks (with reusable components for recognizing dogs, classifying colors, etc.). The resulting compound networks are jointly trained. We evaluate our approach on two challenging datasets for visual question answering, achieving state-of-the-art results on both the VQA natural image dataset and a new dataset of complex questions about abstract shapes.

Neural Module Networks

http://arxiv.org/pdf/1511.02799v4

Title Neural Module Networks Summary Visual question answering fundamentally compositional naturea question like dog share substructure question like color dog cat paper seek simultaneously exploit representational capacity deep network compositional linguistic structure question describe procedure constructing learning neural module network compose collection jointlytrained neural module deep network question answering approach decomposes question linguistic substructure us structure dynamically instantiate modular network reusable component recognizing dog classifying color etc resulting compound network jointly trained evaluate approach two challenging datasets visual question answering achieving stateoftheart result VQA natural image dataset new dataset complex question abstract shape Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03032113052904606, 0.04285570979118347, -0.05058463290333748, 0.021224964410066605, -0.01112926285713911, 0.04416812211275101, 0.020102521404623985, -0.005148149561136961, -0.01478614378720522, -0.02363499067723751, -0.027765372768044472, 0.009290046989917755, -0.015773294493556023, 0.03814404830336571, 0.023192064836621284, -0.08409348875284195, 0.020600808784365654, 0.022446639835834503, -0.05754339322447777, -0.0059337373822927475, 0.04706820845603943, 0.007209664676338434, 0.0120700066909194, 0.04013754427433014, -0.019264476373791695, -0.016891086474061012, -0.04943600669503212, -0.0060898191295564175, -0.028730612248182297, -0.037596944719552994, 0.017979390919208527, 0.027693700045347214, 0.025712573900818825, 0.016324322670698166, 1.9617129964899505e-06, 0.017269708216190338, 0.001951830112375319, -0.02329745516180992, 0.026917850598692894, -0.06171092018485069, 0.028547316789627075, -0.01854371652007103, 0.021680140867829323, 0.017104685306549072, -0.04496710002422333, -0.011085877195000648, 0.048926372081041336, 0.06544551998376846, 0.05541270971298218, 0.03448942303657532, -0.006929853465408087, -0.07372879236936569, 0.017879048362374306, -0.0029566052835434675, 0.02875771000981331, 0.0028744153678417206, 0.0014669292140752077, 0.0515374056994915, 0.02557825669646263, -0.0038184316363185644, -0.021765945479273796, 0.036064546555280685, 0.047824859619140625, -0.018059687688946724, 0.014889238402247429, 0.05886790156364441, 0.00737269502133131, -0.018613697960972786, 0.01418407540768385, 0.11069965362548828, -0.021844716742634773, -0.0019519865745678544, -0.0024404465220868587, -0.008679904043674469, -0.007206883281469345, 0.01905815862119198, -0.036067407578229904, 0.023313678801059723, -0.027272308245301247, 0.0122228330001235, 0.008332718163728714, 0.012942113913595676, -0.021494437009096146, 0.0014331081183627248, -0.01607629470527172, 0.00714548584073782, 0.0219230018556118, 0.005763648077845573, -0.025343021377921104, 0.013611778616905212, 0.01174840796738863, -0.059411484748125076, 0.0012327146250754595, 0.05018959194421768, 0.01765480637550354, 0.007276537362486124, -0.02745569497346878, -0.079874187707901, 0.02799607254564762, -0.04831920564174652, 0.02484545111656189, -0.024747787043452263, -0.035692501813173294, 0.04546359181404114, -0.007604888174682856, 0.04097144305706024, -0.02610885165631771, 0.042387597262859344, -0.07680465281009674, -0.013031878508627415, -0.0860753282904625, -0.024998068809509277, -0.04437802731990814, 0.077266164124012, -0.02612374909222126, -0.037103112787008286, -0.015116605907678604, 0.011370865628123283, -0.0023160965647548437, -0.006580363027751446, 0.007672008592635393, 0.06223190203309059, -0.009318669326603413, -0.003686594543978572, -0.03052779845893383, 0.025055278092622757, -0.0666489452123642, 0.03648577257990837, -0.01934729889035225, -0.018872812390327454, 0.03738526999950409, 0.012015287764370441, 0.01792503520846367, -0.0171882975846529, 0.004770745523273945, 0.06414882093667984, -0.013771429657936096, -0.014737796038389206, -0.03061877004802227, -0.04910756275057793, 0.015789948403835297, -0.05503368005156517, 0.039713919162750244, -0.07718680053949356, 0.0411137230694294, -0.02789854258298874, -0.013527904637157917, 0.00260177836753428, -0.012835781089961529, 0.023659013211727142, -0.022299835458397865, 0.12344922125339508, -0.00520099513232708, -0.02616736851632595, 0.03625190258026123, 0.015893427655100822, 0.05242752283811569, 0.03502962365746498, 0.014236953109502792, 0.03733178600668907, 0.012636382132768631, 0.002120523015037179, 0.030517585575580597, -0.02459423802793026, -0.01533899549394846, -0.020752208307385445, 0.005914177745580673, 0.020964281633496284, -0.0015450740465894341, 0.03843910992145538, -0.04553593695163727, 0.056248411536216736, -0.001662784954532981, -0.02835249900817871, 0.05640392005443573, 0.05642015486955643, 0.05472111329436302, 0.0018920897273346782, 0.01940583996474743, -0.017001880332827568, 0.019095750525593758, 0.0483536571264267, -0.018918709829449654, 0.06377457827329636, -0.05773218348622322, -0.03759584203362465, -0.032676201313734055, 0.025532769039273262, -0.06738046556711197, -0.04768732190132141, 0.003917002119123936, -0.02213980071246624, 0.05892490595579147, -0.015928709879517555, 0.049187593162059784, 0.00014292393461801112, -0.004195493180304766, -0.02985176257789135, -0.01037873700261116, 0.005521127488464117, 0.006607140880078077, -0.03533615916967392, 0.046392492949962616, -0.007534493692219257, 0.0018424022709950805, -0.07343120127916336, -0.028902502730488777, 0.0026618088595569134, 0.0004111949820071459, 0.006194017827510834, -0.021773027256131172, -0.019543150439858437, 0.009854438714683056, -0.025394903495907784, -0.0006851967773400247, -0.02638191543519497, -0.0013874584110453725, -0.01108810119330883, -0.02551387809216976, 0.008955638855695724, 0.005486640147864819, 0.04004741460084915, 0.03827959671616554, 0.05770980939269066, 0.01655060239136219, 0.01761491969227791, -0.0023588857147842646, 0.03931450471282005, 0.013677369803190231, 0.0066540781408548355, 0.0064409454353153706, 0.022840730845928192, 0.03350155055522919, -0.05290308967232704, -0.05260125920176506, 0.0077739376574754715, -0.026443613693118095, -0.07561884075403214, 0.02662312053143978, -0.07858685404062271, -0.00830880831927061, 0.00548448134213686, -0.04603150114417076, -0.023129766806960106, 0.02429673820734024, -0.048131175339221954, -0.031807269901037216, -0.042526088654994965, -0.006567281670868397, 0.02902449108660221, 0.014600255526602268, -0.05038352683186531, 0.047827787697315216, -0.0018013385124504566, 0.005466681905090809, -0.027493443340063095, -0.016921378672122955, 0.0338115356862545, -0.011348049156367779, -0.01934998668730259, 0.03109929896891117, -0.01718083955347538, 0.01342916302382946, -0.017994072288274765, -0.007098180241882801, -0.05067784711718559, -0.023800577968358994, -0.0350368469953537, -0.030323313549160957, -0.0020735766738653183, -0.02483467012643814, 0.02371433936059475, -0.01754124090075493, 0.030414529144763947, -0.035528119653463364, -0.06683715432882309, 0.0343482606112957, 0.009532039985060692, 0.03193436935544014, 0.0599556528031826, 0.00904889591038227, 0.026165729388594627, -0.012532549910247326, -0.03862437233328819, -0.02301446907222271, 0.0615505613386631, 0.014704140834510326, -0.001783208455890417, -0.011152198538184166, -0.06170635670423508, -0.05772677809000015, 0.03638610616326332, 0.01770813576877117, -0.07962796092033386, 0.02592289447784424, -0.05273875221610069, 0.03218018263578415, 0.060219068080186844, 0.009336637333035469, 0.03747666999697685, 0.031481124460697174, 0.011198076419532299, -0.00615674490109086, 0.007301968522369862, -0.012170151807367802, 0.05883513018488884, 0.029804779216647148, -0.008137769065797329, 0.0031737794633954763, 0.044166453182697296, 0.003577484982088208, -0.024661310017108917, -0.020202454179525375, 0.0804658830165863, -0.005722906906157732, -0.02207498997449875, -0.035643234848976135, -0.05162733048200607, 0.040912553668022156, 0.03622947633266449, -0.024728747084736824, -0.042669251561164856, 0.055928293615579605, 0.01436692476272583, -0.003646252676844597, -0.014366771094501019, -0.03536062315106392, -0.045985158532857895, 0.08824964612722397, 0.044725991785526276, -0.004446676466614008, 0.03544153645634651, -0.0310507919639349, -0.06381303071975708, -0.0014498824020847678, 0.012539323419332504, -0.028313767164945602, 0.015628473833203316, -0.045320551842451096, 0.014598539099097252, -0.059411678463220596, -0.0394195057451725, -0.029796455055475235, 0.016479505226016045, 0.005346613936126232, 0.02873406931757927, -0.016017479822039604, 0.0027116129640489817, -0.008014076389372349, 0.005014472175389528, -0.00046867894707247615, -0.008030046708881855, -0.008455312810838223, 0.025230105966329575, -0.006158607546240091, 0.10411547124385834, 0.046631284058094025, 0.0532662495970726, 0.006616073194891214, -0.025993594899773598, 0.0245619285851717, 0.0241249967366457, -0.004452085588127375, 0.015093041583895683, -0.05077742785215378, 0.02166379801928997, -0.011311627924442291, -0.014996649697422981, -0.030180230736732483, -0.028733721002936363, 0.01501629687845707, -0.08026407659053802, 0.02649206668138504, 0.030287913978099823, 0.041929952800273895, -0.04337455704808235, -0.0266592837870121, 0.022490469738841057, -0.03911885991692543, 0.03241042047739029, 0.04660945385694504, -0.07825065404176712, 0.008887827396392822, -0.01544012501835823, -0.040645699948072433, -0.02373986318707466, -0.03842070326209068, 0.004911881405860186, -0.08964034169912338, 0.02027236670255661, -0.025969456881284714, -0.09571898728609085, -0.050595082342624664, 0.01950526237487793, -0.03433087840676308, 0.02080901898443699, -0.04168722406029701, -0.01888592168688774, 0.011967291124165058, -0.03289956972002983, 0.004083526320755482, -0.05062035098671913, 0.03271535411477089, 0.004974778275936842, -0.05302351340651512, 0.016072425991296768, 0.023269306868314743, 0.039372481405735016, -0.01056868676096201, -0.0313057079911232, 0.012936779297888279, -0.07326871156692505, -0.019873758777976036, -0.009369040839374065, 0.043206099420785904, 0.010440969839692116, -0.014984684064984322, -0.015273344703018665, 0.05057293176651001, -0.00212762295268476, 0.01077506598085165, -0.026148539036512375, 0.04788725823163986, -0.038069963455200195, -0.0015437600668519735, -0.08924181014299393, 0.0451354905962944, 0.017388131469488144, 0.015325515531003475, 0.03650018200278282, -0.022513629868626595, -0.040861260145902634, 0.000379121775040403, -0.006758084055036306, -0.055796775966882706, -0.009075663052499294, 0.04459776729345322, -0.006998986937105656, 0.03994828090071678, -0.10228393226861954, -0.03529130667448044, 0.042103372514247894, 0.02233743853867054, 0.0007632225169800222, -0.0001966051058843732, 0.006269014906138182, -0.0008279223111458123, -0.058368295431137085, 0.017583273351192474, 0.017706895247101784, 0.018165552988648415, -0.030561745166778564, -0.020481208339333534, 0.02549370750784874, -0.05141839012503624, -0.02445623092353344, -0.06250988692045212, -0.06903804838657379, -0.031029565259814262, -0.019989177584648132, 0.05753276124596596, 0.0060435133054852486, -0.023874599486589432, -0.020977895706892014, -0.08808556199073792, -0.008907679468393326, 0.01129073090851307, -0.006074362434446812, -0.03681850805878639, 0.010233759880065918, 0.012515331618487835, 0.01004751492291689, 0.03389706090092659, -0.00392485223710537, 0.04723834618926048, 0.01783837005496025, -0.028330257162451744, -0.0038332121912389994, -0.010588707402348518, 0.029057832434773445, -0.01215414796024561, -0.01150667853653431, 0.0396784283220768, 0.009634303860366344, -0.0452023409307003, 0.033671606332063675, 0.007500193081796169, -0.03268367797136307, -0.05133277550339699, -0.027066949754953384, 0.034490447491407394, 0.015276769176125526, -0.011537902057170868, 0.007689848076552153, 0.018134906888008118, 0.06387592107057571, 0.018090663477778435, 0.05438375845551491, 0.03918196260929108, -0.011457206681370735, -0.04372435808181763, 0.03090309165418148, -0.016394076868891716, -0.0066518927924335, -0.023797564208507538, 0.0347791351377964, -0.025079375132918358, 0.03970126062631607, 0.009305630810558796, 0.0027540691662579775, -0.07214733213186264, 0.03383979573845863, -0.026996925473213196, -0.041928526014089584, -0.027072280645370483, 0.04771538823843002, 0.03474811837077141, -0.017841069027781487, -0.07274179905653, 0.019266964867711067, -0.023849796503782272, -0.022640705108642578, 0.05413428321480751, -0.010161819867789745, -0.003969923127442598, 0.08390338718891144, 0.026130011305212975, 0.012742486782371998, -0.059846892952919006, 0.06476380676031113, 0.011409558355808258, 0.01637735217809677, 0.021503109484910965, 0.0010723922168835998, -0.01577378623187542, 0.02956503815948963, 0.04926257207989693, 0.01421356201171875, -0.02466914989054203, 0.0280123483389616, -0.027560465037822723, -0.026333171874284744, 0.007344231940805912, 0.051218803972005844, 0.023946991190314293, 0.05759958550333977, 0.05104369670152664, 0.025240158662199974, 0.04297560453414917, -0.00941617414355278, -0.01995730772614479, 0.007011395413428545, -0.001606813631951809, -0.022515712305903435, 0.011788642965257168, -5.99586607575832e-33, -0.02646922878921032, -0.019844574853777885, 0.028026394546031952, -0.021288251504302025, -0.05420411005616188, 0.028406916186213493, -0.015532363206148148, 0.015033752657473087, -0.04525154083967209, 0.00867469422519207, -0.010024797171354294, -0.005095199681818485, 0.006178989540785551, 0.026404155418276787, 0.030861077830195427, -0.00234507885761559, -0.003278078744187951, -0.0064589097164571285, 0.017596445977687836, 0.011566582135856152, -0.007524746935814619, 0.03161758929491043, 0.03966313228011131, -0.06340186297893524, -0.04787694662809372, 0.0363973043859005, 0.030400948598980904, 0.013922233134508133, -0.02860451489686966, 0.06059132143855095, -0.02620016597211361, -0.014417773112654686, 0.06924988329410553, 0.009327830746769905, -0.010440629906952381, 0.03816327080130577, -0.10573448240756989, -0.03706487640738487, -0.03404397517442703, -0.0015110330423340201, -0.09120532870292664, -0.023326842114329338, 0.05147532373666763, -0.02595919743180275, 0.06296870112419128, -0.029483536258339882, 0.08191213756799698, -0.022089356556534767, -0.012136525474488735, 0.004305298440158367, -0.06708057224750519, 0.0035190763883292675, -0.023288100957870483, 0.016970857977867126, 0.008895514532923698, 0.019073432311415672, 0.024726606905460358, 0.06333307176828384, -0.027454987168312073, 0.0267932191491127, -0.0011781506473198533, 0.03912044316530228, 0.015043755993247032, 0.03245143964886665, 0.024776071310043335, 0.05931643769145012, 0.06775328516960144, -0.0010090338764712214, -0.05750042572617531, 0.00027380348183214664, 0.022543201223015785, 0.0897451713681221, 0.10689502209424973, 0.03921221196651459, 0.05953490734100342, 0.0343775600194931, -0.07711779326200485, 0.029965251684188843, -0.005951876752078533, 0.029139768332242966, -0.0669856071472168, 0.015369560569524765, 0.031177600845694542, 0.03685957193374634, -0.01159429457038641, 0.02001071907579899, -0.041130706667900085, -0.024990763515233994, 0.001347354263998568, 0.01052080001682043, -0.04583468660712242, 0.039634667336940765, 0.05058223009109497, -0.05663711950182915, 0.015947874635457993, -0.04828007519245148, 0.040537748485803604, 0.04063601791858673, 0.023783190175890923, 0.00481464434415102, -0.03542197868227959, -0.018603047356009483, 0.03532310947775841, -0.009188942611217499, 0.0025859957095235586, 0.015626167878508568, 0.04759243503212929, 0.021084319800138474, -0.013327221386134624, -0.017030639573931694, -0.01511723455041647, -0.029322229325771332, -0.006943115498870611, 0.08365677297115326, 0.018404891714453697, 0.03238864615559578, -0.03010997548699379, -0.04037367179989815, 0.011619340628385544, -0.00342226168140769, -0.05123663321137428, -0.042360153049230576, 0.0201705489307642, 0.03657564893364906, -0.028872551396489143, -0.01716172881424427, -0.09289048612117767, -0.03862493112683296, 0.060604289174079895, -0.06366094946861267, -0.008802099153399467, 0.03146852180361748, 2.6228894967061933e-07, 0.05368383601307869, -0.005954680498689413, 0.04327762499451637, 0.022445395588874817, 0.037013761699199677, 0.0021364812273532152, -0.04681533947587013, 0.04058586806058884, -0.050630711019039154, 0.012211582623422146, 0.030738307163119316, 0.027877839282155037, 0.029145700857043266, 0.04390100762248039, -0.06767508387565613, 0.023018203675746918, -0.034065138548612595, -0.00822488497942686, -0.055807117372751236, -0.030132317915558815, 0.07314049452543259, 0.0889999195933342, 0.023611852899193764, -0.013427206315100193, 0.014063139446079731, -0.027452340349555016, 0.03160620853304863, 0.026719525456428528, 0.03785546496510506, 0.00340312160551548, -0.013992095366120338, 0.05620172619819641, -0.007481400854885578, 0.012314854189753532, -0.005409850273281336, -0.014626388438045979, 0.03708350285887718, -0.015150051563978195, -0.006499381270259619, -0.054523810744285583, 0.019243771210312843, -0.00800351332873106, 0.006556236185133457, -0.04154856875538826, 0.08657698333263397, -0.05063929781317711, -0.00972120463848114, -0.01924235373735428, -0.017565716058015823, 0.0005248083034530282, 0.0465351901948452, -0.010658521205186844, -0.01940486766397953, 0.045566581189632416, 0.023112405091524124, -0.05120590701699257, 0.012646663933992386, -0.08436450362205505, 0.015625908970832825, -0.03603341430425644, -0.04833712428808212, 0.002387786051258445, -0.03935687988996506, -0.011052371002733707, 0.01766340620815754, -0.05705339461565018, -0.0637725293636322, 2.141607903001682e-34, 0.010062012821435928, 0.0017346377717331052, 0.00030581647297367454, 0.052195530384778976, 0.009258163161575794, -0.04049985855817795, -0.046229999512434006, -0.00803594384342432, -0.006319273728877306, -0.07435847818851471, -0.03073234297335148]

['Federico Raue', 'Andreas Dengel', 'Thomas M. Breuel', 'Marcus Liwicki']

1511.04401v5

In this paper, we extend a symbolic association framework for being able to handle missing elements in multimodal sequences. The general scope of the work is the symbolic associations of object-word mappings as it happens in language development in infants. In other words, two different representations of the same abstract concepts can associate in both directions. This scenario has been long interested in Artificial Intelligence, Psychology, and Neuroscience. In this work, we extend a recent approach for multimodal sequences (visual and audio) to also cope with missing elements in one or both modalities. Our method uses two parallel Long Short-Term Memories (LSTMs) with a learning rule based on EM-algorithm. It aligns both LSTM outputs via Dynamic Time Warping (DTW). We propose to include an extra step for the combination with the max operation for exploiting the common elements between both sequences. The motivation behind is that the combination acts as a condition selector for choosing the best representation from both LSTMs. We evaluated the proposed extension in the following scenarios: missing elements in one modality (visual or audio) and missing elements in both modalities (visual and sound). The performance of our extension reaches better results than the original model and similar results to individual LSTM trained in each modality.

Symbol Grounding Association in Multimodal Sequences with Missing Elements

http://arxiv.org/pdf/1511.04401v5

Title Symbol Grounding Association Multimodal Sequences Missing Elements Summary paper extend symbolic association framework able handle missing element multimodal sequence general scope work symbolic association objectword mapping happens language development infant word two different representation abstract concept associate direction scenario long interested Artificial Intelligence Psychology Neuroscience work extend recent approach multimodal sequence visual audio also cope missing element one modality method us two parallel Long ShortTerm Memories LSTMs learning rule based EMalgorithm aligns LSTM output via Dynamic Time Warping DTW propose include extra step combination max operation exploiting common element sequence motivation behind combination act condition selector choosing best representation LSTMs evaluated proposed extension following scenario missing element one modality visual audio missing element modality visual sound performance extension reach better result original model similar result individual LSTM trained modality Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.00641487305983901, 0.02614639326930046, -0.01266532950103283, 0.02603224106132984, -0.014365623705089092, 0.02258208394050598, 0.0633237436413765, -0.0059031276032328606, -0.040016911923885345, -0.03117685206234455, -0.019343946129083633, -0.042571887373924255, 0.048582714051008224, 0.028821134939789772, 0.014397303573787212, -0.06138869747519493, 0.03406192362308502, 0.04333372786641121, -0.010068751871585846, 0.014840049669146538, -0.004874357022345066, -0.00678999163210392, -0.02535007707774639, 0.028292054310441017, -0.036181382834911346, -0.0019527205731719732, -0.01988203637301922, -0.016628628596663475, 0.04839533567428589, -0.0614570789039135, -0.023338153958320618, 0.019766448065638542, 0.03796554356813431, 0.019819147884845734, 2.1463813482114347e-06, -0.0074588581919670105, -0.007713868748396635, -0.05172751471400261, 0.07468719035387039, -0.07420431822538376, -0.006418481003493071, -0.0038451263681054115, -0.020328953862190247, 0.0431024432182312, -0.03771749138832092, -0.008742885664105415, 0.101564422249794, 0.032194819301366806, -0.01743321865797043, 0.03383670747280121, -0.025433817878365517, -0.0261298269033432, 0.018919402733445168, -0.0026909797452390194, 0.08995281159877777, 0.03313061594963074, 0.025475583970546722, -0.031089795753359795, 0.045651841908693314, -0.0497925840318203, -0.041851241141557693, 0.033249735832214355, 0.027772150933742523, 0.029842615127563477, 0.005765795242041349, 0.023732377216219902, 0.019507866352796555, -0.0324350968003273, -0.03531350940465927, 0.0737522765994072, -0.006028103642165661, 0.003713741898536682, 0.026174360886216164, 0.021167906001210213, -0.032804008573293686, -0.021525707095861435, -0.05445754900574684, 0.04456004872918129, -0.022590290755033493, 0.015806319192051888, -0.003942479845136404, 0.0007655683439224958, 0.02039581537246704, 0.014005600474774837, -0.006109131965786219, 0.005484896246343851, 0.021750282496213913, 0.00013129509170539677, -0.059922024607658386, -0.05638033151626587, -0.026774059981107712, -0.05008680745959282, 0.05245276913046837, 0.03951328620314598, -0.01228457409888506, -0.011660337448120117, -0.04507944732904434, -0.04747588932514191, 0.007569813169538975, -0.033577609807252884, 0.027657845988869667, 0.04780527204275131, -0.07003758102655411, 0.02603636123239994, -0.03687570244073868, -0.005521921440958977, -0.005457861814647913, 0.025004204362630844, -0.03433902561664581, 0.028750145807862282, -0.0401003360748291, -0.027752337977290154, 0.019830167293548584, 0.03119967319071293, 2.7793710614787415e-05, -0.053115759044885635, -0.04079844430088997, 0.00876631960272789, -0.026704054325819016, -0.022216886281967163, -0.0344175361096859, 0.040938958525657654, -0.009109372273087502, -0.001967029646039009, -0.03133592754602432, 0.05155671760439873, 0.009890029206871986, 0.06784038990736008, -0.011753715574741364, -0.022805629298090935, 0.031442221254110336, 0.03840929642319679, 0.014202607795596123, 0.0004922377411276102, 0.0008603633032180369, 0.10685181617736816, 0.0012200202327221632, -0.0280571561306715, -0.07896211743354797, -0.011993616819381714, 0.01682478003203869, -0.00790746882557869, 0.028260210528969765, -0.0388193354010582, -0.01707770675420761, -0.0008887748699635267, -0.027225982397794724, -0.01695101708173752, 0.016828954219818115, 0.03174406662583351, 0.02771398425102234, 0.0723009705543518, -0.023092828691005707, -0.009192602708935738, 0.026319263502955437, 0.023393405601382256, 0.05210575833916664, 0.01589708961546421, 0.06596766412258148, 0.004635578021407127, -0.009758374653756618, -0.03645186126232147, -0.009157306514680386, 0.015061061829328537, -0.0345555916428566, -0.007412096951156855, -0.07917530834674835, -0.07553271949291229, 0.005720381159335375, 0.05614142864942551, 0.003195118624716997, 0.027154115960001945, -0.016069350764155388, -0.04495876282453537, 0.027862580493092537, 0.061007820069789886, 0.04942810907959938, 0.021312253549695015, 0.030212432146072388, -0.07903639227151871, -0.00860424991697073, 0.00902494415640831, -0.025018254294991493, 0.12037007510662079, -0.025349969044327736, -0.020337145775556564, -0.02845480479300022, 0.052174296230077744, -0.003744726534932852, -0.008556133136153221, -0.006016978994011879, -0.06135685741901398, 0.04965554550290108, -0.05188149958848953, 0.030750103294849396, -0.0034526106901466846, -0.0550265833735466, 0.008074852637946606, -0.03029056265950203, -0.011822480708360672, -0.007124690804630518, -0.008024650625884533, 0.008337109349668026, 0.005755067802965641, 0.027038563042879105, -0.026165083050727844, -0.05046266317367554, -0.02625022828578949, -0.006146286614239216, 0.04166395589709282, -0.05420835316181183, 0.019716620445251465, -0.0066911024041473866, -0.07846876233816147, -0.04616858437657356, 0.071036197245121, -0.01460692472755909, 0.059711385518312454, -0.09901323914527893, 0.035131096839904785, 0.02495012804865837, 0.025086436420679092, 0.05266227573156357, 0.0086718974635005, -0.017939569428563118, 0.02527093142271042, 0.011419553309679031, 0.02942376397550106, 0.017994748428463936, 0.00723485229536891, 0.018992487341165543, 0.022647101432085037, 0.048938095569610596, -0.033576324582099915, -0.025357604026794434, 0.02791905775666237, -0.08675455302000046, -0.01456635631620884, 0.0381210595369339, -0.045227911323308945, 0.003949860576540232, 0.0444151908159256, 0.0048429579474031925, -0.05974858999252319, 0.06653470546007156, -0.013177722692489624, 0.060155000537633896, -0.03580102324485779, 0.02434145286679268, 0.0468611977994442, 0.000268233212409541, 0.016739189624786377, 0.03579528629779816, -0.011253444477915764, 0.007470129057765007, -0.019356491044163704, 0.01336854137480259, 0.046447981148958206, -0.0436428003013134, -0.00222946354188025, 0.048810917884111404, -0.04082704335451126, -0.020171402022242546, -0.002167794154956937, -0.006187540479004383, -0.06171819567680359, -0.0014802274527028203, -0.09113296866416931, -0.015120676718652248, 0.03227647766470909, 0.0039865304715931416, -0.041239183396101, -0.007337888702750206, 0.008859480731189251, -0.04479425400495529, -0.00979017373174429, 0.05633937940001488, 0.006084012798964977, 0.00752265052869916, 0.03651706501841545, 0.021187754347920418, -0.04820183664560318, -0.010894564911723137, -0.00016449569375254214, -0.036894768476486206, 0.020252900198101997, -0.015534643083810806, -0.05733524635434151, 0.001601281575858593, -0.03887664154171944, -0.05691175162792206, 0.03069809451699257, 0.01320698019117117, -0.02828003279864788, 0.00577413197606802, -0.0033908251207321882, 0.05933355540037155, -0.001995853381231427, 0.04019910842180252, -0.00018301824457012117, 0.027540231123566628, -0.020999282598495483, 0.00457683065906167, -0.010381399653851986, 0.02133551426231861, 0.06757865846157074, 0.00680680712684989, 0.01754467748105526, -0.0699153020977974, 0.07207436114549637, 0.06623823195695877, 0.02085989899933338, -0.018360814079642296, 0.01057677622884512, 0.014719672501087189, 0.04371257871389389, -0.029935531318187714, -0.05943320319056511, -0.02291031740605831, 0.03548802435398102, -0.02432882785797119, -0.046399932354688644, 0.03359729424118996, 0.0003743082343135029, -0.01885831728577614, -0.02654074877500534, -0.005341410171240568, -0.013049347326159477, 0.04264108091592789, 0.0015601621707901359, 0.016883958131074905, 0.0063721900805830956, -0.05676305666565895, -0.07279019802808762, 0.0008914606878533959, 0.007605129852890968, -0.04796912893652916, 0.013714821077883244, -0.05120564624667168, 0.02156495861709118, -0.010420932434499264, 0.017804313451051712, -0.028752880170941353, 0.032260823994874954, 0.007140155881643295, -0.03938153758645058, -0.05676307901740074, 0.008251694031059742, -0.05043352022767067, 0.0176702868193388, 0.010682953521609306, 0.02007291093468666, 0.011222733184695244, 0.01720091514289379, 0.005015887785702944, 0.04894784092903137, 0.0432022362947464, -0.018974164500832558, -0.03429489955306053, -0.014523322694003582, 0.011067927815020084, 0.00939649622887373, -2.6906633138423786e-05, -0.02020740881562233, -0.07912035286426544, 0.05162115767598152, 0.005119651090353727, 0.008513476699590683, -0.03040030226111412, 0.051171351224184036, -0.04379437118768692, -0.047320231795310974, 0.06215079128742218, 0.062372416257858276, 0.02206919901072979, -0.06110623478889465, 0.006363886408507824, 0.004873201716691256, -0.04881740361452103, -0.0099248718470335, -0.04196859896183014, -0.08084191381931305, -0.027337944135069847, -0.018270613625645638, -0.04007524624466896, -0.007760058157145977, -0.019617583602666855, -0.014394802041351795, -0.023823682218790054, 0.012079070322215557, 0.017938466742634773, -0.09160919487476349, -0.048182807862758636, 0.00903249066323042, -0.004399361088871956, 0.025165127590298653, 0.015918388962745667, 0.025844933465123177, -0.02756337821483612, -0.011671570129692554, 0.05287538841366768, -0.010889454744756222, -0.034378066658973694, 0.006494848057627678, -0.027282590046525, 0.05955056473612785, 0.059817325323820114, 0.049559108912944794, -0.025698861107230186, -0.10818606615066528, 0.0016802693717181683, 0.021123172715306282, 0.028676947578787804, -0.03636229783296585, -0.018657973036170006, 0.007017831318080425, -0.011066178791224957, -0.011036784388124943, 0.03521830961108208, -0.030788544565439224, -0.020301546901464462, -0.02991192787885666, 0.08869150280952454, -0.04127630963921547, 0.022617166861891747, -0.051633864641189575, 0.016605613753199577, 0.012046920135617256, 0.02082081325352192, 0.0017572579672560096, -0.013119836337864399, 0.017986390739679337, 0.043094322085380554, 0.01852548122406006, 0.03392655774950981, -0.002312451833859086, -0.0317133367061615, -0.02393835410475731, -0.010416767559945583, -0.07072832435369492, -0.032228440046310425, -0.006415486801415682, 0.08158761262893677, 0.03171771019697189, 0.032720230519771576, -0.01500419620424509, -0.03211722895503044, -0.07912426441907883, 0.021287722513079643, 0.059355899691581726, 0.01617117039859295, -0.03072384186089039, 0.037172846496105194, 0.00688690971583128, -0.04635906219482422, 0.005764810834079981, -0.030527573078870773, -0.06063609942793846, -0.02892903797328472, -0.006370498798787594, -0.007017157040536404, 0.02268380858004093, 0.001300242729485035, 0.025464171543717384, -0.007531777955591679, 0.016015244647860527, 0.019515840336680412, 0.03752624988555908, 0.01409594900906086, -0.004132755100727081, 0.022440597414970398, -0.023937014862895012, -0.016403604298830032, -0.018648555502295494, 0.05071976035833359, -0.008979304693639278, 0.01866311952471733, 0.02574026770889759, 0.04040040820837021, -0.0002920559491030872, -0.03190520405769348, 0.05851175636053085, -0.013276680372655392, 0.004932560957968235, -0.05204588174819946, 0.00708960322663188, 0.004466649144887924, 0.027642425149679184, -0.014773229137063026, -0.005249400623142719, 0.03567963093519211, 0.021088413894176483, -0.03566263988614082, -0.08674351125955582, 0.011086354963481426, -0.04817177355289459, 0.0027269606944173574, 0.08301059156656265, 0.009935489855706692, -0.00677856570109725, -0.043059151619672775, 0.0010291490470990539, 0.023361841216683388, 0.0072452533058822155, 0.009335057809948921, 0.038131650537252426, -0.018982183188199997, 0.07567375898361206, 0.008469502441585064, 0.01162276417016983, -0.01556991133838892, 0.01649758405983448, 0.07507187873125076, 0.004181559197604656, -0.057706430554389954, 0.008004586212337017, 0.037921417504549026, -0.05180485174059868, -0.022480295971035957, 0.00628882460296154, 0.02898358181118965, -0.015249351039528847, 0.038361046463251114, -0.04516496881842613, 0.006065594498068094, 0.050384972244501114, -0.0001617819507373497, -0.01299916859716177, -0.008939318358898163, 0.025891007855534554, -0.057458389550447464, 0.05139225721359253, -0.0330519825220108, -0.01054344978183508, 0.0035720812156796455, 0.037647925317287445, 0.0650605708360672, -0.0018264163518324494, -0.028756601735949516, -0.012442131526768208, -0.021259088069200516, -0.04538245499134064, 0.02851523458957672, 0.0059364112094044685, 0.06846379488706589, 0.020642811432480812, 0.03084460087120533, 0.020174741744995117, 0.001967547694221139, 0.010528961196541786, 0.01997346803545952, -0.06972154229879379, 0.029146702960133553, -0.0502789206802845, -0.03661823645234108, -6.425014083988582e-33, -0.033496398478746414, -0.052056603133678436, 0.033238016068935394, -0.04031064733862877, -0.01803535781800747, 0.011156119406223297, -0.017945406958460808, -0.0022436678409576416, 0.027226781472563744, -0.008308036252856255, 0.04758881777524948, -0.013606143184006214, 0.01965104602277279, 0.028510242700576782, 0.081428661942482, 0.04665083810687065, -0.01218613050878048, -0.008019919507205486, 0.0287693589925766, -0.0504516176879406, 0.06523840874433517, 0.029027653858065605, 0.09402577579021454, -0.02427823096513748, -0.05555078014731407, 0.05731254443526268, -0.022988751530647278, -0.025164635851979256, 0.015645937994122505, 0.0358242392539978, -0.0270074512809515, -0.012470235116779804, 0.0052148327231407166, -0.011025072075426579, -0.009908054023981094, -0.0024815609212964773, -0.04353734105825424, -0.05023001879453659, -0.006117021199315786, -0.020812634378671646, -0.03702501207590103, 0.01148168183863163, 0.06428194791078568, -0.033425260335206985, 0.009405492804944515, 0.04039310663938522, 0.05362750589847565, -0.04388279467821121, 0.008577289059758186, 0.004280047491192818, -0.05926608666777611, 0.025262197479605675, -0.010535131208598614, -0.020975342020392418, 0.026724450290203094, -0.02032482996582985, -0.01856638677418232, 0.0009528562077321112, -0.060997746884822845, 0.04335504397749901, -0.010124137625098228, 0.020606689155101776, 0.06014475226402283, 0.0021092561073601246, 0.004911388736218214, 0.06117639318108559, 0.021783124655485153, -0.04749342054128647, 0.0010301502188667655, 0.03815875202417374, 0.04046407714486122, 0.043033916503190994, 0.025088844820857048, 0.004475763067603111, 0.08377443253993988, -0.017468860372900963, -0.03595159575343132, 0.06319504976272583, -0.005462374538183212, 0.06626241654157639, -0.008918287232518196, 0.06685551255941391, 0.0005863240803591907, 0.028612807393074036, 0.014734028838574886, 0.02146066352725029, -0.047130484133958817, -0.08224542438983917, 0.022066006436944008, -0.00011964993609581143, 0.005603501107543707, -0.0032865784596651793, 0.05654104799032211, 0.018554307520389557, 0.028665507212281227, -0.030511004850268364, 0.03462747856974602, 0.017034495249390602, 0.020375583320856094, -0.034562207758426666, -0.010111303068697453, -0.06396593898534775, 0.08318406343460083, -0.031601447612047195, 0.024489594623446465, -0.014162987470626831, -0.002911403076723218, 0.05059174820780754, -0.056396398693323135, -0.03136710077524185, 0.027201486751437187, -0.05356982722878456, 0.04004693776369095, -0.036354802548885345, 0.033932559192180634, -0.008696980774402618, -0.03532358631491661, 0.02885141596198082, -0.01739056222140789, -0.01662622205913067, -0.06633477658033371, -0.038981929421424866, -0.05235746130347252, 0.023253483697772026, -0.03748716041445732, 0.010085458867251873, -0.041356444358825684, -0.03501826524734497, 0.04955649748444557, -0.034443654119968414, -0.014596839435398579, 0.005510514136403799, 2.973906134684512e-07, -0.01990785263478756, 0.019556259736418724, 0.02318570949137211, -0.013482148759067059, 0.039152730256319046, -0.0036029296461492777, -0.02116510272026062, 0.02246515452861786, -0.002385910367593169, -0.0026622808072715998, 0.06191246211528778, -0.02181488648056984, 0.021021481603384018, 0.013952120207250118, -0.007642460986971855, 0.027869632467627525, -0.025215210393071175, 0.019702766090631485, -0.04050954803824425, 0.007800076622515917, 0.04437604174017906, 0.08319691568613052, 0.008922784589231014, -0.03388356789946556, 0.036821287125349045, 0.007544448133558035, 0.03069048561155796, -0.006440040189772844, 0.00031403961475007236, -0.07288321107625961, 0.009630833752453327, -0.03863588348031044, 0.008787599392235279, -0.01212508324533701, -0.030239643529057503, 0.0015661778161302209, 0.04546835646033287, -0.04144381731748581, -0.04610743746161461, -0.03661118447780609, 0.03669107332825661, 0.06601979583501816, -0.01754625514149666, 0.023935412988066673, 0.04191116616129875, -0.012098780833184719, -0.03942570090293884, 0.0014483975246548653, -0.046464093029499054, 0.0010459768818691373, 0.027935955673456192, 0.022360676899552345, -0.040909864008426666, -0.010471736080944538, -0.013646688312292099, -0.006562154274433851, -0.02243388630449772, -0.07463304698467255, 0.023263856768608093, 0.042154960334300995, -0.024867098778486252, -0.005257987882941961, -0.053635384887456894, -0.034642014652490616, 0.028188636526465416, -0.06731554865837097, -0.07703587412834167, 2.8561906892778103e-34, -0.004637882113456726, -0.05868914723396301, -0.0038067393470555544, 0.02890007011592388, 0.012039903551340103, 0.015667252242565155, -0.011887633241713047, 0.04406808689236641, 0.0001850626285886392, -0.05773022770881653, -0.047489844262599945]

['Dan Hendrycks', 'Mantas Mazeika', 'Duncan Wilson', 'Kevin Gimpel']

1802.05300v1

The growing importance of massive datasets with the advent of deep learning makes robustness to label noise a critical property for classifiers to have. Sources of label noise include automatic labeling for large datasets, non-expert labeling, and label corruption by data poisoning adversaries. In the latter case, corruptions may be arbitrarily bad, even so bad that a classifier predicts the wrong labels with high confidence. To protect against such sources of noise, we leverage the fact that a small set of clean labels is often easy to procure. We demonstrate that robustness to label noise up to severe strengths can be achieved by using a set of trusted data with clean labels, and propose a loss correction that utilizes trusted examples in a data-efficient manner to mitigate the effects of label noise on deep neural network classifiers. Across vision and natural language processing tasks, we experiment with various label noises at several strengths, and show that our method significantly outperforms existing methods.

Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise

http://arxiv.org/pdf/1802.05300v1

Title Using Trusted Data Train Deep Networks Labels Corrupted Severe Noise Summary growing importance massive datasets advent deep learning make robustness label noise critical property classifier Sources label noise include automatic labeling large datasets nonexpert labeling label corruption data poisoning adversary latter case corruption may arbitrarily bad even bad classifier predicts wrong label high confidence protect source noise leverage fact small set clean label often easy procure demonstrate robustness label noise severe strength achieved using set trusted data clean label propose loss correction utilizes trusted example dataefficient manner mitigate effect label noise deep neural network classifier Across vision natural language processing task experiment various label noise several strength show method significantly outperforms existing method Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0499345101416111, 0.06746858358383179, 0.0007473518489859998, 0.04109011963009834, -0.011891260743141174, -0.01363668404519558, 0.04493304342031479, 0.00044890728895552456, 0.008615335449576378, -0.03051946870982647, -0.03643353655934334, 0.005021167453378439, 0.010708912275731564, 0.0793510153889656, 0.009104130789637566, -0.028915662318468094, 0.055408988147974014, -0.0013842409243807197, 0.031061075627803802, 0.01772702857851982, -0.008117301389575005, -0.016850633546710014, 0.010190052911639214, 0.034851688891649246, -0.05851738899946213, -0.01757567934691906, 0.018880825489759445, 0.006047873292118311, 0.013978020288050175, -0.030179167166352272, 0.0420844666659832, 0.022130386903882027, -0.013979674316942692, 0.07928121834993362, 2.151839225916774e-06, -0.012995904311537743, -0.03743728622794151, 0.005791862029582262, 0.00750636775046587, 0.026607703417539597, 0.019243504852056503, -0.0008667287766002119, -0.02253013849258423, 0.01297256350517273, -0.02127246931195259, -0.04859378561377525, 0.050949446856975555, 0.0899193286895752, 0.051708951592445374, 0.047954022884368896, -0.013170578517019749, -0.022007770836353302, 0.02156054973602295, -0.011388115584850311, 0.001648841891437769, -0.06151682138442993, 0.04382004216313362, -0.023160530254244804, -0.03457976132631302, 0.03264455497264862, -0.018892517313361168, 0.03235812485218048, 0.010597840882837772, -0.04858919605612755, 0.03639214485883713, 0.009427621960639954, -0.014034505002200603, -0.03376993164420128, -0.01849363185465336, 0.07035087049007416, -0.01712304726243019, 0.027096448466181755, -0.012476959265768528, -0.004192899446934462, -0.008420794270932674, -0.024809150025248528, 0.013491353020071983, 0.030976133421063423, 0.001586137106642127, 0.01656915806233883, -0.05156473442912102, 0.03299539536237717, 0.01925487071275711, 0.027999894693493843, 0.03289234638214111, 0.02741493098437786, -0.005474061239510775, -0.024292323738336563, 0.043744612485170364, -0.003913560416549444, 0.006245634518563747, -0.058456867933273315, 0.05066461116075516, -0.001135022845119238, -0.01894177496433258, 0.009490559808909893, -0.07130631804466248, -0.06561238318681717, 0.030941292643547058, -0.024329490959644318, -0.0036401187535375357, -0.048106785863637924, -0.05828731134533882, 0.01669939048588276, -0.000590152048971504, 0.025493664667010307, 0.008654427714645863, 0.0561247244477272, 0.016442028805613518, 0.005177070386707783, -0.031238384544849396, 0.005139692220836878, -0.05022795870900154, 0.04159609600901604, -0.00768192857503891, -0.01646612584590912, -0.0830116719007492, -0.0007767581846565008, -0.04017045348882675, 0.045329347252845764, 0.005273417569696903, 0.05313803255558014, -0.0206752922385931, 0.022795366123318672, -0.008755144663155079, 0.011872097849845886, -0.017410967499017715, 0.04608966410160065, 0.018184011802077293, -0.03863741457462311, 0.036408405750989914, 0.002449912251904607, -0.0036456489469856024, -0.011575129814445972, 0.023563548922538757, 0.08946090191602707, 0.014990495517849922, -0.02490806207060814, -0.06347253173589706, -0.037908464670181274, -0.062545545399189, -0.005768848117440939, -0.03693777695298195, -0.04786962270736694, -0.03416217118501663, -0.0658804178237915, -0.0058032735250890255, -0.04848373308777809, 0.005245070438832045, 0.005250793881714344, -0.07223271578550339, 0.08834768086671829, -0.07665983587503433, -0.03561373054981232, 0.04642949625849724, 0.015177570283412933, 0.03862663730978966, -0.013624881394207478, 0.03432798385620117, 0.022312648594379425, 0.0750102624297142, -0.0028416381683200598, 0.03608061373233795, -0.005220869090408087, -0.003629915416240692, -0.02202601172029972, -0.0066106305457651615, -0.04219773784279823, -0.005358752328902483, 0.008543618954718113, -0.034412749111652374, 0.093296118080616, 0.023306922987103462, -0.022868381813168526, 0.10255923122167587, 0.017278581857681274, 0.01522995624691248, 0.0020811769645661116, -0.04890788719058037, 0.002151563297957182, 0.012267112731933594, -0.016199100762605667, -0.03606930747628212, 0.006778493523597717, -0.027317970991134644, -0.03632050380110741, -0.0008519055554643273, -0.0010449577821418643, -0.01923874206840992, -0.08159327507019043, -0.025285763666033745, -0.0372086763381958, -0.013894893229007721, 0.0018388484604656696, 0.04564760997891426, 0.03831334784626961, -0.009454574435949326, -0.017322979867458344, 0.013171746395528316, -0.013136210851371288, -0.023721549659967422, -0.029099207371473312, 0.040790218859910965, 0.024172252044081688, -0.01296855229884386, -0.03169233351945877, 0.007680079899728298, -0.058211490511894226, 0.02981998212635517, -0.0012547574006021023, 0.009029937908053398, -0.004347915295511484, 0.03249143436551094, -0.05708647146821022, -0.03601808100938797, 0.027121104300022125, -0.0019411741523072124, 0.004219930153340101, -0.005319283343851566, 0.04330914467573166, 0.008572337217628956, -0.02048831805586815, -0.04892413318157196, 0.051749423146247864, 0.07926402986049652, -0.027195239439606667, 0.052478060126304626, 0.04473761469125748, 0.0036332516465336084, 0.04514595493674278, -0.028351280838251114, -0.014375771395862103, 0.030077829957008362, 0.01096195075660944, -0.03379203379154205, -0.0071027809754014015, -0.026537826284766197, 0.030815089121460915, 0.025272931903600693, -0.0787535011768341, -0.021694811061024666, 0.045929498970508575, -0.06518577039241791, -0.02287977747619152, -0.013502329587936401, -0.02884729392826557, -0.052616264671087265, -0.029086947441101074, -0.009010137058794498, -0.011223564855754375, 0.033296260982751846, -0.024923047050833702, 0.03195479139685631, 0.015977397561073303, -0.004042213782668114, -0.05969342961907387, 0.02434864640235901, 0.03713831678032875, -0.002634295728057623, -0.04300050809979439, 0.026726657524704933, -0.04311269521713257, 0.028729865327477455, 0.011757664382457733, 0.03899548575282097, -0.03347530961036682, 0.026594119146466255, 0.017069371417164803, -0.024752125144004822, -0.017958909273147583, -0.020457951352000237, 0.0031975337769836187, -0.023305876180529594, 0.01859494484961033, -0.030887411907315254, -0.05586342141032219, 0.03618834540247917, 0.009767508134245872, 6.034671969246119e-05, 0.06736986339092255, 0.005461233668029308, -0.0018058374989777803, 0.0017070333706215024, -0.02551707625389099, -0.008275612257421017, 0.027560388669371605, 0.050005149096250534, -0.07428663223981857, -0.057158369570970535, 0.02234717644751072, -0.01592235080897808, 0.028277697041630745, 0.03890344128012657, -0.04954712092876434, -0.0033352160826325417, 0.04426461085677147, -0.053857941180467606, 0.02121596410870552, 0.004197082947939634, -0.002414339454844594, 0.0247958917170763, 0.06368543207645416, 0.017720863223075867, -0.029264606535434723, 0.006269070785492659, -0.02758224494755268, 0.030726062133908272, -0.010272206738591194, -0.0022264812141656876, 0.028157206252217293, 0.011328759603202343, -0.01578868180513382, 0.024890774860978127, 0.0041340007446706295, -0.02912045642733574, -0.011685139499604702, -0.03838563710451126, -0.035784363746643066, 0.016497937962412834, 0.05889195576310158, 0.0077674007043242455, -0.05226292461156845, 0.08388566970825195, -0.010273187421262264, -0.004126992542296648, -0.01405163761228323, -0.06599467247724533, 0.029899412766098976, 0.03270775079727173, -0.00996194127947092, 0.03057957999408245, 0.06749818474054337, -0.06923455744981766, -0.010211731307208538, -0.0354437418282032, 0.05719975382089615, -0.037605784833431244, 0.01754184253513813, -0.038500767201185226, 0.0015836686361581087, 0.002457645256072283, -0.01509827096015215, -0.0720776617527008, -0.004472323227673769, -0.006964283529669046, -0.0025806501507759094, -0.010799874551594257, 0.010392386466264725, -0.02591073513031006, 0.0009961952455341816, 0.010718259960412979, 0.03511551767587662, -0.007687956560403109, -0.010215082205832005, -0.0005233606789261103, 0.04621264711022377, 0.019133638590574265, -0.02799668163061142, 0.017450477927923203, 0.009323392994701862, -0.0101550268009305, 0.07210452109575272, 0.013997318223118782, 0.026627015322446823, -0.07713291049003601, 0.007049764972180128, -0.005621779710054398, 0.005399925168603659, 0.00948323868215084, 0.012734477408230305, 0.013750183396041393, -0.07606980949640274, 0.0017173424130305648, 0.05271267145872116, 0.0010776001727208495, -0.03283014893531799, -0.007125188130885363, 0.02482897974550724, -0.01308397762477398, 0.02040787786245346, -0.016481051221489906, -0.07289471477270126, -0.017787721008062363, -0.003389219520613551, 0.04483779892325401, -0.008394649252295494, -0.06934845447540283, 0.0006965261418372393, -0.07134706526994705, 0.036993902176618576, -0.009910744614899158, -0.03935730829834938, -0.044825732707977295, -0.03858937323093414, -0.010085996240377426, -0.040536295622587204, 0.06150069087743759, -0.03719085827469826, 0.04761076346039772, -0.040424007922410965, 0.03273928537964821, -0.03878345340490341, -0.05184454098343849, 0.015632400289177895, -0.08919297158718109, 0.05600305646657944, 0.06068654730916023, 0.018637068569660187, -0.0550575889647007, -0.07104775309562683, 0.05445006117224693, 0.007222428452223539, -0.010887593030929565, 0.007522845175117254, 0.10577919334173203, -0.030272984877228737, -0.03203177824616432, 0.01678987219929695, 0.03929705172777176, -0.022203851491212845, 0.011074871756136417, 0.009177419357001781, 0.01649578846991062, 0.0034086783416569233, -0.004051206633448601, -0.024444442242383957, 0.01663968339562416, 0.04018668085336685, 0.023573480546474457, -0.00011401648225728422, -0.03701770678162575, -0.017782406881451607, -0.03277209773659706, 0.02131965011358261, -0.012029445730149746, -0.007841442711651325, 0.09224719554185867, -0.033493101596832275, -0.09944197535514832, -0.08569618314504623, -0.04266216605901718, 0.00516083836555481, 0.026803765445947647, 0.04909883439540863, -0.0020603861194103956, 0.022641586139798164, 0.0350838229060173, -0.0473441556096077, -0.010735235176980495, 0.018724611029028893, 0.030846131965517998, -0.04796107858419418, 0.05320240929722786, 0.006612129043787718, 0.030748555436730385, -0.015988433733582497, 0.021305792033672333, -0.034932468086481094, -0.05524803325533867, 0.009003981947898865, 0.04692542552947998, 0.01944410242140293, 0.008124206215143204, -0.041158247739076614, -0.064496248960495, 0.028024772182106972, 0.050576236099004745, -0.003717283485457301, -0.05133207142353058, 0.054010167717933655, -0.050693511962890625, 0.002642379142343998, 0.01541271060705185, -0.0273416917771101, 0.054074179381132126, 0.03302909433841705, -0.042668040841817856, -0.012280681170523167, -0.020703013986349106, 0.014458243735134602, 0.037357740104198456, 0.08537470549345016, -0.011803840287029743, -0.002433273708447814, -0.029167737811803818, 0.03106352500617504, -0.009484627284109592, -0.029140830039978027, -0.007454623468220234, 0.042054273188114166, 0.040117744356393814, 0.002274524886161089, -0.0026450594887137413, 0.01312422938644886, 0.0022118345368653536, 0.062457289546728134, -0.004941636696457863, 0.03010849840939045, -0.012540226802229881, 0.05373149737715721, 0.006084791384637356, 0.017704522237181664, -0.00945258792489767, 0.029916897416114807, 0.05451372265815735, 0.05145885422825813, 0.012555407360196114, -0.019974712282419205, 0.022556953132152557, 0.0030169973615556955, -0.00042914043297059834, 0.020329074934124947, -0.04695354774594307, -0.022373436018824577, -0.04074397683143616, 0.0372525230050087, 0.025157485157251358, -0.021827813237905502, -0.029802467674016953, -0.03049542009830475, -0.0016138131031766534, -0.022213434800505638, 0.042476143687963486, -0.004105533007532358, -0.007457922212779522, 0.030414627864956856, -0.0062262313440442085, -0.02660514973104, 0.023366883397102356, 0.03301023691892624, 0.025002319365739822, -0.0006244727992452681, -0.014989139512181282, -0.0449393205344677, -0.04383495822548866, 0.03905565291643143, -0.015541603788733482, 0.021120700985193253, -0.03419933095574379, -0.019794538617134094, 0.010919643566012383, -0.08034046739339828, 0.049412935972213745, -0.008465712890028954, 0.07142473757266998, 0.016285788267850876, 0.0231045912951231, 0.034687019884586334, 0.04511067271232605, 0.023787319660186768, -0.012925648130476475, -0.017953908070921898, 0.05943508446216583, -0.025414252653717995, -0.0244279932230711, -5.9763862976552713e-33, 0.030385972931981087, -0.052393220365047455, -0.04055561497807503, -0.019083529710769653, -0.00046019486035220325, 0.051330603659152985, -0.002863723086193204, -0.028649913147091866, -0.01940982975065708, 0.03570839762687683, -0.020304694771766663, 0.020717205479741096, 0.0271670613437891, 0.02967480942606926, 0.01970013417303562, -0.03392179682850838, 0.04387230798602104, -0.03584999218583107, 0.0021498603746294975, 0.0032230885699391365, 0.015318418852984905, 0.039939459413290024, 0.08515717834234238, -0.1269974559545517, 0.03753625974059105, 0.04448229447007179, -0.04854394868016243, -0.01578870229423046, -0.004339360166341066, 0.03929804638028145, 0.011086325161159039, 0.06055857241153717, -0.0053396569564938545, -0.033272434026002884, -0.0027747531421482563, 0.03107600472867489, -0.07991252839565277, 0.009647189639508724, -0.06353114545345306, 0.04840714856982231, -0.05100630596280098, 0.010160320438444614, 0.08823426067829132, -0.023591378703713417, -0.023309316486120224, 0.010731196962296963, 0.058192845433950424, -0.06572186946868896, -0.05114671215415001, -0.0527058020234108, -0.019541937857866287, 0.0013986378908157349, -0.0018268970306962729, 0.02204579859972, 0.025141414254903793, 0.027575340121984482, -0.005342351272702217, 0.03501882776618004, -0.0882587879896164, -0.0069574895314872265, 0.020757032558321953, 0.012795140966773033, 0.021812714636325836, 0.009193646721541882, -0.024168770760297775, 0.03755583241581917, 0.04240482300519943, -0.001022007898427546, 0.0003755319048650563, -0.03503347560763359, -0.006040750537067652, 0.057282254099845886, 0.08542586863040924, 0.06678299605846405, 0.04182346165180206, -0.06386326998472214, -0.09315936267375946, 0.011883602477610111, -0.017120806500315666, -0.009324071928858757, -0.024448392912745476, 0.0005450720782391727, -0.04677718132734299, 0.00769559433683753, -0.009547664783895016, -0.033847734332084656, -0.031743116676807404, 0.010076087899506092, 0.007019055541604757, -0.005766111426055431, -0.029810650274157524, 0.04426289349794388, -0.016764957457780838, -0.05552254617214203, -0.020319150760769844, -0.03432389348745346, 0.031126976013183594, 0.01646648719906807, -0.0014198982389643788, -0.009265763685107231, -0.028744764626026154, -0.006719333119690418, -0.00887970719486475, 0.018488498404622078, 0.023915184661746025, -0.00601929659023881, 0.07967973500490189, 0.015492387115955353, -0.07415664196014404, 0.009866474196314812, -0.001160253188572824, 0.02599244751036167, 0.059967078268527985, 0.03103073686361313, 0.015382743440568447, -0.04545057937502861, -0.0060778106562793255, 0.04444737359881401, 0.02716752700507641, 0.019295629113912582, -0.006708695087581873, 0.0065526654943823814, -0.008584507741034031, 0.008102331310510635, -0.05087878182530403, -0.04222743958234787, -0.025647902861237526, -0.026445580646395683, 0.06227656453847885, -0.06148950383067131, 0.006020127795636654, -0.023022426292300224, 2.7856000883730303e-07, -0.016722699627280235, 0.03264578431844711, 0.03314581140875816, -0.015423957258462906, 0.0015273501630872488, 0.05075468495488167, -0.006297809537500143, 0.03885705769062042, -0.023615486919879913, -0.05597084388136864, 0.005739408545196056, -0.06279527395963669, 0.048998814076185226, 0.03879840672016144, -0.05673208832740784, -0.05289698764681816, -0.04985234886407852, 0.00974705908447504, -0.046144697815179825, 0.02867761068046093, 0.06570830196142197, 0.1220090389251709, 0.05305808410048485, -0.07277809083461761, 0.02395622245967388, -0.04684128984808922, -0.014873027801513672, 0.005887902341783047, 0.03590702638030052, -0.020404554903507233, 0.043367985635995865, 0.035033464431762695, -0.02180987410247326, 0.03985019773244858, -0.05443841964006424, -0.03757121041417122, 0.025112811475992203, 0.019917022436857224, -0.03621039167046547, 0.0018234062008559704, -0.023812001571059227, -0.014123164117336273, 0.023585442453622818, -0.006815297529101372, 0.049770161509513855, -0.015004277229309082, -0.016657646745443344, -0.020748663693666458, -0.013355344533920288, -0.042231298983097076, 0.06682398915290833, -0.030593596398830414, 0.02334294654428959, 0.0065461499616503716, 0.0033938242122530937, -0.016271380707621574, -0.03371598944067955, -0.040038079023361206, 0.021423039957880974, -0.0324130617082119, 0.009769783355295658, -0.026735633611679077, 0.02398575469851494, -0.009955234825611115, 0.0347430519759655, -0.04193095117807388, -0.012614584527909756, 2.6253837510262966e-34, 0.010346638970077038, -0.0347212590277195, 0.01809639111161232, 0.0019242255948483944, -0.008423089981079102, 0.012410038150846958, 0.0032256473787128925, -0.020797453820705414, -0.03806644305586815, 0.004720558878034353, -0.04437151551246643]

['Kyunghyun Cho', 'Aaron Courville', 'Yoshua Bengio']

1507.01053v1

Whereas deep neural networks were first mostly used for classification tasks, they are rapidly expanding in the realm of structured output problems, where the observed target is composed of multiple random variables that have a rich joint distribution, given the input. We focus in this paper on the case where the input also has a rich structure and the input and output structures are somehow related. We describe systems that learn to attend to different places in the input, for each element of the output, for a variety of tasks: machine translation, image caption generation, video clip description and speech recognition. All these systems are based on a shared set of building blocks: gated recurrent neural networks and convolutional neural networks, along with trained attention mechanisms. We report on experimental results with these systems, showing impressively good performance and the advantage of the attention mechanism.

Describing Multimedia Content using Attention-based Encoder--Decoder Networks

http://arxiv.org/pdf/1507.01053v1

Title Describing Multimedia Content using Attentionbased EncoderDecoder Networks Summary Whereas deep neural network first mostly used classification task rapidly expanding realm structured output problem observed target composed multiple random variable rich joint distribution given input focus paper case input also rich structure input output structure somehow related describe system learn attend different place input element output variety task machine translation image caption generation video clip description speech recognition system based shared set building block gated recurrent neural network convolutional neural network along trained attention mechanism report experimental result system showing impressively good performance advantage attention mechanism Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.020975526422262192, -0.010257728397846222, -0.0024284517858177423, 0.04366829991340637, 0.0024071575608104467, -0.023577744141221046, 0.032206058502197266, -0.036669131368398666, -0.06916859745979309, -0.06539066880941391, -0.032877132296562195, -0.012988226488232613, 0.014521989040076733, 0.09337498992681503, 0.025251124054193497, -0.07798454910516739, 0.022445933893322945, 0.018387218937277794, -0.011624282225966454, 0.05532706156373024, 0.026212895289063454, -0.013929164037108421, 0.017429249361157417, 0.030638158321380615, -0.014471681788563728, 0.014642185531556606, -0.04804094135761261, 0.003794293384999037, 0.006860558874905109, -0.019921887665987015, 0.012153368443250656, 0.03918760269880295, 0.05255404859781265, 0.010846595279872417, 2.3866048195486655e-06, -0.012216998264193535, -0.007280558813363314, -0.04501757770776749, 0.034917622804641724, 0.012073345482349396, 0.014712901785969734, -0.042761463671922684, -0.004842880181968212, 0.012781809084117413, 0.0029405446257442236, -0.00896204449236393, 0.05965467914938927, 0.07358851283788681, 0.040461465716362, 0.03768536448478699, -0.03440957888960838, -0.08272082358598709, 0.03933250159025192, -0.036092426627874374, 0.014813724905252457, -0.008699902333319187, -0.006667665205895901, -0.004423538688570261, 0.02267366088926792, -0.0119317090138793, -0.03131432458758354, 0.0470573827624321, 0.02504776231944561, -0.03353670984506607, 0.07717479020357132, 0.045925773680210114, -0.03788338601589203, -0.008036242797970772, 0.0016108541749417782, 0.0758628398180008, -0.05808871611952782, 0.01709011010825634, -0.019805975258350372, 0.001134550548158586, -0.016900846734642982, -0.012050707824528217, -0.0421694777905941, 0.043880313634872437, -0.02929656207561493, 0.00807130802422762, -0.03052426315844059, 0.03214746713638306, -0.002205662662163377, -0.006951726973056793, 0.0151414405554533, -0.02763139270246029, 0.010706172324717045, -0.012915053404867649, -0.019949156790971756, -0.023435425013303757, -0.0029345809016376734, -0.07156138122081757, 0.041633497923612595, 0.038037534803152084, 0.03358614817261696, -0.021764161065220833, -0.04742259532213211, -0.08077210932970047, -0.0015782195841893554, -0.06673017144203186, 0.04565396159887314, -0.008814390748739243, -0.0684354156255722, 0.05015378072857857, -0.013686168938875198, 0.07551630586385727, -0.03804519400000572, -0.0063674477860331535, 0.0015231078723445535, 0.041920360177755356, -0.06407267600297928, -0.01096656359732151, -0.032019373029470444, 0.06595855951309204, -0.028537560254335403, -0.05957303196191788, -0.04183085635304451, 0.02017674595117569, -0.009576670825481415, 0.022163651883602142, 0.00351726938970387, 0.05293891206383705, -0.042476873844861984, 0.0050097801722586155, -0.00962415523827076, 0.02676199935376644, -0.049680981785058975, 0.031981419771909714, 0.013070561923086643, -0.010040093213319778, 0.013224771246314049, 0.05710678547620773, 0.0053155492059886456, 0.002864616457372904, -0.00532880611717701, 0.0671229138970375, 0.010070998221635818, -0.004045860376209021, -0.015530719421803951, 0.0044626337476074696, -0.011202995665371418, -0.025643490254878998, 0.03886357694864273, -0.06835449486970901, 0.03464852273464203, -0.010396257974207401, -0.035522639751434326, 0.004865811672061682, -0.009840908460319042, -0.0017882315441966057, -0.015723248943686485, 0.07540007680654526, -0.003503508633002639, -0.024146132171154022, 0.06790096312761307, 0.025829356163740158, 0.022178294137120247, 0.010565987788140774, 0.032420363277196884, 0.028535224497318268, 0.010471847839653492, -0.02208525687456131, 0.05294126272201538, -0.004390328656882048, -0.020427249372005463, 0.0019720536656677723, -0.01941002532839775, -0.011171061545610428, -0.019524605944752693, 0.027335382997989655, 0.03826092183589935, 0.0364006869494915, -0.004608155228197575, -0.010728028602898121, 0.06968913972377777, 0.06716014444828033, 0.014255053363740444, 0.05783470347523689, 0.01442487072199583, 0.014757687225937843, 0.007739451248198748, 0.041016586124897, -0.029565947130322456, 0.10528349876403809, 0.014842786826193333, 0.010863822884857655, 0.0023774439468979836, -0.021482201293110847, -0.04913996905088425, -0.022470099851489067, 0.012991995550692081, -0.031072013080120087, -0.00033903069561347365, -0.035190049558877945, 0.03764595091342926, 0.03235743194818497, -0.055521268397569656, -0.006200699135661125, -0.019114255905151367, 0.0003406533505767584, 0.00459703803062439, -0.031520139425992966, -0.030354544520378113, 0.033561915159225464, -0.00702478876337409, -0.05516154319047928, -0.005049400497227907, -0.062496572732925415, 0.0047833784483373165, 0.023565927520394325, -0.03116316720843315, 0.0055861747823655605, -0.019687283784151077, -0.06052311882376671, -0.02532794512808323, -0.07978484034538269, -0.014006550423800945, 0.031736861914396286, -0.09208463132381439, 0.027401015162467957, 0.0019454405410215259, 0.06885215640068054, -0.0222562737762928, 0.018580080941319466, 0.04171058163046837, -0.008943936787545681, 0.004259064793586731, 0.0268552303314209, 0.0456542894244194, 0.02206444926559925, 4.743757745018229e-05, 0.021501613780856133, 0.015499626286327839, -0.016571057960391045, -0.01037343218922615, 0.023818928748369217, -0.008787131868302822, -0.04649762064218521, -0.0015043444000184536, -0.07073640823364258, 0.029054995626211166, 0.056589122861623764, -0.013055022805929184, -0.05200877785682678, 0.04778303578495979, -0.04615642875432968, 0.0248868465423584, -0.023267611861228943, 0.04643576219677925, 0.01843675971031189, 0.023020289838314056, 0.000578931299969554, 0.039068978279829025, -0.010301444679498672, -0.010830550454556942, 0.002281822497025132, -0.010767447762191296, 0.039617206901311874, -0.03983428701758385, -0.023533131927251816, -0.004424831364303827, -0.0214841291308403, -0.01679885946214199, 0.0030112003441900015, 0.0002629094524309039, -0.044203054159879684, 0.00821018498390913, -0.027450213208794594, -0.017510447651147842, -0.029230281710624695, -0.006606752518564463, 0.031053761020302773, 0.021998465061187744, 0.02768273837864399, -0.032911885529756546, -0.039784613996744156, 0.023411694914102554, -0.007309884764254093, 0.012922925874590874, 0.044003430753946304, 0.028570100665092468, 0.008258143439888954, -0.02744474448263645, -0.036089297384023666, 0.02670035883784294, 0.049776963889598846, 0.03162159398198128, -0.09302981942892075, -0.023892076686024666, 0.0018518631113693118, -0.00202009454369545, 0.03652748838067055, -0.004096036311239004, -0.040688641369342804, -0.026706701144576073, -0.001350637641735375, 0.0006440052529796958, 0.07464296370744705, 0.017978087067604065, 0.02924145758152008, 0.025636035948991776, 0.036102794110774994, 0.0014596228720620275, 0.01106589287519455, 0.002150603337213397, 0.018644174560904503, 0.04083848372101784, 0.0213382039219141, 0.012749011628329754, -0.005214083008468151, 0.040273517370224, 0.05651739984750748, -0.0011535839876160026, -0.0020895511843264103, 0.010568498633801937, 0.015328495763242245, -0.04194759204983711, -0.05504973977804184, -0.010884570889174938, 0.023115335032343864, -0.013274193741381168, -0.05134601145982742, 0.0500275082886219, 0.007744110655039549, -0.019168583676218987, -0.012884953059256077, 0.008876080624759197, -0.006455989554524422, 0.008348341099917889, -0.007182026281952858, 0.023714879527688026, 0.013935176655650139, -0.09389598667621613, -0.03879183530807495, 0.020913362503051758, 0.02387932501733303, -0.01216837577521801, 0.039365049451589584, 0.017518561333417892, -0.010725795291364193, -0.04167283698916435, -0.023390106856822968, -0.034061498939991, 0.009133858606219292, 0.013502988032996655, 0.0293906070291996, 0.0011411793529987335, -0.0062415325082838535, -0.048434194177389145, 0.06177658587694168, 0.03214148432016373, 0.04073407128453255, -0.05033101886510849, -0.008657616563141346, -0.0025009328965097666, 0.09481678903102875, 0.05344172939658165, -0.028008336201310158, -0.032913874834775925, 0.00043900395394302905, 0.010092787444591522, 0.02939458377659321, -0.03716062754392624, 0.01678953878581524, -0.08250325173139572, 0.024428715929389, -0.0006396233220584691, -0.033184219151735306, -0.06344381719827652, 0.017647376284003258, 0.033165693283081055, -0.0762905403971672, -0.017252063378691673, 0.07801596075296402, 0.0019308965420350432, -0.08272258937358856, -0.03017994575202465, 0.006293080281466246, -0.0595054067671299, 0.04535110294818878, 0.009567635133862495, -0.03993332386016846, -0.008480623364448547, -0.020231956616044044, 0.00039709947304800153, 0.04917149618268013, -0.006463259924203157, 0.00250063999556005, -0.06430645287036896, 0.06678150594234467, 0.0010501424549147487, -0.07129248976707458, -0.0689132809638977, -0.02085215225815773, -0.005086596589535475, 0.03448683023452759, -0.010331651195883751, -0.009584115818142891, 0.020161999389529228, -0.037812795490026474, 0.014913094229996204, -0.025710605084896088, -0.04530754312872887, -0.006111048627644777, -0.07946621626615524, 0.03898816928267479, 0.09110964834690094, 0.023010339587926865, -0.049480196088552475, -0.05303188040852547, -0.00776683259755373, 0.021201051771640778, 0.018388276919722557, 0.013841050677001476, 0.06695958971977234, -0.03345818072557449, 0.0002428039297228679, 0.030966216698288918, 0.032361626625061035, -0.00896360445767641, 0.01747853495180607, -0.004519371315836906, 0.047917090356349945, -0.031212424859404564, -0.002925936598330736, -0.08467091619968414, 0.028288790956139565, 0.05916239693760872, 0.024168869480490685, 0.016607558354735374, -0.02186521328985691, -0.028054289519786835, 0.0004891531425528228, 0.005715423263609409, -0.06091216206550598, 0.007910571992397308, 0.01862935908138752, 0.019303105771541595, -0.04251864179968834, -0.09099683165550232, -0.04381411895155907, 0.007750301156193018, 0.001317154848948121, 0.024072682484984398, -0.04225027188658714, 0.015067334286868572, 0.023506956174969673, -0.07735288888216019, 0.0011994801461696625, 0.07305252552032471, -0.016153747215867043, -0.043905965983867645, -0.018121516332030296, 0.05069001391530037, -0.02569783851504326, 0.013757805339992046, -0.028910411521792412, -0.03759630769491196, 0.010262928903102875, -0.061439014971256256, 0.036801066249608994, 0.005724978167563677, 0.057266950607299805, -0.03183573856949806, -0.04144410789012909, -0.007384766358882189, -0.059443484991788864, -0.011714749969542027, -0.03294837102293968, 0.04248526319861412, -0.04746691510081291, -0.014298880472779274, -0.013247274793684483, -0.049676332622766495, 0.04474622756242752, 0.0025786457117646933, -0.03474678471684456, 0.02441677264869213, -0.041888125240802765, -0.00888641644269228, -0.030559184029698372, 0.02378094010055065, 0.0006375321536324918, 0.009213554672896862, -0.027636079117655754, 0.012757616117596626, 0.009698712266981602, 0.008527382276952267, -0.03901023417711258, 0.008591357618570328, 0.020283499732613564, -0.0019005107460543513, 0.03798513859510422, 0.04295037314295769, -0.0029535978101193905, -0.06733052432537079, -0.02717185579240322, 0.05362335965037346, -0.03368442878127098, -0.018528694286942482, -0.021576471626758575, 0.03247961401939392, -0.010349526070058346, -0.014165425673127174, 0.019658764824271202, 0.05978289619088173, -0.02647017128765583, 0.05318446829915047, 0.0030341295059770346, 0.03443426266312599, -0.002095093484967947, 0.045243293046951294, 0.010647409595549107, 0.01025224756449461, -0.06871235370635986, 0.031123915687203407, 0.06724338978528976, -0.05244866758584976, -0.02318970300257206, 0.014009200036525726, -0.00537630170583725, -0.04865433648228645, 0.06398038566112518, -0.012843873351812363, -0.04111556336283684, 0.035430364310741425, 0.011975308880209923, 0.01574263721704483, 0.002368234097957611, 0.052995648235082626, -0.001555928261950612, -0.018633943051099777, 0.016929779201745987, -0.01209949515759945, -0.021277884021401405, 0.03821171820163727, -0.006659983191639185, 0.04341266304254532, -0.015295285731554031, 0.008746668696403503, 0.03851845860481262, -0.0657203197479248, 0.03278625011444092, -0.01650671847164631, 0.04302780702710152, 0.02647671289741993, 0.06488332897424698, 0.024969810619950294, 0.04294966906309128, -0.013046268373727798, -0.006176345515996218, -0.021286843344569206, -0.01803479716181755, -0.002927885390818119, -0.05965697392821312, -6.303556130189869e-33, 0.015989020466804504, -0.022948533296585083, -0.011743242852389812, -0.010389091446995735, -0.02226865664124489, 0.005928272847086191, -0.030056718736886978, -0.015212620608508587, 0.013889077119529247, -0.011490941047668457, -0.004462715238332748, 0.021177591755986214, 0.00012511915701907128, 0.04231896251440048, 0.03691134229302406, -0.012180316261947155, 0.019311806187033653, -0.041472770273685455, -0.004168527200818062, 0.01668061502277851, 0.029871977865695953, 0.011692768894135952, 0.06183170899748802, -0.08068053424358368, -0.05567564442753792, 0.016040021553635597, 0.0011701961047947407, -0.04930839315056801, 0.02405884489417076, 0.05569426715373993, -0.009657666087150574, 0.012477409094572067, 0.011157512664794922, -0.086790069937706, -0.029567088931798935, 0.03999811410903931, -0.07361860573291779, -0.004566785413771868, -0.030453626066446304, 0.014679336920380592, -0.08368749916553497, -0.0010415101423859596, 0.07921481132507324, 0.007920431904494762, 0.020227640867233276, -0.04642091318964958, 0.07495003938674927, -0.035393450409173965, -0.01737208105623722, -0.05092558637261391, -0.07906357198953629, -0.013756269589066505, -0.025489000603556633, -0.002291216515004635, 0.03244151175022125, 0.029049327597022057, -0.008128304034471512, 0.008156929165124893, -0.0727749764919281, 0.02007085271179676, 0.005774662829935551, 0.04156342148780823, 0.08080723881721497, 0.043105076998472214, 0.003930067643523216, 0.014498334378004074, -0.00695493770763278, -0.01510836835950613, -0.03285367041826248, 0.000610336079262197, 0.011560067534446716, 0.06311356276273727, 0.08324301242828369, -0.038034699857234955, 0.02708425745368004, -0.02333754301071167, -0.06580435484647751, 0.027653878554701805, -0.04663455858826637, 0.04470774531364441, 0.024229124188423157, 0.00531215313822031, -0.033517368137836456, -0.00338562554679811, 0.026151444762945175, 0.037018537521362305, -0.023618124425411224, -0.043601810932159424, 0.033140916377305984, -0.0036409501917660236, 0.030800098553299904, 0.02008613385260105, 0.03076106682419777, -0.038563746958971024, 0.06740502268075943, 0.008141088299453259, -0.003074448322877288, 0.06134626269340515, 0.008586122654378414, -0.016899438574910164, -0.042685505002737045, 0.022367749363183975, 0.01604790799319744, 0.046603914350271225, 0.01674461178481579, 0.01538852695375681, 0.04636677727103233, 0.04375983029603958, -0.006760031916201115, -0.02245672419667244, 0.02069435827434063, -0.005860981997102499, 0.02217854931950569, 0.06099981442093849, -0.004274347797036171, -0.048964448273181915, -0.025067081674933434, 0.06511450558900833, -0.0202452652156353, -0.01794683001935482, -0.043228548020124435, -0.031547412276268005, 0.023772209882736206, 0.03288966417312622, -0.0738891214132309, 0.01894022710621357, -0.07440796494483948, 0.005017601419240236, 0.05052053928375244, -0.06017237529158592, -0.027221687138080597, 0.039884451776742935, 3.012212346220622e-07, -0.00896607805043459, 0.007997401058673859, 0.02254132181406021, -0.007947728037834167, 0.03627752885222435, 0.00329583790153265, 0.005692495033144951, 0.033588606864213943, 0.029330728575587273, -0.024034924805164337, 0.04336285963654518, 0.0013805713970214128, 0.008270125836133957, -0.014540162868797779, -0.08485876023769379, -0.031284209340810776, -0.06401653587818146, 0.044290658086538315, -0.018100064247846603, 0.005394882056862116, 0.057481762021780014, 0.1237802729010582, -0.016192970797419548, -0.0010816685389727354, 0.032629042863845825, -0.016718879342079163, 0.03046976588666439, 0.06382057070732117, 0.03588442876935005, -0.041086774319410324, 0.011641938239336014, 0.039020221680402756, -0.0679500624537468, 0.016375476494431496, -0.05529152601957321, -0.02784014493227005, 0.022564107552170753, 0.027333371341228485, -0.03206900134682655, -0.033987484872341156, -0.005602754186838865, 0.007849669083952904, 0.007096314802765846, -0.02681024745106697, 0.04453316703438759, -0.06244640052318573, -0.047280292958021164, 0.009898846037685871, -0.029146013781428337, 0.008652359247207642, -0.036790765821933746, -0.016193484887480736, 0.00386604736559093, -0.036201901733875275, -0.0027800542302429676, -0.013230961747467518, -0.016616154462099075, -0.07106252014636993, 0.0529370941221714, 0.019646944478154182, -0.0031825511250644922, 0.02841043286025524, -0.02583467587828636, -0.05095253884792328, 0.08237767219543457, 0.0029016744811087847, -0.044459909200668335, 2.5847210596262016e-34, 0.0031448197551071644, -0.0004853775317315012, 0.00497617619112134, 0.010562923736870289, -0.025444861501455307, -0.018479177728295326, -0.01472755428403616, 0.0020523699931800365, 0.011916786432266235, -0.041260648518800735, -0.06859854608774185]

['Desmond Elliott', 'Stella Frank', 'Eva Hasler']

1510.04709v2

In this paper we present an approach to multi-language image description bringing together insights from neural machine translation and neural image description. To create a description of an image for a given target language, our sequence generation models condition on feature vectors from the image, the description from the source language, and/or a multimodal vector computed over the image and a description in the source language. In image description experiments on the IAPR-TC12 dataset of images aligned with English and German sentences, we find significant and substantial improvements in BLEU4 and Meteor scores for models trained over multiple languages, compared to a monolingual baseline.

Multilingual Image Description with Neural Sequence Models

http://arxiv.org/pdf/1510.04709v2

Title Multilingual Image Description Neural Sequence Models Summary paper present approach multilanguage image description bringing together insight neural machine translation neural image description create description image given target language sequence generation model condition feature vector image description source language andor multimodal vector computed image description source language image description experiment IAPRTC12 dataset image aligned English German sentence find significant substantial improvement BLEU4 Meteor score model trained multiple language compared monolingual baseline Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.03873835876584053, 0.03974294289946556, 0.011122329160571098, 0.07812575995922089, -0.030448313802480698, 0.031966615468263626, 0.01927098073065281, -0.019631776958703995, -0.045805588364601135, -0.03218648210167885, -0.026834923774003983, -0.060991425067186356, 0.032955825328826904, 0.025300851091742516, 0.030947955325245857, -0.11732463538646698, 0.007599785923957825, -0.0008908407180570066, -0.032204627990722656, 0.005631844513118267, 0.02918928675353527, 0.030138438567519188, 0.03817012906074524, 0.05087313428521156, -0.019743818789720535, -0.004869498778134584, 0.001300185453146696, 0.014456073753535748, -0.0016012773849070072, -0.043865498155355453, -0.02697576768696308, 0.05420488491654396, 0.0040824199095368385, 0.014238576404750347, 2.057935262200772e-06, -0.00024437051615677774, 0.02441893145442009, 4.786137287737802e-05, 0.07139905542135239, -0.051095664501190186, 0.029965637251734734, -0.0674673318862915, 0.015122946351766586, -0.02301688864827156, -0.010202978737652302, -0.020013369619846344, 0.06578495353460312, 0.08523169159889221, 0.04949124529957771, 0.04386785998940468, -0.022246163338422775, -0.07212550938129425, -0.032788630574941635, -0.03594139218330383, 0.014399828389286995, -0.007284578401595354, 0.005891122855246067, -0.012824604287743568, -0.03397633507847786, 0.0098976856097579, -0.02778523787856102, 0.0648735985159874, 0.01766764558851719, -0.028245026245713234, -0.01330023817718029, 0.019522903487086296, 0.014145993627607822, -0.06803400069475174, -0.001709360396489501, 0.06380820274353027, -0.039560653269290924, 0.015910735353827477, -0.044969815760850906, 0.004848309326916933, -0.01831895112991333, -0.034056469798088074, -0.03398651257157326, 0.07162953913211823, -0.019075553864240646, 0.005936984438449144, -0.01594679430127144, 0.03054855763912201, 0.026956478133797646, -0.0022187677677720785, 0.010201009921729565, -0.0022722682915627956, 0.008189466781914234, 0.007783747743815184, -0.053257036954164505, -0.007220469415187836, 0.011612500995397568, -0.05427988991141319, -0.008337680250406265, 0.02597159333527088, 0.013336475007236004, 0.009010042063891888, -0.026522256433963776, -0.061124224215745926, 0.04477260634303093, -0.06135542318224907, 0.04180646315217018, 0.007439896930009127, -0.08001638948917389, 0.05961587652564049, -0.013397055678069592, 0.08199384063482285, 0.014913390390574932, -0.005755609832704067, -0.08147639036178589, -0.02171766199171543, -0.004734422545880079, -0.009848532266914845, -0.013636074960231781, 0.01590706594288349, -0.022885041311383247, -0.045684561133384705, -0.07747939974069595, 0.0009535738499835134, 0.008790959604084492, 0.0012408570619300008, 0.00826248712837696, 0.022609619423747063, -0.03466476872563362, -0.0012232898734509945, -0.033252183347940445, 0.014272267930209637, 0.022937975823879242, -0.02878567948937416, -0.025449052453041077, -0.015578092075884342, 0.007959587499499321, 0.06644318997859955, -0.04755580797791481, -0.0009364706347696483, -0.023376379162073135, 0.05559961497783661, -0.001183502608910203, -0.0298327449709177, -0.0011544907465577126, -0.010863987728953362, -0.023369688540697098, -0.05941819027066231, -0.008817270398139954, -0.04802599549293518, 0.04460000619292259, -0.01764163002371788, 0.006579438224434853, -0.055912964046001434, 0.014955559745430946, 0.025431405752897263, -0.01195817906409502, 0.09266237914562225, -0.043288689106702805, -0.013419746421277523, 0.008304334245622158, 0.009264521300792694, 0.04185714200139046, 0.06454464793205261, 0.01973821222782135, 0.025304347276687622, 0.04996918514370918, -0.01028739009052515, -0.00012183802027720958, 0.057600121945142746, -0.04047684371471405, -0.019440067932009697, -0.035245560109615326, -0.021351834759116173, 0.03281582519412041, 0.03168044984340668, 0.02935664728283882, 0.0491645485162735, 0.012636213563382626, 0.029892684891819954, 0.05200169235467911, 0.07324430346488953, 0.011523482389748096, 0.02851344645023346, 0.062378548085689545, 0.0032322031911462545, -0.0290747731924057, 0.0360184870660305, -0.01341281272470951, 0.0667865052819252, 0.03464580699801445, 0.038354650139808655, 0.0012876404216513038, 0.06803081929683685, -0.030807260423898697, -0.03905845433473587, 0.005969316698610783, -0.00906713493168354, 0.03833644092082977, -0.020264551043510437, 0.02950727753341198, 0.023731041699647903, -0.04063529521226883, 0.030393550172448158, 0.021840734407305717, -0.01895437389612198, 0.005703342612832785, -0.004624726716428995, -0.03113512322306633, 0.05513923615217209, 0.015527636744081974, 0.014036104083061218, -0.0228650514036417, 0.016167931258678436, -0.019251806661486626, 0.0689525380730629, 0.000423251447500661, 0.01028703898191452, -0.005174557212740183, -0.07016797363758087, -0.04556578770279884, -0.02831690013408661, -0.020754924044013023, 0.034498706459999084, -0.04277098551392555, 0.016146134585142136, 0.05574207007884979, 0.07914872467517853, -0.08355637639760971, 0.030481185764074326, 0.01264867465943098, 0.0016307997284457088, 0.029783260077238083, 0.01577596738934517, -0.007803760003298521, -0.000337581877829507, -0.009936698712408543, 0.007917048409581184, 0.020810192450881004, -0.013979678973555565, -0.0070772236213088036, 0.07357972860336304, -0.04794330522418022, -0.035703498870134354, 0.022428007796406746, -0.027767520397901535, 0.02356746233999729, -0.042578890919685364, -0.03594519570469856, -0.04455766826868057, -0.010728455148637295, -0.04165758937597275, -0.026394139975309372, -0.03639386594295502, 0.056892286986112595, -0.005032015033066273, 0.04164508357644081, -0.02325276844203472, 0.02926665171980858, -0.028222905471920967, -0.018323006108403206, -0.009101063013076782, -0.05939662083983421, 0.016263870522379875, -0.02659090794622898, -0.037542860954999924, 0.05069334805011749, 0.0201005507260561, 0.016000444069504738, 0.029070446267724037, 0.053304970264434814, -0.005947464145720005, 0.030295316129922867, -0.05403406545519829, -0.028755679726600647, -0.019970009103417397, -0.007532911840826273, -0.008112078532576561, 0.0030269233975559473, 0.024814292788505554, -0.05997133255004883, -0.06241897866129875, 0.03331740200519562, 0.033890724182128906, -0.0033307585399597883, 0.06576558202505112, 0.03598320856690407, 0.018314775079488754, 0.011215324513614178, -0.0011410149745643139, 0.03341969847679138, 0.08645127713680267, 0.031669698655605316, -0.09389276057481766, -0.03931877389550209, -0.007627161219716072, -0.040986623615026474, 0.03422008454799652, 0.0015153911663219333, -0.03563939034938812, -0.015157610177993774, 0.016574649140238762, 0.011333874426782131, 0.024228742346167564, 0.02569574862718582, -0.009843241423368454, 0.0233383197337389, 0.021335214376449585, 0.010608679614961147, -0.0005478305974975228, -0.02171577513217926, 0.03711097687482834, 0.0109886908903718, -0.050836119800806046, 0.007941549643874168, 0.02855326235294342, -0.015587483532726765, 0.024168040603399277, -0.044950298964977264, -0.01761208102107048, -0.02500828728079796, -0.009032956324517727, -0.07643803209066391, 0.0014326811069622636, 0.0077933333814144135, 0.03242366388440132, -0.03416253626346588, -0.04008913412690163, 0.049183718860149384, -0.04164447262883186, -0.012024527415633202, -0.04590592533349991, -0.026688214391469955, -0.04914252460002899, 0.08241972327232361, 0.036757927387952805, 0.056697409600019455, 0.01735740154981613, 0.020119553431868553, 0.0097409188747406, -0.042507972568273544, 0.014521108940243721, -0.006456382106989622, 0.03327351436018944, -0.04826756566762924, -0.013838636688888073, -0.024099446833133698, -0.03514320030808449, -0.02833709679543972, -0.0019328448688611388, 0.0023922647815197706, -0.01968819834291935, -0.0016605148557573557, -0.03249676153063774, -0.0301431342959404, 0.055939219892024994, 0.04408085346221924, 0.026211611926555634, -0.026278698816895485, 0.026184871792793274, 0.013686848804354668, 0.02520439587533474, 0.054619770497083664, -0.028097236528992653, -0.04455205425620079, -0.03409301117062569, 0.022495262324810028, 0.0022335397079586983, -0.0659954622387886, 0.020411254838109016, -0.05178392305970192, -0.0269196555018425, 0.019059384241700172, 0.0056457845494151115, -0.04289132356643677, 0.001718364073894918, 0.02500944770872593, -0.039379797875881195, 0.01635698974132538, 0.052536752074956894, 0.001363564864732325, -0.08460468798875809, -0.017943229526281357, 0.004807629156857729, -0.02037748694419861, 0.04620042070746422, 0.03061104007065296, -0.07130002975463867, -0.012680432759225368, -0.04409121349453926, -0.016921164467930794, 0.006834160070866346, 0.03237078711390495, -0.07373522222042084, -0.05343790352344513, 0.008630162104964256, 0.01195740420371294, -0.04545467346906662, -0.050311557948589325, 0.007291887421160936, -0.06356599181890488, -0.0012976914877071977, -0.008249952457845211, -0.028706131502985954, 0.03571493551135063, -0.03131721168756485, 0.0006628233240917325, -0.0050234622322022915, -0.04933926463127136, -0.012456821277737617, -0.03733791410923004, -0.02818608097732067, 0.05577867850661278, 0.029298480600118637, -0.031068312004208565, -0.03424292430281639, 0.01350824162364006, 0.04490698128938675, 0.03266434744000435, -0.011993196792900562, 0.027650833129882812, 0.000590435869526118, -0.038334257900714874, 0.021175606176257133, -0.009706121869385242, 0.01691940799355507, 0.020651016384363174, 0.03409653902053833, 0.020143575966358185, -0.005032181274145842, 0.009518948383629322, -0.05416740104556084, 0.031513430178165436, -0.0015557296574115753, 0.0019963306840509176, 0.008761395700275898, -0.04996975511312485, 0.014776305295526981, -0.027371227741241455, -0.037793099880218506, -0.10084733366966248, 0.0006649780552834272, 0.03769645094871521, -0.06843487918376923, -0.0325748585164547, -0.08141476660966873, -0.03895898908376694, -0.0138998469337821, 0.01564841717481613, 0.06168043613433838, -3.858663694700226e-05, -0.007779761217534542, -0.026250142604112625, -0.05937487259507179, 0.04773499071598053, 0.03431596979498863, 0.011750947684049606, -0.02108451910316944, 0.02498491108417511, 0.043123651295900345, -0.03545425459742546, 0.01888200268149376, -0.004727732390165329, -0.04635774344205856, -0.024475520476698875, -0.04493207111954689, 0.07126037776470184, -0.0029922528192400932, 0.050317734479904175, 0.004754660185426474, -0.06071091443300247, -0.0026707034558057785, -0.0010675443336367607, 0.05378090590238571, -0.044526442885398865, -9.670064901001751e-05, -0.023619895800948143, -0.033648550510406494, 0.01589379832148552, -0.007995040155947208, 0.034482650458812714, -0.0048787700943648815, -0.014321397989988327, -0.02081436477601528, -0.06716157495975494, 0.009609547443687916, -0.0024602387566119432, -0.016336848959326744, -0.054866086691617966, 0.0032206608448177576, -0.010935059748589993, 0.003181138774380088, -0.018337035551667213, -0.061868369579315186, -0.01877058669924736, 0.0010510419961065054, 0.025537319481372833, -0.009908737614750862, 0.01950642839074135, -0.0018334463238716125, -0.016674699261784554, -0.05837075039744377, -0.015610693953931332, 0.01973348669707775, 0.006092903204262257, -0.012857604771852493, -0.02324734628200531, 0.025749539956450462, -0.03458862006664276, 0.025758182629942894, -0.016377074643969536, 0.016037998721003532, -0.029155515134334564, 0.07100910693407059, 0.0026212313678115606, 0.01747122034430504, -0.0014634537510573864, 0.035960085690021515, 0.05798497423529625, 0.03516590595245361, -0.05284964293241501, 0.015456962399184704, 0.1142934113740921, 0.008207263424992561, 0.04314948618412018, 0.010570123791694641, -0.016944022849202156, -0.005971072241663933, 0.07643166929483414, -0.020750338211655617, -0.07047797739505768, 0.04616663604974747, -0.008760002441704273, -0.00374773726798594, -0.02357873134315014, 0.05821126326918602, -0.01039960514754057, 0.007007479202002287, 0.018677249550819397, -0.04090788960456848, -0.041056107729673386, 0.01671326905488968, 0.023713726550340652, 0.0006658359779976308, -0.030283363536000252, 0.014087202027440071, 0.007608418352901936, -0.047761574387550354, 0.014462165534496307, 0.021685106679797173, 0.024508759379386902, 0.04402351379394531, 0.07181438058614731, 0.04267389327287674, 0.031192440539598465, 0.004823586903512478, -0.02445511519908905, -0.03986265882849693, -0.030800217762589455, 0.004227704834192991, -0.037548139691352844, -5.6808137532707766e-33, -0.01042091567069292, -0.0433034710586071, 0.03423551842570305, -0.048101168125867844, -0.02494700998067856, 0.007695434615015984, -0.024404186755418777, -0.021460259333252907, -0.00047342773177661, 0.0067832013592123985, 0.04262111335992813, -0.04189327731728554, 0.015247046016156673, 0.07083209604024887, 0.02773912250995636, 0.054295044392347336, 0.03190264105796814, 0.02172998897731304, 0.01574631966650486, 0.02110939659178257, 0.01563958451151848, 0.01549617387354374, 0.09302480518817902, -0.022890955209732056, 0.0318901389837265, 0.0035991529002785683, -0.014714214950799942, 0.020203815773129463, 0.025477265939116478, 0.023116426542401314, -0.03594561666250229, 0.02075313590466976, 0.01556982658803463, -0.021680818870663643, -0.018960239365696907, -0.026183074340224266, -0.02671893872320652, -0.0031799818389117718, 0.018358347937464714, 0.05153859034180641, -0.03946838900446892, -0.025485554710030556, 0.034334804862737656, -0.06891024112701416, -0.008780591189861298, 0.021415723487734795, 0.060644421726465225, -0.03477239981293678, -0.014607490971684456, -0.01772979088127613, -0.06946483254432678, 0.016326051205396652, -0.011888519860804081, -0.016000863164663315, 0.049539413303136826, 0.03857027739286423, -0.000686046842020005, 0.00742193590849638, -0.06564465165138245, 0.030320115387439728, -0.014636551961302757, 0.04049789533019066, 0.10196501016616821, 0.06417323648929596, 0.001455263583920896, 0.019495131447911263, 0.01387366559356451, -0.01651463285088539, 0.0006919007864780724, 0.03176053240895271, 0.0029004814568907022, 0.012923045083880424, 0.08545979857444763, 0.04241074621677399, 0.014890987426042557, 0.007454752456396818, -0.04428200423717499, 0.04239918664097786, -0.02229403518140316, 0.04147583246231079, 0.027575742453336716, -0.026920726522803307, -0.007093285676091909, -0.0006325094727799296, -0.01864391751587391, -0.03192810341715813, -0.011506171897053719, -0.04463949799537659, 0.00860385037958622, -0.0007908128900453448, 0.004607346374541521, 0.042447611689567566, 0.03381240367889404, -0.012178202159702778, 0.016479643061757088, -0.030445056036114693, -0.023631542921066284, 0.010659582912921906, -0.007226691581308842, 0.03571004420518875, -0.007034929934889078, -0.05926458537578583, -0.014350075274705887, 0.048954714089632034, 0.017051346600055695, 0.019282707944512367, 0.09365321695804596, -0.02196476235985756, 0.0018594337161630392, 0.008104480803012848, -0.003751240437850356, -0.012274621985852718, -0.00858301855623722, 0.04432113468647003, -0.009443992748856544, 0.0001855263253673911, -0.08354495465755463, 0.030675606802105904, 0.037180472165346146, -0.05041169375181198, 0.0010702104773372412, -0.05808344483375549, 0.033036213368177414, 0.07895725220441818, -0.06281495094299316, 0.06220553070306778, -0.06173451989889145, -0.03476378694176674, 0.014846893027424812, -0.029728000983595848, -0.03918520733714104, 0.07723785191774368, 2.5792223823373206e-07, 0.021402060985565186, 0.0015081397723406553, 0.022514708340168, 0.015009919181466103, 0.013446077704429626, 0.017626121640205383, -0.03324628993868828, 0.010539046488702297, -0.04377099126577377, 0.04842601343989372, -2.56653074757196e-05, -0.013269846327602863, 0.034085579216480255, -0.018655847758054733, -0.06160619854927063, -0.03795652464032173, -0.06049972027540207, -0.007199672982096672, -0.0654258280992508, 0.02749914489686489, 0.06785932183265686, 0.10434844344854355, -0.020220480859279633, 0.0020851765293627977, 0.014348247088491917, -0.04205820709466934, 0.05037548765540123, -0.0020008536521345377, -0.0298483707010746, -0.011033625341951847, -0.016670361161231995, 0.05149673670530319, -0.056018438190221786, 0.03117799572646618, -0.010082412511110306, -0.004293014295399189, 0.05829627439379692, -0.0018225910607725382, -0.017382673919200897, 0.016311628744006157, 0.020416034385561943, 0.03404683992266655, -0.02724507637321949, -0.07459205389022827, 0.05043516680598259, -0.025212060660123825, -0.04220923036336899, -0.03683727607131004, 0.02695215865969658, 0.02709861658513546, 0.07692746818065643, -0.05179625749588013, -0.03936454653739929, 0.0025265009608119726, 0.07523506134748459, -0.03250369429588318, -0.03443611413240433, -0.04324566200375557, -0.013394284062087536, 0.018381459638476372, 0.003810230875387788, 0.059494104236364365, -0.03873175010085106, -0.041130904108285904, 0.010827094316482544, -0.03920085355639458, 0.01448105089366436, 2.181106120310494e-34, 0.039934247732162476, -0.013109288178384304, 0.005005214363336563, 0.005961735267192125, -0.00651168916374445, -0.022463839501142502, -0.04254274442791939, 0.012565547600388527, -0.023924827575683594, -0.022469166666269302, -0.04681827127933502]

['Oswaldo Ludwig', 'Xiao Liu', 'Parisa Kordjamshidi', 'Marie-Francine Moens']

1603.08474v1

This paper introduces the visually informed embedding of word (VIEW), a continuous vector representation for a word extracted from a deep neural model trained using the Microsoft COCO data set to forecast the spatial arrangements between visual objects, given a textual description. The model is composed of a deep multilayer perceptron (MLP) stacked on the top of a Long Short Term Memory (LSTM) network, the latter being preceded by an embedding layer. The VIEW is applied to transferring multimodal background knowledge to Spatial Role Labeling (SpRL) algorithms, which recognize spatial relations between objects mentioned in the text. This work also contributes with a new method to select complementary features and a fine-tuning method for MLP that improves the $F1$ measure in classifying the words into spatial roles. The VIEW is evaluated with the Task 3 of SemEval-2013 benchmark data set, SpaceEval.

Deep Embedding for Spatial Role Labeling

http://arxiv.org/pdf/1603.08474v1

Title Deep Embedding Spatial Role Labeling Summary paper introduces visually informed embedding word VIEW continuous vector representation word extracted deep neural model trained using Microsoft COCO data set forecast spatial arrangement visual object given textual description model composed deep multilayer perceptron MLP stacked top Long Short Term Memory LSTM network latter preceded embedding layer VIEW applied transferring multimodal background knowledge Spatial Role Labeling SpRL algorithm recognize spatial relation object mentioned text work also contributes new method select complementary feature finetuning method MLP improves F1 measure classifying word spatial role VIEW evaluated Task 3 SemEval2013 benchmark data set SpaceEval Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.049278587102890015, 0.006925229914486408, -0.00891056563705206, 0.05675702169537544, -0.02547542192041874, 0.002801428083330393, 0.013896778225898743, -0.05079101771116257, -0.00027351450989954174, -0.03531043604016304, -0.017839377745985985, 0.005415066611021757, 0.013618972152471542, 0.030895709991455078, 0.0001007936371024698, -0.05133795738220215, 0.026189368218183517, 0.02510637231171131, 0.014689276926219463, 0.023746812716126442, 0.00795659888535738, 0.019533634185791016, 0.0017322745407000184, 0.03275136277079582, -0.07284006476402283, -0.014837400987744331, 0.012333458289504051, -0.03446930646896362, 0.025123683735728264, -0.053866878151893616, 0.02853933349251747, 0.007977655157446861, 0.05338812246918678, -0.019200244918465614, 2.460861878716969e-06, 0.010361230932176113, -0.030571220442652702, -0.012539910152554512, 0.039090171456336975, -0.046472497284412384, -0.001379920868203044, -0.047557901591062546, 0.02430410496890545, -0.015040894970297813, -0.044863708317279816, -0.012282139621675014, 0.06561233848333359, 0.0574897862970829, -0.01044142059981823, 0.01323490310460329, -0.027017634361982346, -0.05792059376835823, -0.021962517872452736, -0.009015134535729885, 0.012025327421724796, 0.002362515078857541, 0.00607691053301096, 0.005921856500208378, 0.007474648300558329, 0.032642170786857605, -0.06390687823295593, 0.044990167021751404, 0.014195415191352367, -0.0200215931981802, 0.040750645101070404, 0.0724160447716713, 0.005633477587252855, 0.011874846182763577, 0.014886423945426941, 0.06161770597100258, -0.015180375427007675, -0.0013703913427889347, 0.0014070287579670548, 0.00989976804703474, -0.026833688840270042, 0.04531208053231239, -0.018561000004410744, 0.02354857698082924, 0.027070961892604828, -0.0034184898249804974, 0.001955735497176647, 0.08850090205669403, -0.005909415893256664, 0.02785431407392025, -0.014982110820710659, 0.059675369411706924, -0.02301762066781521, -0.03873290866613388, -0.050300948321819305, -0.014963177032768726, 0.0110574746504426, -0.0174026470631361, 0.036028362810611725, 0.03210914134979248, 0.019885074347257614, 0.03902826085686684, -0.008154070936143398, 0.0171342846006155, 0.0047252303920686245, -0.08536013960838318, 0.0022350854706019163, -0.04188608005642891, -0.03120928257703781, 0.05548297241330147, -0.031722698360681534, 0.016633227467536926, -0.003517990466207266, 0.06961654871702194, -0.013772591948509216, 0.0066595738753676414, -0.04155126214027405, -0.07108671963214874, -0.025320952758193016, 0.02731146663427353, -0.03942335769534111, -0.05602356418967247, -0.01859133318066597, -0.018701035529375076, -0.025761093944311142, 0.02994946762919426, 0.020105864852666855, 0.08791586756706238, 0.0009918700670823455, 0.0009688437567092478, -0.003383987583220005, 0.004739868920296431, -0.009055220521986485, 0.0030563385225832462, -0.045583322644233704, 0.006031266879290342, 0.01310262642800808, 0.051586855202913284, 0.041202835738658905, -0.02208941988646984, -0.03885864093899727, 0.036699261516332626, 0.02235550619661808, -0.03422073647379875, 0.029690371826291084, -0.04152350872755051, -0.0725959837436676, 0.019870243966579437, 0.013694655150175095, -0.04452364519238472, -0.014906835742294788, -0.03511061519384384, 0.011167017742991447, 0.008148991502821445, 0.0011156515683978796, 0.011217818595468998, -0.01872912421822548, 0.09891434758901596, -0.025155531242489815, -0.0031352518126368523, 0.08997578173875809, 0.026175733655691147, 0.08306863158941269, 0.011158887296915054, 0.045257389545440674, 0.056254513561725616, 0.0315251387655735, 0.005078630521893501, 0.01894189789891243, 0.0018709716387093067, -0.051967281848192215, -0.040359869599342346, -0.01426804531365633, 0.0019319785060361028, -0.004672436509281397, 0.029598690569400787, -0.007932903245091438, -0.0045906854793429375, 0.016293924301862717, -0.008869574405252934, 0.054748255759477615, 0.06892219930887222, 0.019720764830708504, -0.016605446115136147, 0.0004202222335152328, 0.048916641622781754, -0.04123673215508461, -0.017483722418546677, -0.029115743935108185, 0.05177133157849312, 0.03853807598352432, -0.033206865191459656, -0.06297822296619415, -0.013865106739103794, 0.0015934336697682738, -0.017102278769016266, 0.014446023851633072, -0.01954936608672142, 0.009648799896240234, -0.022674253210425377, 0.02513023465871811, -0.006478650029748678, -0.012377110309898853, 0.04533081129193306, 0.004243906121701002, 0.006935064680874348, -0.014269388280808926, 0.008312864229083061, -0.007836418226361275, 0.024489251896739006, 0.023699989542365074, -0.04329703748226166, -0.047654889523983, -0.0011190414661541581, 0.04160775989294052, -0.005661024246364832, 0.02192452736198902, -0.001902956166304648, -0.005101118702441454, -0.04322897642850876, -0.05049881711602211, 0.01930953748524189, -0.002110952977091074, 0.012052345089614391, -0.01212430652230978, 0.029077067971229553, 0.054500870406627655, 0.021077780053019524, -0.03162948414683342, 0.03602280467748642, 0.06310561299324036, -0.03194613382220268, -0.0032470847945660353, 0.062014833092689514, -0.013715428300201893, 0.011289563030004501, -0.0092117078602314, 0.011356131173670292, 0.05283249542117119, -0.03950212523341179, -0.02061140164732933, 0.0509415827691555, -0.0952853262424469, -0.04101549834012985, 0.00832434929907322, -0.06223888695240021, 0.005277404561638832, 0.02170594409108162, -0.025492608547210693, -0.026963386684656143, 0.0005305475206114352, -0.029053563252091408, -0.019894016906619072, -0.020605020225048065, -0.00962924025952816, 0.02197067253291607, 0.020885715261101723, -0.062125906348228455, 0.06666357070207596, 0.002886313246563077, 0.01171526126563549, -0.024974999949336052, 0.04518923535943031, 0.027383487671613693, -0.0060678026638925076, -0.012678327038884163, -0.022668994963169098, -0.023854944854974747, -0.025455044582486153, 0.014101107604801655, 0.014093711972236633, -0.0023589266929775476, -0.012175546027719975, -0.05580611899495125, -0.0346028208732605, 0.002737168688327074, -0.029673689976334572, -0.0002215296117356047, -0.037188805639743805, 0.00148895347956568, -0.0278183501213789, -0.060579728335142136, -0.011014732532203197, -0.028981005772948265, -0.005563071928918362, 0.054604340344667435, -0.025061555206775665, -0.004313824698328972, -0.011654073372483253, 0.018058137968182564, -0.031462159007787704, 0.01802550069987774, 0.03901474550366402, -0.07969425618648529, 0.002518834313377738, -0.009434756822884083, 0.04030648618936539, 0.015937719494104385, 0.009535529650747776, -0.023645758628845215, -0.024192461743950844, -0.017404329031705856, -0.05068094655871391, 0.019516292959451675, 0.01672838255763054, 0.04064877703785896, 0.013510464690625668, -0.011934788897633553, -0.0014269056264311075, 0.009408131241798401, 0.0006048292852938175, 0.049368735402822495, 0.012254788540303707, -0.004571124911308289, -0.016136471182107925, 0.047329507768154144, 0.013645214959979057, 0.021777143701910973, -0.009605574421584606, -0.03222548961639404, -0.051395103335380554, -0.00665564090013504, -0.03740523383021355, -0.0335044227540493, -0.011994380503892899, 0.0019582265522331, -0.059276606887578964, -0.011580592952668667, -0.002236671047285199, -0.013024464249610901, -0.01532319188117981, -0.05312259495258331, -0.018486855551600456, -0.04290208965539932, 0.10447044670581818, 0.03477364778518677, 0.0313088558614254, -0.05217216908931732, -0.03134353458881378, -0.012780342251062393, -0.012750535272061825, 0.003265653969720006, 0.017378097400069237, -0.02098078653216362, -0.023489350453019142, 0.010459274053573608, -0.03177451714873314, -0.03499792888760567, -0.011989849619567394, -0.04191965609788895, -0.02455112151801586, -0.006876800209283829, 0.03215007111430168, -0.008269385434687138, 0.00863039493560791, 0.04141208529472351, -0.010152301751077175, 0.03693225234746933, -0.027471274137496948, 0.018295900896191597, -0.01730422116816044, 0.0736280083656311, 0.071048803627491, 0.04694156348705292, -0.08348993957042694, 0.03075462020933628, -0.026509983465075493, 0.03000042773783207, -0.10629751533269882, 0.02892250381410122, -0.033980101346969604, 0.027939733117818832, 0.01741223968565464, -0.009350370615720749, -0.034252822399139404, -0.012340250425040722, 0.042465098202228546, -0.061095934361219406, -0.025067541748285294, 0.08483143150806427, 0.07628241926431656, -0.086807020008564, -0.005413537845015526, 0.01888800598680973, -0.06429298967123032, 0.025471774861216545, 0.012189041823148727, -0.0310197900980711, -0.013940483331680298, -0.029768291860818863, -0.07998565584421158, 0.012230033986270428, -0.033510271459817886, -0.015550042502582073, -0.07804825156927109, 0.05307460203766823, -0.017547033727169037, -0.06664857268333435, -0.033362168818712234, -0.024069668725132942, -0.032478079199790955, 0.0027849790640175343, -0.07043889909982681, -0.026961244642734528, 0.010709487833082676, -0.056698303669691086, 0.025228463113307953, -0.10153359174728394, 0.027962710708379745, -0.006249194499105215, -0.062444090843200684, 0.021579723805189133, 0.0393044613301754, 0.0835728719830513, -0.03514454513788223, -0.042858485132455826, -0.02210095152258873, 0.06202441081404686, 0.023317139595746994, -0.003580340649932623, 0.04488639533519745, -0.03250214830040932, -0.004450155422091484, -0.005463325884193182, -0.003771592630073428, 0.02381259575486183, -0.013826240785419941, 0.013656781055033207, 0.052085526287555695, -0.010043473914265633, 0.02636643499135971, -0.048333097249269485, 0.05246582627296448, 0.028810422867536545, 4.337189966463484e-05, 0.015351241454482079, 0.004999931436032057, -0.04256122559309006, -0.03937097266316414, 0.05182288959622383, -0.02937234938144684, -0.00813058577477932, 0.014678296633064747, -0.019899215549230576, -0.01952802762389183, -0.04452214390039444, -0.035395704209804535, 0.053670573979616165, 0.03484468534588814, 0.05075612664222717, 0.025295820087194443, -0.004496482200920582, -0.03924941271543503, -0.10387805849313736, -0.04840310662984848, 0.0021977827418595552, 0.056510284543037415, 0.01673755794763565, 0.024137277156114578, 0.06777780503034592, -0.032149333506822586, -0.007500151637941599, -0.02450067177414894, 0.003081708215177059, 0.0025156077463179827, -0.012068575248122215, 0.042673517018556595, -0.0008571397629566491, -0.006375575438141823, -0.03465571627020836, -0.06805209815502167, 0.06885729730129242, 0.015585417859256268, -0.029937129467725754, -0.050029173493385315, -0.012926004827022552, -0.0013736438704654574, -0.017640167847275734, -0.013010835275053978, -6.874561222502962e-05, 0.04063372313976288, -0.02254284732043743, -0.052189089357852936, -0.024887600913643837, 0.011081285774707794, -0.010756349191069603, -0.06596723198890686, 0.0837053582072258, -0.0026236441917717457, 0.0213179849088192, -0.03140117973089218, 0.025190144777297974, -0.03356822952628136, -0.020967088639736176, 0.008463102392852306, 0.016982942819595337, 0.054419342428445816, 0.010217098519206047, -0.013916668482124805, -0.022314229980111122, 0.04718543961644173, -0.008316979743540287, 0.018202684819698334, 0.04190436005592346, 0.03203529492020607, -0.0005619808216579258, -0.019701538607478142, 0.05185085907578468, -0.02960495464503765, 0.017623119056224823, -0.013627271167933941, 0.039890654385089874, 0.019300466403365135, -0.039865314960479736, 0.013427799567580223, -0.01158037781715393, -0.06350161880254745, 0.06437525153160095, 0.007088677026331425, -0.011652889661490917, -0.023437457159161568, 0.03758171945810318, 0.05613324046134949, -0.0979764387011528, -0.003107123076915741, -0.0023965362925082445, 0.00825209729373455, 0.02813505381345749, 0.020605681464076042, -0.01851091906428337, -0.04461235925555229, 0.04344279691576958, 0.004896028898656368, -0.00924233254045248, -0.03141077235341072, 0.04316055029630661, 0.061386339366436005, -0.02395521104335785, 0.017044225707650185, -0.04551970213651657, -0.009057163260877132, 0.06235292926430702, 0.03915856406092644, 0.051276423037052155, -0.03735433146357536, 0.043824732303619385, -0.0283258855342865, -0.031275004148483276, 0.031567346304655075, -0.013425634242594242, 0.018252724781632423, 0.03494522348046303, 0.016706978902220726, 0.0009481741581112146, 0.04583539068698883, -0.025868047028779984, -0.04228859022259712, -0.03577804937958717, 0.047977838665246964, -0.037709034979343414, -0.01959732547402382, -6.467836608505069e-33, -0.018694911152124405, -0.1058371365070343, 0.029943300411105156, 0.010742261074483395, -0.015534008853137493, 0.037376221269369125, -2.6764093490783125e-05, -0.03302657976746559, 0.014209097251296043, 0.035069312900304794, -0.010324399918317795, 0.003609166946262121, 0.022953184321522713, 0.0399557501077652, 0.04302216321229935, -0.002378928940743208, -0.00664451764896512, 0.0363815538585186, 0.04349454864859581, -0.014442283660173416, 0.01405741460621357, 0.06397466361522675, 0.08370687812566757, -0.0860074833035469, 0.00798659399151802, 0.03747502714395523, 0.0014548045583069324, -0.0054158675484359264, -0.004501701332628727, 0.024421002715826035, -0.03024260140955448, -0.01564623787999153, 0.04643377661705017, -0.0335409939289093, 0.01565210148692131, 0.07298760861158371, -0.05621879920363426, -0.04317053407430649, -0.028511295095086098, 0.052272628992795944, -0.014476584270596504, 0.002794472500681877, 0.007389484904706478, 0.036724694073200226, 0.014520935714244843, 0.00350211258046329, 0.08661749213933945, -0.006948697380721569, -0.05120342969894409, 0.01892893947660923, -0.06581263244152069, 0.032512519508600235, -0.00456012599170208, -0.0229469146579504, 0.047412652522325516, -0.038576461374759674, 0.03555440530180931, 0.025033747777342796, -0.0856829360127449, 0.017075208947062492, -0.03127063810825348, 0.04376814514398575, 0.03330233320593834, 0.055111631751060486, -0.01039564423263073, 0.07611500471830368, 0.007412134204059839, 0.004178838338702917, -0.0537346713244915, 0.006799020804464817, 0.013362943194806576, 0.07456425577402115, 0.02221641130745411, -0.0031580289360135794, 0.04629134759306908, -0.024886595085263252, -0.05295184254646301, 0.051589235663414, -0.03934251144528389, 0.016832679510116577, 0.012565381824970245, -0.011045831255614758, -0.06287960708141327, -0.04419960081577301, 0.011339494958519936, 0.020316878333687782, -0.012255015783011913, -0.0009756065555848181, 0.022644545882940292, -0.009387750178575516, -0.022368649020791054, 0.08288627862930298, -0.003503084648400545, -0.04764424264431, -0.022814244031906128, -0.03557388857007027, 0.038139183074235916, 0.031726498156785965, -0.037400998175144196, 0.01811804249882698, -0.03581888601183891, -0.035748641937971115, -0.03711620718240738, 0.01480299886316061, 0.008073817938566208, 0.017739085480570793, 0.05080525949597359, 0.021222343668341637, -0.0375310443341732, -0.026237642392516136, 0.014471725560724735, -0.06987369805574417, 0.01841086708009243, 0.06727167963981628, -0.009900398552417755, -0.02262873575091362, -0.015036394819617271, 0.04802975058555603, 0.049540337175130844, -0.00418245792388916, 0.01039262767881155, -0.06358642876148224, -0.020666813477873802, 0.00468195928260684, -0.006005066446959972, -0.009023768827319145, -0.05428020656108856, -0.015540105290710926, 0.027531007304787636, -0.08315025269985199, -0.0012555225985124707, -0.025876088067889214, 2.981674640523124e-07, 0.04914278909564018, 0.025184238329529762, 0.043467771261930466, -0.045527536422014236, -0.00678029702976346, -0.011539108119904995, 0.01765010692179203, 0.06139495596289635, -0.07547847181558609, 0.007208156865090132, 0.0641222894191742, 0.018810506910085678, 0.023284880444407463, 0.00797235406935215, -0.11533093452453613, 0.027150819078087807, -0.06602199375629425, -0.013941682875156403, -0.03806596249341965, 0.0038579008542001247, 0.07095564156770706, 0.0693935677409172, 0.014080495573580265, -0.02062297612428665, -0.0009080673335120082, -0.03146999329328537, -0.003790265880525112, -0.0010274711530655622, 0.0418282113969326, 0.004924736451357603, 0.03563177213072777, -0.011701366864144802, -0.04705008491873741, -0.005741587374359369, -0.013693761080503464, 0.014895349740982056, 0.026547232642769814, 0.015083970502018929, -0.045951757580041885, 0.012129288166761398, -0.008038460277020931, -0.007722782902419567, -0.01914197951555252, -0.046964067965745926, 0.05940694734454155, -0.03931291401386261, -0.00961814634501934, -0.01642524264752865, -0.0001410709519404918, 0.016461491584777832, 0.02636736072599888, 0.005012135021388531, -0.008710709400475025, -0.010746278800070286, 0.011424983851611614, -0.06464627385139465, -0.021674394607543945, -0.10424220561981201, -0.018700744956731796, -0.018139788880944252, 0.005252715200185776, 0.06371297687292099, -0.003450018586590886, -0.021150190383195877, 0.06081317365169525, 0.01515708677470684, -0.014135953970253468, 2.8565883369761744e-34, -0.01297822967171669, 0.0271836519241333, -0.022401120513677597, 0.046400249004364014, 0.016548477113246918, -0.007115177810192108, -0.02531607076525688, 0.02531866915524006, -0.004309958312660456, -0.015204877592623234, -0.03146802634000778]

['Yuntian Deng', 'Anssi Kanervisto', 'Jeffrey Ling', 'Alexander M. Rush']

1609.04938v2

We present a neural encoder-decoder model to convert images into presentational markup based on a scalable coarse-to-fine attention mechanism. Our method is evaluated in the context of image-to-LaTeX generation, and we introduce a new dataset of real-world rendered mathematical expressions paired with LaTeX markup. We show that unlike neural OCR techniques using CTC-based models, attention-based approaches can tackle this non-standard OCR task. Our approach outperforms classical mathematical OCR systems by a large margin on in-domain rendered data, and, with pretraining, also performs well on out-of-domain handwritten data. To reduce the inference complexity associated with the attention-based approaches, we introduce a new coarse-to-fine attention layer that selects a support region before applying attention.

Image-to-Markup Generation with Coarse-to-Fine Attention

http://arxiv.org/pdf/1609.04938v2

Title ImagetoMarkup Generation CoarsetoFine Attention Summary present neural encoderdecoder model convert image presentational markup based scalable coarsetofine attention mechanism method evaluated context imagetoLaTeX generation introduce new dataset realworld rendered mathematical expression paired LaTeX markup show unlike neural OCR technique using CTCbased model attentionbased approach tackle nonstandard OCR task approach outperforms classical mathematical OCR system large margin indomain rendered data pretraining also performs well outofdomain handwritten data reduce inference complexity associated attentionbased approach introduce new coarsetofine attention layer selects support region applying attention Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.037048403173685074, 0.06474770605564117, 0.023353565484285355, 0.04908118024468422, 0.0032489988952875137, -0.007392432540655136, 0.045315228402614594, 0.01213331799954176, -0.050541844218969345, -0.025739675387740135, -0.02434820681810379, 0.039918601512908936, 0.017113251611590385, 0.07616622745990753, 0.044789139181375504, -0.08738067746162415, -0.028303584083914757, -0.017935311421751976, -0.021970264613628387, 0.016584064811468124, 0.03579102084040642, -0.04105408117175102, 0.027282865718007088, 0.02678757533431053, -0.06189464405179024, -0.04044114053249359, -0.005782558582723141, -0.00966650154441595, 0.017376119270920753, -0.02608742006123066, -0.013498639687895775, 0.047091320157051086, 0.05618675425648689, -0.007533226162195206, 2.4541336642869283e-06, -0.0237654447555542, -0.014895482920110226, 0.011275253258645535, 0.025618355721235275, 0.008236822672188282, 0.04813980311155319, -0.07810592651367188, -0.028426647186279297, -0.03284554183483124, -0.03249920532107353, -0.012332288548350334, 0.07469625025987625, 0.09717988967895508, 0.06518528610467911, 0.04827679693698883, -0.02786317840218544, -0.04639797657728195, 0.007068864535540342, -0.0164638739079237, 0.02561715617775917, -0.01227108109742403, 0.005949485581368208, -0.0036965140607208014, -0.03427264094352722, 0.0037187524139881134, -0.055039383471012115, 0.05342448875308037, 0.03776860609650612, -0.06136162951588631, 0.06068028509616852, 0.05546414107084274, 0.001684430055320263, 0.029518717899918556, -0.04226470738649368, 0.0842188149690628, -0.06471782177686691, 0.01079275831580162, -0.018764851614832878, -0.009133603423833847, -0.004920861218124628, -0.019841527566313744, -0.09325594455003738, 0.02839062549173832, -0.007841330952942371, 0.007899255491793156, -0.03439288213849068, 0.0354919396340847, -0.019491514191031456, -0.005890040658414364, 0.00638969149440527, -0.02540474757552147, -0.01682315766811371, -0.003449557116255164, -0.0734630823135376, 0.005990869365632534, -0.0534047931432724, -0.029595764353871346, 0.09034908562898636, 0.06886795908212662, 0.06191639229655266, -0.0009226629626937211, -0.07723461091518402, -0.11254528164863586, 0.00855767261236906, -0.0985211506485939, 0.08302030712366104, 0.024363044649362564, -0.03975159302353859, 0.02005622908473015, -0.028081312775611877, 0.08179254829883575, -0.0401088111102581, 0.028075052425265312, 0.0021309780422598124, 0.03399665281176567, -0.00031132492586039007, 0.0006736272480338812, -0.08385385572910309, 0.010781882330775261, -0.03344320133328438, -0.032232169061899185, -0.03036070056259632, -0.01154119148850441, -0.028424737975001335, -0.025163130834698677, 0.05109334737062454, 0.032683663070201874, -0.03356410562992096, -0.03099565953016281, 0.0006699090590700507, -0.007005471270531416, -0.006508939899504185, -0.03584563732147217, -0.008807924576103687, -0.014230073429644108, -0.019796129316091537, 0.07392788678407669, 0.02124747261404991, 0.023440856486558914, -0.026311542838811874, 0.08058803528547287, -0.005878760013729334, 0.000778096029534936, 0.006566081661731005, 0.005864955950528383, -0.012781020253896713, 0.02042735554277897, 0.026629047468304634, -0.04318464547395706, 0.01676081493496895, -0.008822438307106495, -0.04002658277750015, -0.0513693131506443, 0.00401997659355402, 0.03904718905687332, 0.005527139641344547, 0.05259392037987709, -0.014449423179030418, -0.03985759988427162, 0.053160637617111206, -0.010826368816196918, 0.010284793563187122, -0.0034248472657054663, 0.07385201752185822, 0.03838890790939331, -0.0012886481126770377, -0.027765287086367607, 0.030978446826338768, 0.016658898442983627, 0.025947608053684235, -0.04655448719859123, -0.06000461056828499, 0.004150951746851206, 0.04905106872320175, 0.012983459047973156, 0.07252556830644608, 0.0385405607521534, -0.027299217879772186, -0.010561894625425339, 0.03335055336356163, 0.041154228150844574, 0.0022901147603988647, 0.024240687489509583, 0.005439160857349634, 0.002470606006681919, 0.003397346707060933, -0.01347993966192007, -0.06046216934919357, 0.11608555912971497, 0.023969339206814766, 0.005656790919601917, 0.014093968085944653, 0.011218944564461708, -0.0030282968655228615, -0.039147671312093735, 0.022858040407299995, 0.007650312501937151, -0.016304893419146538, -0.01740194298326969, 0.03439459577202797, 0.040153391659259796, -0.057003770023584366, 0.024795986711978912, 0.0019388156943023205, 0.00028173471218906343, -0.020712781697511673, -0.024569636210799217, -0.013923538848757744, 0.009554604068398476, 0.025338705629110336, -0.022828124463558197, 0.03768965229392052, -0.018587758764624596, -0.0065063186921179295, 0.06724104285240173, -0.02245905064046383, 0.0368155762553215, -0.016888951882719994, -0.09222172200679779, 0.0016863855998963118, -0.03430799022316933, -0.002422031946480274, 0.0019407252548262477, -0.03627515584230423, 0.0189371258020401, 0.000827631214633584, 0.029290882870554924, -0.04416581243276596, 0.03659478574991226, 0.05949896574020386, -0.06175391003489494, -0.03381984308362007, 0.022547198459506035, 0.015393764711916447, -0.02230449579656124, 0.0005544627783820033, 0.02213713712990284, 0.02506803721189499, -0.03590301796793938, 0.03379986807703972, -0.02491833083331585, -0.04935603216290474, -0.06683704257011414, 0.019920919090509415, -0.07952232658863068, -0.017860395833849907, -0.01496204175055027, -0.0194398146122694, -0.012290006503462791, 0.024964816868305206, -0.07049450278282166, 0.009759290143847466, -0.03215145319700241, 0.011197195388376713, 0.003967995755374432, 0.02879137545824051, -0.03657510504126549, 0.07378778606653214, -0.03623200207948685, -0.015019824728369713, 0.028270989656448364, 0.009293447248637676, -0.004498706664890051, -0.04158230498433113, 0.04372074827551842, -0.009564055129885674, -0.03464479371905327, 0.0026343967765569687, -0.037269216030836105, 0.05223830044269562, -0.0026510399766266346, 0.0017738949973136187, 0.009006359614431858, -0.05257002264261246, -0.011547383852303028, 0.026433855295181274, 0.038252297788858414, -0.004610719624906778, 0.01869925670325756, -0.03598126396536827, -0.04339410737156868, 0.05084043741226196, -0.0395677350461483, -0.03454769775271416, 0.052491094917058945, -0.026154285296797752, 0.038632094860076904, -0.019084932282567024, -0.02635961025953293, 0.003798443591222167, 0.05283276364207268, 0.0771285742521286, -0.0661199688911438, -0.02688477747142315, 0.023908281698822975, -0.012566284276545048, 0.009787114337086678, 0.027760451659560204, -0.027352605015039444, 0.006601275410503149, -0.03331157565116882, 0.023232141509652138, 0.13055051863193512, 0.016308583319187164, 0.040834009647369385, -0.014825035817921162, -0.01629773899912834, -0.03688471019268036, 0.024368176236748695, -0.0022170289885252714, 0.0483454093337059, 0.047305844724178314, -0.015248916111886501, 0.024076923727989197, 0.08085673302412033, -0.03453138470649719, 0.03673679754137993, -0.03263307362794876, 0.021242501214146614, 0.011234167031943798, 0.015584769658744335, -0.034824568778276443, 0.026278384029865265, -0.004272742662578821, 0.01189796905964613, -0.04174529016017914, -0.053823865950107574, 0.023768575862050056, -0.00681461812928319, -0.022760942578315735, -0.0019549077842384577, 0.05039826035499573, -0.02936508320271969, -0.022965257987380028, -0.01154316309839487, 0.024841858074069023, -0.012224076315760612, -0.06010918319225311, 0.01733139343559742, -0.008272560313344002, -0.018180470913648605, -0.023794690147042274, 0.043561894446611404, 0.03174209967255592, 0.021747279912233353, -0.04352099075913429, -0.005954516585916281, -0.00985362846404314, 0.029747599735856056, -0.007031859830021858, 0.014273646287620068, -0.004495924338698387, -0.016976553946733475, -0.05799102410674095, 0.04526834189891815, 0.014526569284498692, 0.04027601704001427, -0.02168489620089531, -0.011153237894177437, -0.007916662842035294, 0.033661138266325, 0.029617436230182648, -0.006836542394012213, -0.015774739906191826, -0.047609295696020126, -0.0056594661436975, 0.033613722771406174, -0.035461172461509705, 0.016988681629300117, -0.03331967815756798, 0.007642683573067188, 0.00833540316671133, 0.010075083002448082, 0.025754665955901146, 0.01723564602434635, -0.003387364326044917, -0.09699118882417679, -0.024063603952527046, 0.03088502399623394, 0.01275467500090599, -0.06380243599414825, -0.012112883850932121, -0.04599742218852043, -0.016806062310934067, 0.008716018870472908, 0.018623806536197662, -0.031244326382875443, -0.01592293009161949, -0.011518621817231178, 0.004803934600204229, 0.03812558203935623, -0.023663457483053207, -0.005959046073257923, -0.03966441750526428, 0.06306704878807068, 0.0018333957996219397, -0.07223371416330338, -0.03398038446903229, -0.004510761704295874, 0.02605237439274788, 0.038271211087703705, -0.03123101405799389, 0.03416834771633148, 0.004724572412669659, -0.012547369115054607, -0.0004715407849289477, 0.02720191888511181, 0.0032430989667773247, -0.03784169256687164, -0.0282193124294281, -0.03884750232100487, 0.04106276109814644, 0.04800539091229439, 0.007640764117240906, -0.0893486961722374, -0.006024549249559641, 0.05297718197107315, 0.024967845529317856, -0.01926012709736824, 0.05543757975101471, 0.007192402612417936, -0.04468095675110817, -0.03195395693182945, 0.03697189688682556, -0.033939022570848465, 0.03307338431477547, -0.01328570581972599, 0.05159258097410202, -0.010445729829370975, 0.019198033958673477, -0.06790696829557419, 0.010764856822788715, -0.02214936725795269, -0.02564438059926033, 0.025420036166906357, -0.007331572473049164, -0.04639343544840813, -0.03995640203356743, 0.027221862226724625, -0.07229519635438919, -0.02170354686677456, 0.015702221542596817, 0.001636347733438015, -0.07218724489212036, -0.0436798520386219, -0.011264107190072536, 0.03236427158117294, 0.08178991824388504, 0.008721387945115566, -0.0794965848326683, 0.039254095405340195, -0.03378836810588837, -0.07260560244321823, 0.025804836302995682, -0.01975621096789837, -0.012531746178865433, -0.049981631338596344, 0.01937348209321499, 0.02546941302716732, -0.01917046494781971, 0.01054056640714407, -0.016386959701776505, -0.05600722134113312, -0.020513426512479782, -0.03213249146938324, 0.08807922899723053, 0.005843454971909523, -0.023475559428334236, -0.03012150526046753, -0.05088223144412041, 0.045881472527980804, 0.013770239427685738, 0.005789395421743393, -0.005334104411303997, 0.005959663074463606, -0.003624045755714178, 0.018382994458079338, -0.010655462741851807, -0.020694948732852936, 0.020024972036480904, 0.028904400765895844, -0.01046024914830923, -0.009220145642757416, -0.01887865550816059, 0.02955886721611023, -0.018383009359240532, 0.0032277328427881002, 0.028910374268889427, 0.022640343755483627, -0.013571884483098984, 0.018888531252741814, -0.012119492515921593, 0.0015753433108329773, -0.0666385143995285, 0.02868104912340641, -0.01941155083477497, 0.024034131318330765, 0.012387624941766262, -0.011186506599187851, 0.00910954363644123, -0.022447753697633743, -0.008120598271489143, 0.07645310461521149, -0.0361761748790741, 0.013429909013211727, -0.017566215246915817, 0.014049341902136803, -0.004891754128038883, -0.023115040734410286, -0.03145095333456993, 0.029414817690849304, 0.0026966051664203405, 0.04779744893312454, 0.01985420659184456, 0.01700211875140667, -0.020369868725538254, 0.012974772602319717, 0.015861444175243378, -0.009964748285710812, -0.06968341767787933, 0.002426715102046728, 0.03828093409538269, -0.0025339850690215826, 0.006013863254338503, 0.02887064963579178, -0.009778832085430622, -0.0038868021219968796, 0.055641960352659225, -0.020051777362823486, -0.025887295603752136, 0.03488783910870552, 0.006441784556955099, 0.026662850752472878, -0.08821707218885422, 0.058161914348602295, -0.03123055025935173, -0.05716795101761818, 0.00586922001093626, 0.0012153030838817358, -0.04788602888584137, 0.011791324242949486, 0.013767112046480179, -0.0035671077203005552, 0.011075705289840698, 0.014855860732495785, 0.02857535146176815, -0.03189797326922417, 0.033646561205387115, 0.002852499019354582, -0.032850462943315506, 0.021613363176584244, 0.05887404829263687, -0.017589733004570007, -0.015418090857565403, -0.03166205435991287, 0.02079697884619236, 0.037064507603645325, -0.018436331301927567, -0.04110177978873253, -0.038701124489307404, -6.0754992058708064e-33, -0.011628170497715473, -0.0457628034055233, -0.006135004572570324, 0.024755027145147324, -0.03617122024297714, 0.014659921638667583, -0.03777742013335228, -0.022254183888435364, 0.0018358337692916393, 0.011880038306117058, 5.107977631269023e-05, -0.0032931382302194834, 0.019095472991466522, 0.05812968313694, -0.0020998872350901365, 0.011503665708005428, 0.021624751389026642, -0.01620754413306713, 0.010202431119978428, 0.026744043454527855, -0.005524336826056242, 0.03516805171966553, 0.08595508337020874, -0.05619562789797783, -0.0352492518723011, 0.030663346871733665, -0.004640194121748209, -0.04131585359573364, 0.014000990428030491, 0.0339854396879673, -0.020021872594952583, 0.03892968222498894, 0.005837900564074516, -0.0456833690404892, -0.02592436783015728, 0.041458532214164734, -0.05595460161566734, -0.010682806372642517, -0.059668052941560745, 0.037491943687200546, -0.05305570363998413, -0.04776470363140106, 0.0607403926551342, -0.028245525434613228, -0.012670302763581276, -0.052049558609724045, 0.06292827427387238, -0.033643003553152084, -0.015341553837060928, -0.030583089217543602, -0.048611827194690704, 0.015381962060928345, -0.012989464215934277, -0.023383306339383125, 0.03942302241921425, 0.01877574436366558, -0.007394547574222088, 0.026136528700590134, -0.08232516795396805, 0.010109854862093925, 0.05500762537121773, 0.032289404422044754, 0.06677582859992981, 0.04262523353099823, 0.048529915511608124, -0.03267989307641983, 0.010897879488766193, 0.02219933085143566, -0.00842208694666624, -0.030871793627738953, 0.03999979421496391, 0.03170584887266159, 0.08947616070508957, -0.014334402978420258, 0.07308951765298843, 0.03891643136739731, -0.030773060396313667, 0.0016773553797975183, -0.06427217274904251, 0.07741031050682068, 0.04465007781982422, 0.029080118983983994, -0.0074628437869250774, 0.0043702637776732445, 0.019486229866743088, -0.01194957084953785, -0.03578583523631096, -0.01021303329616785, 0.01351109053939581, 0.003158904379233718, 0.0007997541106306016, 0.028656823560595512, 0.03657293692231178, -0.020542938262224197, 0.02162136137485504, -0.03435053303837776, 0.045043688267469406, 0.06273934990167618, -0.002818333450704813, -0.023521261289715767, -0.03425012156367302, 0.01359863393008709, -0.0008368134731426835, 0.018324241042137146, 0.021109117195010185, 0.02256244793534279, 0.038270577788352966, 0.009720091708004475, -0.029620526358485222, -0.03421863168478012, -0.009457454085350037, -0.018972022458910942, 0.05385645851492882, 0.05080171674489975, 0.009105067700147629, -0.03332257643342018, -0.019348157569766045, 0.053340502083301544, 0.015313937328755856, -0.032342467457056046, -0.007837457582354546, -0.009340222924947739, 0.00174537708517164, 0.054579537361860275, -0.05444969981908798, 0.01893668994307518, -0.06576569378376007, 0.013261633925139904, 0.030983656644821167, -0.08327793329954147, -0.022656528279185295, 0.07169108092784882, 2.924993793840258e-07, 0.02775426208972931, 0.03034643828868866, 0.008630136959254742, 0.008247341960668564, 0.017071597278118134, -0.006544051691889763, 0.016562744975090027, 0.048153575509786606, 0.0037204476539045572, -0.04335130378603935, 0.01220161747187376, 0.02012152411043644, 0.046878211200237274, -0.01914524845778942, -0.052843235433101654, 0.008703493513166904, -0.043119318783283234, 0.0019694201182574034, -0.016311107203364372, 0.021071314811706543, 0.06227611005306244, 0.06655983626842499, -0.030788933858275414, -0.013048999011516571, 0.0403815396130085, 0.02082967571914196, 0.035080548375844955, 0.03623128682374954, 0.0468367338180542, -0.008676812052726746, -0.025794271379709244, -0.02099425718188286, -0.0530662015080452, 0.010617141611874104, 0.001038221875205636, -0.007728927303105593, 0.04465638846158981, 0.023399583995342255, -0.05254605785012245, 0.02491993084549904, 0.02215403877198696, -0.020141055807471275, 0.010300354100763798, -0.0770799070596695, 0.02651378884911537, -0.054757010191679, -0.044285356998443604, -0.01585078425705433, -0.0042138476856052876, 0.019866319373250008, 0.0050516617484390736, -0.034446317702531815, 0.016930803656578064, -0.0046582818031311035, 0.043843336403369904, -0.041461579501628876, -0.03304198756814003, -0.03676259145140648, -0.030676143243908882, -0.011559788137674332, -0.001206271001137793, 0.04066377878189087, -0.07706760615110397, -0.01638597995042801, 0.048636194318532944, 0.020562613382935524, -0.04380166158080101, 2.7083458719567623e-34, 0.01369821559637785, -0.016219787299633026, 0.008893403224647045, 0.055426351726055145, 0.005534046329557896, -0.013828666880726814, -0.018425822257995605, 0.010504545643925667, 0.019114729017019272, -0.08812258392572403, -0.030102740973234177]

['Sumeet S. Singh']

1802.05415v1

We present a deep recurrent neural network model with soft visual attention that learns to generate LaTeX markup of real-world math formulas given their images. Applying neural sequence generation techniques that have been very successful in the fields of machine translation and image/handwriting/speech captioning, recognition, transcription and synthesis, we construct an image-to-markup model that learns to produce syntactically and semantically correct LaTeX markup code of over 150 words long and achieves a BLEU score of 89%; the best reported so far for the Im2Latex problem. We also visually demonstrate that the model learns to scan the image left-right / up-down much as a human would read it.

Teaching Machines to Code: Neural Markup Generation with Visual Attention

http://arxiv.org/pdf/1802.05415v1

Title Teaching Machines Code Neural Markup Generation Visual Attention Summary present deep recurrent neural network model soft visual attention learns generate LaTeX markup realworld math formula given image Applying neural sequence generation technique successful field machine translation imagehandwritingspeech captioning recognition transcription synthesis construct imagetomarkup model learns produce syntactically semantically correct LaTeX markup code 150 word long achieves BLEU score 89 best reported far Im2Latex problem also visually demonstrate model learns scan image leftright updown much human would read Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.01412122044712305, 0.043919309973716736, -0.006231324747204781, 0.030719632282853127, 0.0054451823234558105, 0.0015950931701809168, 0.04878579080104828, -0.0071022603660821915, -0.03350820392370224, -0.03550293669104576, -0.004475708119571209, -0.005813692230731249, 0.01067198533564806, 0.10894140601158142, 0.061574164777994156, -0.07339513301849365, 0.011313141323626041, 0.0119698541238904, -0.002821974689140916, 0.010130190290510654, 0.012585260905325413, 0.0007596163777634501, 0.01120658591389656, 0.044467754662036896, 0.0035414122976362705, -0.02555481530725956, -0.012996413744986057, -0.013194850645959377, -0.02330104075372219, -0.03903956338763237, 0.010729782283306122, 0.036415569484233856, 0.025786031037569046, 0.062252312898635864, 2.3073689590091817e-06, -0.028599584475159645, -0.004893365781754255, -0.023082811385393143, 0.044366683810949326, 0.015604947693645954, 0.036389533430337906, -0.02450343407690525, 0.0017907543806359172, 0.013370382599532604, -0.0514051578938961, -0.03275314345955849, 0.04678034037351608, 0.05805027857422829, 0.03609327971935272, 0.04095218703150749, -0.004512788727879524, -0.04789922386407852, 0.014015267603099346, -0.025106385350227356, 0.07926711440086365, -0.010259544476866722, -0.001324765500612557, 0.00207312498241663, 0.018252545967698097, -0.007789262104779482, -0.038988009095191956, 0.06395815312862396, 0.017230931669473648, -0.07653114199638367, 0.06848295032978058, 0.04683379828929901, 0.0034564367961138487, -0.029526468366384506, -0.014057270251214504, 0.07045891135931015, -0.03942522779107094, -0.014250230975449085, 0.009463263675570488, 0.006924240384250879, -0.030206313356757164, -0.029094701632857323, -0.08177628368139267, 0.03642944246530533, -0.022522924467921257, -0.016634266823530197, 0.011338835582137108, -0.011810721829533577, -0.023690566420555115, 0.02305539697408676, 0.023806022480130196, -0.03461192175745964, -0.0017223465256392956, -0.029816072434186935, -0.027299262583255768, 0.005169087089598179, 0.011561823077499866, -0.06438256800174713, 0.051041461527347565, 0.0831541046500206, 0.043478477746248245, -0.0024072809610515833, -0.02199682593345642, -0.13152822852134705, 0.02911287732422352, -0.08160500973463058, 0.054385844618082047, -0.007065898738801479, -0.004973830189555883, 0.04370154067873955, -0.028257543221116066, 0.05116941034793854, -0.007062550634145737, 0.021132817491889, -0.0018488190835341811, 0.08111051470041275, -0.0305192768573761, -0.01464905682951212, -0.019859569147229195, 0.04031231254339218, -0.005483048502355814, -0.02170473523437977, -0.04396993666887283, -0.00998038798570633, -0.0037363460287451744, 0.03393233194947243, 0.01692117378115654, 0.04497184976935387, -0.03784401714801788, 0.027950717136263847, -0.019127674400806427, 0.01640710048377514, -0.004743398632854223, -0.022428032010793686, -0.017429666593670845, -0.002741964301094413, 0.00909180473536253, 0.03704550489783287, 0.009816177189350128, 0.019936731085181236, -0.0007732430822215974, 0.08079682290554047, -0.017813991755247116, 0.0033812010660767555, -0.03448725491762161, -0.04624384641647339, 0.020540904253721237, -0.01719571277499199, 0.026418635621666908, -0.07520986348390579, 0.014505121856927872, -0.017855070531368256, -0.03174448013305664, -0.038731709122657776, 0.009178186766803265, 0.024890564382076263, 0.01564912497997284, 0.06918967515230179, -0.011800971813499928, -0.013168859295547009, 0.08680498600006104, -0.003967295866459608, 0.018528901040554047, -0.0010118233039975166, 0.05735011771321297, 0.03701173514127731, 0.010815784335136414, -0.03613799065351486, 0.05615660920739174, 0.013803726062178612, -0.009606905281543732, -0.036676909774541855, 0.016128787770867348, -0.02676061913371086, 0.05340079963207245, 0.05035659670829773, 0.0285264290869236, 0.022613320499658585, 0.0023691989481449127, 0.054489053785800934, 0.04533526301383972, 0.050898514688014984, 0.02519042044878006, 0.04351430386304855, 0.036743924021720886, 0.015284048393368721, 0.01879846677184105, -0.02107364684343338, -0.05041690543293953, 0.06497875601053238, -0.006152756046503782, 0.031103413552045822, -0.028572408482432365, 0.028541095554828644, -0.020435653626918793, -0.0462786890566349, 0.011128604412078857, 0.005394716747105122, -0.011573001742362976, -0.03777509927749634, 0.05530044436454773, 0.02970745973289013, -0.056028299033641815, -0.03451300784945488, -0.004912994801998138, -0.022633181884884834, 0.018715757876634598, -0.00809247512370348, 0.008786742575466633, 0.04624788463115692, 0.03339703008532524, -0.04248858615756035, 0.006791956722736359, -0.056692592799663544, -0.003228165442124009, 0.047054775059223175, 0.025858476758003235, 0.0011103241704404354, -0.02367216721177101, -0.05116817727684975, -0.018647368997335434, -0.021837608888745308, -0.009844189509749413, 0.004047789610922337, -0.042886700481176376, 0.03094477578997612, 0.02168811485171318, 0.04864666983485222, -0.09070643037557602, 0.06687269359827042, -0.02837887592613697, -0.05380360782146454, -0.025441335514187813, 0.03144098073244095, 0.004112147260457277, 0.023005390539765358, 0.014894370920956135, 0.017021941021084785, 0.040488351136446, -0.03357092663645744, -0.020749252289533615, -0.021845441311597824, -0.035200051963329315, -0.03630923852324486, 0.038693588227033615, -0.10966204851865768, -0.02682597003877163, 0.020680982619524002, -0.022426797077059746, -0.025645161047577858, 0.04319785535335541, -0.060998015105724335, 0.011308709159493446, -0.017582468688488007, 0.015832729637622833, -0.004216591361910105, -0.0045010061003267765, -0.02719111554324627, 0.0515778586268425, -0.015036996454000473, 0.03795784339308739, 0.01607024110853672, -0.0371251180768013, -0.01026687491685152, -0.020027415826916695, 0.0007213364006020129, 0.00022435876599047333, -0.026661017909646034, 0.03282826766371727, -0.012265121564269066, 0.08108648657798767, -0.047246482223272324, -0.022481437772512436, 0.002701748860999942, -0.024603337049484253, -0.006193992216140032, -0.008794683031737804, 0.021481188014149666, -0.013539903797209263, 0.020832767710089684, -0.0307796411216259, -0.05948038026690483, 0.006460755132138729, -0.017886843532323837, -0.029104696586728096, 0.07399624586105347, -0.0011567930923774838, 0.01961282640695572, -0.04057541489601135, -0.028766723349690437, -0.04048895090818405, 0.05357631668448448, 0.09883961081504822, -0.036838799715042114, -0.01902513951063156, 0.018010996282100677, -0.006022667977958918, 0.016270169988274574, 0.01808028109371662, -0.045683354139328, 0.012884227558970451, -0.02998949959874153, -0.015542447566986084, 0.1259216070175171, 0.02044018730521202, 0.029329514130949974, 0.019132347777485847, 0.010154690593481064, -0.0176630150526762, 0.004955067299306393, -0.0039047328755259514, -0.017114542424678802, 0.05157662183046341, -0.027079476043581963, -0.00632223067805171, 0.04148581251502037, -0.009096714667975903, 0.02064296044409275, -0.02980806678533554, 0.0294941496104002, -0.02133137360215187, -0.00527110556140542, -0.0020393033046275377, 0.007574921473860741, -0.005699640139937401, 0.02780649997293949, -0.0038059696089476347, -0.04274874925613403, 0.05076169967651367, -0.019312402233481407, -0.02067694440484047, -0.036465756595134735, 0.00712795602157712, -0.02937697432935238, 0.011928060092031956, 0.013208124786615372, 0.018454045057296753, -0.0017571334028616548, -0.05715550109744072, -0.030320322141051292, 0.034624531865119934, 0.013393410481512547, -0.03831758722662926, 0.02992798015475273, -0.01433976087719202, -0.014984631910920143, -0.044497907161712646, -0.02458059787750244, -0.028065888211131096, 0.015920303761959076, 0.01054514478892088, -0.011197029612958431, 0.000624176231212914, 0.00674842856824398, -0.043375853449106216, 0.004010078031569719, 0.064581960439682, 0.05338166654109955, -0.02021414414048195, -0.013509761542081833, -0.016936199739575386, 0.013416028581559658, 0.046347130089998245, -0.016581818461418152, -0.047856830060482025, -0.03047008626163006, -0.01332761812955141, 0.01152284350246191, -0.032193563878536224, 0.021818166598677635, -0.046779368072748184, 0.02339964173734188, 0.007174057886004448, -0.03505963459610939, -0.006293237209320068, 0.022705180570483208, -0.0016949349083006382, -0.08198409527540207, 0.0011280032340437174, 0.07669075578451157, 0.013338624499738216, -0.055034395307302475, -0.018353067338466644, -0.026985174044966698, -0.04193653166294098, 0.04108082503080368, 0.04243604466319084, -0.05049150064587593, 0.0027306152042001486, -0.022829607129096985, 0.03499710559844971, 0.018347248435020447, -0.044220879673957825, -0.005595151335000992, -0.059261199086904526, 0.02164832502603531, -0.0035509367007762194, -0.07700837403535843, -0.04712122306227684, -0.017800895497202873, -0.046935103833675385, 0.0035758346784859896, -0.03821723535656929, 0.03998589888215065, -0.0320013165473938, 0.008964608423411846, 0.014271296560764313, 0.003574361791834235, -0.008744875900447369, -0.023833345621824265, -0.026626363396644592, 0.0011817360064014792, 0.09404581040143967, 0.04008821025490761, -0.04022521153092384, -0.0729774683713913, -0.0430326946079731, 0.03235112130641937, 0.009595764800906181, -0.03733499348163605, 0.06763766705989838, -0.05860614404082298, -0.002444811398163438, -0.005083939991891384, 0.0891348272562027, -0.02471110038459301, 0.039177313446998596, 0.023426473140716553, 0.047476403415203094, 0.012440159916877747, -0.007917044684290886, -0.05363510921597481, 0.0359780415892601, 0.008271154016256332, -0.012682081200182438, 0.06079108268022537, -0.04123809188604355, -0.03424406424164772, -0.056474845856428146, 0.034762755036354065, -0.061873555183410645, -0.03635984659194946, -0.028633050620555878, -0.0291636623442173, -0.04562316834926605, -0.08761338889598846, -0.0691843256354332, 0.06110396981239319, 0.0523560531437397, 0.04755057021975517, -0.03869811072945595, 0.026468152180314064, -0.019015902653336525, -0.08893228322267532, -0.004474514629691839, 0.025125715881586075, -0.005187004338949919, -0.06832417100667953, -0.015833159908652306, 0.03083893097937107, -0.0223985705524683, -0.010868641547858715, -0.005014822818338871, -0.030318379402160645, -0.05443207547068596, 0.0010093721793964505, 0.07345378398895264, 0.022863619029521942, -0.01172587275505066, -0.015755370259284973, -0.04945136606693268, 0.006609381176531315, 0.008514353074133396, -0.00931803323328495, 0.003575631882995367, 0.021682539954781532, -0.015503233298659325, -0.00555725721642375, 3.4303822758374736e-05, -0.047042448073625565, 0.0021735981572419405, 0.005090910941362381, -0.02655954472720623, -0.0020058737136423588, -0.016404254361987114, -0.0025717015378177166, 0.015460742637515068, 0.010704854503273964, -0.0024611959233880043, -0.005099653732031584, -0.01882803998887539, 0.023373721167445183, 0.01429816335439682, -0.018193218857049942, -0.043558258563280106, -0.01386294700205326, 0.02742852084338665, 0.04093939810991287, 0.020666781812906265, 0.0026360226329416037, 0.018759386613965034, 0.012422625906765461, 0.002482839860022068, 0.07457336038351059, -0.03021172620356083, 0.05713643506169319, -0.005725862458348274, 1.222673563461285e-05, -0.03668117895722389, -0.0062647853046655655, -0.02237301878631115, 0.04385056719183922, -0.0065537141636013985, 0.05523836612701416, 0.02406386472284794, 0.05781957879662514, -0.00644174637272954, 0.022326795384287834, -0.012109972536563873, -0.03883596137166023, -0.05390559509396553, 0.03794911131262779, 0.03459995612502098, -0.02479897253215313, 0.011526943184435368, 0.01492499653249979, 0.000868644448928535, -0.008969400078058243, 0.06362775713205338, -0.026452872902154922, -0.029499927535653114, 0.022903643548488617, 0.016548510640859604, 0.02362176589667797, -0.06778323650360107, 0.08533712476491928, -0.010214537382125854, -0.043819088488817215, 0.031490400433540344, 0.0022621050011366606, -0.027644623070955276, 0.036344196647405624, 0.054677318781614304, -0.0022273866925388575, 0.009151182137429714, -0.011396289803087711, -0.009692777879536152, -0.03653007745742798, 0.050801824778318405, 0.03286629915237427, -0.004974413197487593, 0.023019060492515564, 0.04088129475712776, 0.03145774081349373, 0.010208498686552048, -0.023196758702397346, -0.02797299437224865, 0.05017634853720665, 0.017905056476593018, -0.038531236350536346, -0.04440705105662346, -6.268684355588757e-33, -0.014323067851364613, -0.06300605088472366, -0.0036913910880684853, 0.06992705911397934, -0.023746255785226822, 0.011262592859566212, -0.04763719066977501, -0.01554056815803051, -0.006619517225772142, -0.002568133408203721, -0.034050263464450836, -0.01247915904968977, 0.009052793495357037, 0.05000404268503189, 0.05764202028512955, 0.00460014957934618, 0.03876645117998123, -0.013649971224367619, 0.012273420579731464, 0.020229095593094826, -0.02828914485871792, 0.04479540139436722, 0.09049658477306366, -0.04393225535750389, -0.0011803475208580494, -0.004484148230403662, 0.02761676535010338, -0.04872742295265198, 0.018344132229685783, 0.03259454295039177, -0.01015550084412098, 0.014168589375913143, 0.006718921475112438, -0.04245952516794205, -0.03658292442560196, 0.011664965189993382, -0.09041540324687958, -0.026400316506624222, -0.03387453407049179, 0.036180246621370316, -0.05687199532985687, -0.01441726740449667, 0.08655223250389099, -0.04770534113049507, 0.01030539907515049, -0.03447161614894867, 0.10641390830278397, -0.01027720421552658, -0.03726506978273392, -0.050433602184057236, -0.08663671463727951, 0.0014590010978281498, -0.017991501837968826, 0.0242979284375906, 0.02035958506166935, 0.0002520351263228804, 0.004470243118703365, 0.03490239009261131, -0.10247959941625595, 0.012647117488086224, 0.048105914145708084, 0.06470087915658951, 0.08878474682569504, 0.02289203368127346, 0.02144552581012249, 0.0005314953159540892, -0.005160562228411436, 0.04309208691120148, -0.019068317487835884, -0.025909844785928726, 0.05523686110973358, 0.02214214950799942, 0.0885685607790947, 0.006965999025851488, 0.03699049726128578, 0.0017615185352042317, -0.03697097301483154, 0.03835155442357063, -0.011235644109547138, 0.057922378182411194, -0.004110054112970829, 0.010074534453451633, -0.010711601004004478, -0.00177915976382792, 0.006740888115018606, -0.013042462058365345, -0.024453002959489822, -0.027213552966713905, -0.014736071228981018, -0.013172056525945663, 0.005093814805150032, 0.0015813845675438643, -0.018503999337553978, -0.025355488061904907, 0.02096680738031864, -0.023599794134497643, 0.024451296776533127, 0.05200731381773949, -0.028796691447496414, -0.031129201874136925, -0.05539155751466751, -0.00899700727313757, -0.02627241052687168, 0.033091869205236435, 0.03061930648982525, 0.012768516317009926, 0.04224574938416481, 0.0014679855667054653, -0.037553202360868454, -0.02383018471300602, -0.0026315238792449236, -0.013000703416764736, 0.04772697016596794, 0.002460065996274352, -0.005165466107428074, -0.03219223767518997, -0.007500020321458578, 0.02547767572104931, 0.0203304011374712, -0.03586232662200928, -0.03217955678701401, -0.03876419737935066, 0.02639750763773918, 0.05093091353774071, -0.09947831928730011, -0.013583244755864143, -0.07082843035459518, 0.04252009466290474, 0.07040297240018845, -0.08268280327320099, -0.02066751755774021, 0.022582514211535454, 2.904771179146337e-07, 0.04485873132944107, 0.039305660873651505, 0.03525390103459358, -0.0005272905109450221, -0.004522201605141163, 0.0240614116191864, -0.004565134644508362, 0.05358900874853134, -0.013750405050814152, -0.013801426626741886, 0.02435516193509102, -0.006145215127617121, 0.021756863221526146, -0.027210824191570282, -0.07895724475383759, -0.034736115485429764, -0.06490715593099594, 0.013337429612874985, -0.0414566770195961, 0.008620777167379856, 0.054767392575740814, 0.07607265561819077, 0.005238698795437813, -0.0005355151952244341, 0.027627289295196533, -0.062269240617752075, 0.015067660249769688, 0.039106111973524094, 0.04595364257693291, -0.006307661067694426, 0.011972177773714066, 0.017688848078250885, -0.04625937342643738, -0.03704383596777916, -0.03559553250670433, -0.040841929614543915, 0.04664727300405502, 0.03608909249305725, -0.043122369796037674, 0.04504529386758804, 0.025604380294680595, -0.019994163885712624, -0.0064107137732207775, -0.06614438444375992, 0.034463685005903244, -0.03190114349126816, -0.010168451815843582, 0.013450010679662228, -0.02847178839147091, 0.007405500393360853, 0.025666475296020508, -0.031443677842617035, 0.022274203598499298, 0.016062503680586815, 0.009544504806399345, -0.05577034130692482, -0.016171859577298164, -0.03853406012058258, -0.00844564102590084, 0.00398414209485054, 0.008452074602246284, 0.014281192794442177, -0.04326801374554634, -0.019124818965792656, 0.01641564443707466, -0.009721281006932259, -0.02329646237194538, 2.878303758397693e-34, 0.020896419882774353, -0.029357874765992165, 0.01696122996509075, 0.019958237186074257, 0.0005813474417664111, -0.018265679478645325, -0.03061697632074356, 0.02307184971868992, 0.017083600163459778, -0.03852325677871704, -0.04011265188455582]

['Mohammad Javad Shafiee', 'Elnaz Barshan', 'Alexander Wong']

1704.02081v1

A promising paradigm for achieving highly efficient deep neural networks is the idea of evolutionary deep intelligence, which mimics biological evolution processes to progressively synthesize more efficient networks. A crucial design factor in evolutionary deep intelligence is the genetic encoding scheme used to simulate heredity and determine the architectures of offspring networks. In this study, we take a deeper look at the notion of synaptic cluster-driven evolution of deep neural networks which guides the evolution process towards the formation of a highly sparse set of synaptic clusters in offspring networks. Utilizing a synaptic cluster-driven genetic encoding, the probabilistic encoding of synaptic traits considers not only individual synaptic properties but also inter-synaptic relationships within a deep neural network. This process results in highly sparse offspring networks which are particularly tailored for parallel computational devices such as GPUs and deep neural network accelerator chips. Comprehensive experimental results using four well-known deep neural network architectures (LeNet-5, AlexNet, ResNet-56, and DetectNet) on two different tasks (object categorization and object detection) demonstrate the efficiency of the proposed method. Cluster-driven genetic encoding scheme synthesizes networks that can achieve state-of-the-art performance with significantly smaller number of synapses than that of the original ancestor network. ($\sim$125-fold decrease in synapses for MNIST). Furthermore, the improved cluster efficiency in the generated offspring networks ($\sim$9.71-fold decrease in clusters for MNIST and a $\sim$8.16-fold decrease in clusters for KITTI) is particularly useful for accelerated performance on parallel computing hardware architectures such as those in GPUs and deep neural network accelerator chips.

Evolution in Groups: A deeper look at synaptic cluster driven evolution of deep neural networks

http://arxiv.org/pdf/1704.02081v1

Title Evolution Groups deeper look synaptic cluster driven evolution deep neural network Summary promising paradigm achieving highly efficient deep neural network idea evolutionary deep intelligence mimic biological evolution process progressively synthesize efficient network crucial design factor evolutionary deep intelligence genetic encoding scheme used simulate heredity determine architecture offspring network study take deeper look notion synaptic clusterdriven evolution deep neural network guide evolution process towards formation highly sparse set synaptic cluster offspring network Utilizing synaptic clusterdriven genetic encoding probabilistic encoding synaptic trait considers individual synaptic property also intersynaptic relationship within deep neural network process result highly sparse offspring network particularly tailored parallel computational device GPUs deep neural network accelerator chip Comprehensive experimental result using four wellknown deep neural network architecture LeNet5 AlexNet ResNet56 DetectNet two different task object categorization object detection demonstrate efficiency proposed method Clusterdriven genetic encoding scheme synthesizes network achieve stateoftheart performance significantly smaller number synapsis original ancestor network sim125fold decrease synapsis MNIST Furthermore improved cluster efficiency generated offspring network sim971fold decrease cluster MNIST sim816fold decrease cluster KITTI particularly useful accelerated performance parallel computing hardware architecture GPUs deep neural network accelerator chip Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02147897146642208, 0.025692127645015717, -0.054428599774837494, 0.05017568916082382, 0.0025389394722878933, 0.005992465186864138, 0.030231373384594917, 0.007615628186613321, -0.023921435698866844, 0.016216987743973732, -0.02581300400197506, 0.017828235402703285, -0.03593451902270317, 0.02337166853249073, 0.03265490382909775, -0.021622290834784508, 0.06354871392250061, 0.03605968505144119, -0.026280459016561508, -0.030391797423362732, 0.015511538833379745, -0.030980108305811882, 0.0476289838552475, 0.03167550638318062, -0.009842876344919205, 0.02131708525121212, -0.02287900447845459, -0.004461259115487337, -0.002768561476841569, 0.007991922087967396, 0.014979589730501175, -0.03140563517808914, 0.027180347591638565, 0.0778542160987854, 2.0255365598131903e-06, -0.025842294096946716, 0.012891128659248352, -0.029656847938895226, -0.006739082280546427, -0.016055893152952194, 0.031118342652916908, 0.031494177877902985, -0.027354318648576736, -0.02352679707109928, 0.0016613638726994395, -0.04754234105348587, 0.06922713667154312, -0.0005856553907506168, -0.020414354279637337, 0.008856941014528275, -0.007021341472864151, -0.07002821564674377, 0.0851234644651413, -0.010995900258421898, 0.003507214831188321, 0.014228437095880508, -0.0027959118597209454, 0.01225098967552185, 0.024156544357538223, -0.01754053682088852, 0.010076070204377174, -0.0031261343974620104, 0.03504444286227226, 0.018021540716290474, 0.025803636759519577, -0.00349247083067894, 0.0036307615227997303, -0.02735503390431404, -0.0065404088236391544, -0.00483553484082222, -0.09568390250205994, 0.011850479990243912, -0.007582405582070351, -0.004278989974409342, -0.004538301844149828, -0.052788589149713516, 0.002467059763148427, 0.01952243037521839, -0.02609078399837017, 0.026292167603969574, 0.022844647988677025, 0.03735820949077606, 0.020944122225046158, -0.007499828934669495, 0.038604382425546646, 0.017441000789403915, 0.010727519169449806, 0.028466200456023216, -0.03453642502427101, -0.01938546821475029, -0.017305245622992516, 0.006339905317872763, 0.040261927992105484, -0.005696476902812719, 0.026301102712750435, -0.0076703573577106, -0.04594255983829498, -0.08285576850175858, 0.009021025151014328, -0.024211034178733826, 0.05931854993104935, 0.026873407885432243, -0.004098816774785519, 0.005425724200904369, -0.06886982917785645, 0.030245386064052582, -0.07786466181278229, -0.017736077308654785, -0.048311084508895874, -0.029622668400406837, -0.03587397560477257, 0.01810763031244278, 0.011141004972159863, 0.07171136885881424, 0.012003489769995213, -0.02817472815513611, -0.012557530775666237, 0.03761184588074684, -0.01897408999502659, -0.0571989081799984, -0.061379265040159225, 0.05374693498015404, 0.013047518208622932, 0.03284285217523575, -0.025880418717861176, -0.0016607553698122501, -0.025520578026771545, 0.01648465171456337, -0.013834631070494652, 0.018336221575737, 0.05995529890060425, 0.016769884154200554, 0.026139168068766594, 0.052389033138751984, 0.011720218695700169, 0.05044937878847122, -0.010902018286287785, -0.0050842962227761745, -0.09871228784322739, 0.010953005403280258, 0.050392620265483856, 0.024029795080423355, 0.003891183063387871, -0.02566605433821678, 0.03865905851125717, -0.04372002184391022, -0.05525536462664604, -0.02457832545042038, -0.024146854877471924, -0.018673788756132126, -0.017177609726786613, 0.02757634036242962, -0.09188701957464218, -0.000424200581619516, 0.09570447355508804, -0.006737925577908754, -0.0026553969364613295, 0.03293914347887039, 0.01071782037615776, 0.0228426530957222, -0.006157745607197285, -0.004273571539670229, -0.007982929237186909, -0.019739042967557907, -0.00903004314750433, -0.03689120337367058, 0.011366218328475952, -0.0502864271402359, -0.006854407489299774, 0.04547493904829025, 0.02228863537311554, 0.04332447052001953, -0.02333744429051876, -0.030108485370874405, 0.011394741013646126, 0.08156543970108032, 0.02349972352385521, 0.09069599956274033, 0.0175107941031456, -0.03676250949501991, -0.02530679665505886, -0.028147095814347267, 0.014482234604656696, 0.07244691997766495, -0.033070873469114304, -0.06709037721157074, -0.01843899115920067, 0.006084071937948465, -0.025611503049731255, -0.019939912483096123, 0.029383407905697823, -0.015351548790931702, 0.01057576946914196, -0.04433397948741913, 0.015297560952603817, 0.02044430375099182, -0.01854516938328743, -0.02588152512907982, 0.020519331097602844, 0.036277785897254944, -0.058223623782396317, -0.09859596192836761, 0.04080536961555481, 7.168217507569352e-06, -0.000792322272900492, -0.0039042853750288486, -0.0700780376791954, 0.021381618455052376, -0.04628828167915344, -0.016236886382102966, -0.04214294254779816, -0.02643623948097229, -0.029348058626055717, -0.047334108501672745, 0.0003876186965499073, 0.025609970092773438, -0.005576569586992264, 0.026863081380724907, -0.0031796207185834646, -0.011447601020336151, 0.04088544845581055, 0.09811978042125702, 0.005835524760186672, 0.01691386289894581, 0.020003778859972954, 0.05431044474244118, 0.056170832365751266, -0.003411456709727645, 0.040531616657972336, 0.0006603340734727681, 0.03217873349785805, -0.04602605476975441, 0.04525860399007797, -0.03470269590616226, -0.0037681623362004757, -0.024041930213570595, -0.032402776181697845, 0.011600684374570847, 0.021761175245046616, 0.029492447152733803, 0.043224889785051346, 0.005904151126742363, -0.002750018145889044, -0.042366873472929, 0.05497587472200394, -0.05434035882353783, 0.060832489281892776, -0.01774299517273903, 0.02153976447880268, -0.04882260411977768, 0.047760576009750366, -0.006451712921261787, 0.06413737684488297, 0.03484222665429115, -0.029355116188526154, 0.0011452041799202561, 0.02993232011795044, 0.03742826357483864, -0.04456179589033127, 0.00925889890640974, -0.034091707319021225, -0.031228739768266678, 0.017616519704461098, 0.010298768058419228, 0.020738650113344193, 0.008140875026583672, 0.021658524870872498, -0.014095118269324303, 0.04973996803164482, 0.015725914388895035, 0.006665656343102455, 0.00414088973775506, -0.019848110154271126, 0.05185311287641525, 0.00813258159905672, -0.009226119145751, 0.169352725148201, -0.00187170528806746, -0.03785324469208717, 0.033332016319036484, 0.00928098801523447, -0.01828637905418873, -0.024628860875964165, -0.036934610456228256, -0.03920745104551315, 0.03088483028113842, 0.05799973011016846, -0.015441058203577995, -0.03760519623756409, 0.01450711116194725, -0.005905850324779749, 0.033250004053115845, 0.014024948701262474, -0.02225758694112301, -0.013577524572610855, -0.030104657635092735, 0.000923723098821938, 0.08161550760269165, 0.01660746894776821, -0.0194070003926754, 0.01804201677441597, 0.07672616839408875, 0.023678861558437347, 0.010177976451814175, 0.011504712514579296, 0.06487833708524704, 0.010709889233112335, 0.04828471690416336, -0.0340593196451664, 0.030166491866111755, 0.01973533444106579, -0.01721200719475746, -0.023663338273763657, 0.012793418020009995, 0.02170487679541111, -0.019208800047636032, -0.0012842187425121665, -0.08152090013027191, -0.004140379838645458, -0.0013471844140440226, -0.04234457015991211, -0.027406984940171242, 0.017240509390830994, 0.06649120897054672, 0.00024193078570533544, -0.015171184204518795, -0.050703633576631546, 0.010903512127697468, 0.04303152486681938, 0.045483361929655075, 0.03559804707765579, -0.024368373677134514, 0.008275752887129784, -0.01677202247083187, 0.03949085995554924, -0.05514178425073624, -0.0028726658783853054, 0.03203719109296799, -0.03743971139192581, -0.016552643850445747, -0.014865192584693432, -0.02219640091061592, -0.03132939711213112, 0.05556029453873634, 0.014644136652350426, 0.03949948772788048, 0.03292403742671013, -0.023118283599615097, 0.00040094228461384773, 0.028194347396492958, -0.003384504932910204, 0.048166170716285706, -0.019766736775636673, -0.005570270586758852, -0.017931072041392326, 0.012011783197522163, 0.0059186844155192375, -0.024161670356988907, -0.007777582388371229, 0.04319436475634575, 0.031147195026278496, 0.03493989259004593, -0.0005363000091165304, -0.02485104836523533, -0.12411806732416153, 0.020044157281517982, -0.006054460071027279, 0.016928311437368393, -0.04084642603993416, -0.009704357013106346, -0.03358064964413643, -0.07213515788316727, 0.04530280828475952, -0.019452586770057678, -0.011825642548501492, -0.07282461225986481, -0.02125655859708786, -0.006916115991771221, -0.032313551753759384, 0.013731681741774082, 0.0316179059445858, -0.021270016208291054, -0.01597493700683117, -0.013187449425458908, -0.029979068785905838, -0.021130912005901337, -0.03574521839618683, 0.04261086508631706, -0.02213670127093792, 0.0025969306007027626, -0.014566892758011818, -0.06508150696754456, 0.008942934684455395, -0.012638470157980919, 0.005239177495241165, -0.001479839556850493, -0.0020958699751645327, 0.06070002168416977, 0.058058589696884155, -0.05056695640087128, 0.0016469309339299798, 0.003713323036208749, 0.029986554756760597, 0.013250068761408329, -0.08116485923528671, 0.009850166738033295, 0.07901598513126373, -0.001321367104537785, -0.007535515818744898, -0.03594058007001877, 0.026942022144794464, -0.014269066043198109, 0.013653870671987534, -0.03582393378019333, 0.006798756308853626, 0.02716684155166149, -0.022995201870799065, -0.015090754255652428, 0.048866789788007736, -0.017705311998724937, 0.04964363947510719, -0.0008147088810801506, 0.047456301748752594, 0.0005867377039976418, -0.020728865638375282, -0.06303779035806656, -0.060826633125543594, -0.02202139049768448, -0.014781535603106022, 0.0012086991919204593, -0.0332736074924469, -0.0329609178006649, -0.007486725226044655, -0.016294771805405617, -0.05737655609846115, -0.004059224389493465, 0.0010285699972882867, 0.021352993324398994, -0.054098524153232574, -0.04701925814151764, 0.034186456352472305, -0.005804131738841534, 0.02618412859737873, 0.044063691049814224, -0.057180505245923996, 0.01575447805225849, -0.04118857905268669, -0.053623005747795105, -0.03962692245841026, 0.031023159623146057, -0.05053093656897545, -0.05696767568588257, -0.014874481596052647, 0.0617588609457016, -0.03904746100306511, 0.005146950948983431, -0.02110281214118004, -0.044737640768289566, -0.01777392439544201, 0.0044103763066232204, 0.050015270709991455, -0.007005125284194946, -0.008233750239014626, -0.020234204828739166, -0.06575008481740952, 0.03326056897640228, 0.02499721571803093, 0.005133712198585272, -0.0014279464958235621, -0.014393041841685772, -0.040922317653894424, -0.03814699873328209, 0.01284871157258749, 0.00573296332731843, 0.0673174262046814, 0.0009835581295192242, -0.043374404311180115, -0.05435866117477417, -0.013128896243870258, -0.019321303814649582, 0.006200268864631653, 0.0016311784274876118, 0.0210126843303442, 0.01082887127995491, -0.024502316489815712, -0.005520469509065151, 0.032387834042310715, 0.02731357328593731, -0.020996414124965668, -0.04070546105504036, -0.006100907456129789, 0.0035874799359589815, 0.018037786707282066, -0.022535737603902817, 0.11398229002952576, -0.07469817250967026, -0.004459732212126255, 0.05884495750069618, 0.007008218672126532, 0.08484937250614166, -0.035373810678720474, 0.02513803355395794, 0.006591686047613621, -0.014204311184585094, -0.0024941626470535994, 0.03640769049525261, -0.056394848972558975, -0.005797856487333775, 0.01847296766936779, -0.029030047357082367, -0.06337401270866394, 0.03756774961948395, 0.020614275708794594, -0.03211381658911705, -0.03264928609132767, 0.015538124367594719, 0.05569211393594742, -0.006566456984728575, -0.03591553121805191, -0.020520880818367004, -0.014167780987918377, -0.029734287410974503, -0.02809329330921173, -0.03987017646431923, 0.003126537660136819, 0.007736495696008205, 0.02194627746939659, -0.0031576110050082207, -0.006805171724408865, 0.007127897813916206, -0.02993892878293991, 0.0005183865432627499, -0.003986379597336054, -0.008713480085134506, -0.0033553082030266523, 0.04092973843216896, 0.022210581228137016, 0.0044031087309122086, 0.009128515608608723, -0.014549097046256065, 0.06738395243883133, 0.010470893234014511, 0.014617078937590122, 0.05790342390537262, 0.05746854841709137, 0.012888294644653797, 0.030308213084936142, 0.02379949577152729, 0.0015570026589557528, -0.05743040144443512, 0.03783462569117546, -0.03535850718617439, -0.012367126531898975, 0.017784984782338142, -0.0027735538315027952, -5.8214994885710804e-33, 0.025301558896899223, -0.0032957810908555984, -0.00422623660415411, -0.012405809946358204, -0.01706923171877861, 0.008406566455960274, -0.015610752627253532, -0.014126154594123363, -0.043883826583623886, -0.05141682177782059, -0.001087365671992302, 0.02393287792801857, -0.014514053240418434, 0.0098748579621315, 0.046245284378528595, 0.006637236103415489, -0.012569339945912361, -0.03294515982270241, 0.09069027006626129, 0.020027337595820427, 0.03514644876122475, 0.009236760437488556, 0.011194616556167603, 0.012881831265985966, -0.08904752135276794, 0.043138857930898666, 0.04939884692430496, -0.02307756245136261, -0.028040483593940735, 0.004450404550880194, -0.03672701120376587, 0.02690911665558815, 0.0057778856717050076, -0.037449248135089874, 0.0034228507429361343, -0.024415625259280205, -0.04616227746009827, -0.018962355330586433, -0.07405132800340652, -0.011339835822582245, -0.05835246294736862, -0.03422236442565918, 0.12352000921964645, 0.04002786800265312, -0.02879706211388111, 0.045471854507923126, 0.05106302723288536, -0.05065496638417244, -0.0060099149122834206, 0.011335641145706177, -0.034629710018634796, 0.005696456413716078, 0.020510245114564896, 0.02675686590373516, 0.026212053373456, -0.06187669560313225, -0.04044727608561516, 0.01896243542432785, -0.05262548848986626, 0.038144394755363464, -0.015879884362220764, 0.023810312151908875, -0.007897351868450642, 0.07890963554382324, 0.07818005979061127, -0.022618340328335762, 0.07823261618614197, -0.004897615872323513, -0.008030887693166733, 0.04100621119141579, 0.030607545748353004, 0.0556991882622242, 0.0647013932466507, 0.012196720577776432, 0.052038662135601044, -0.060572344809770584, -0.0640055388212204, 0.04816432669758797, 0.036959681659936905, -0.020732322707772255, 0.0015754200285300612, 0.05362585559487343, -0.019318517297506332, -0.012228317558765411, 0.07723531126976013, -0.01032516360282898, -0.023493275046348572, -0.026446253061294556, -0.018762195482850075, -0.025017742067575455, -0.03802615776658058, 0.04244391620159149, -0.0027233499567955732, -0.06572894752025604, 0.08239156752824783, -0.02056899666786194, -0.006274402607232332, 0.02425522729754448, 0.05311005935072899, 0.01899765245616436, -0.023587679490447044, -0.057025350630283356, -0.025174571201205254, 0.012408887967467308, 0.018254730850458145, 0.016000648960471153, -0.00958323199301958, 0.02294558845460415, 0.013057507574558258, 0.007079956587404013, 0.014737865887582302, -0.05348045006394386, 0.033742040395736694, 0.011826650239527225, -0.024983281269669533, -0.02743717096745968, 0.032706890255212784, 0.008982352912425995, 0.0342494435608387, 0.005198671482503414, -0.040588218718767166, -0.0017243496840819716, 0.0008931070333346725, 0.005807570181787014, -0.05514286458492279, 0.013975725509226322, -0.06480294466018677, 0.02698308601975441, -0.03599724918603897, -0.059719666838645935, -0.04214515537023544, 0.04040989279747009, 2.8228885184944374e-07, -0.02354496531188488, 0.017270604148507118, 0.014960662461817265, -0.07861518859863281, 0.03452851250767708, 0.001004464807920158, 0.041709013283252716, -0.009743068367242813, -0.019931109622120857, -0.010541142895817757, 0.04521700367331505, 0.00562227563932538, -0.026328496634960175, -0.0004740195581689477, -0.0324057973921299, 0.038293883204460144, -0.0061141448095440865, 0.08666957914829254, -0.011850785464048386, 0.03898115083575249, 0.016839098185300827, 0.07183816283941269, 0.0258872602134943, -0.03481437638401985, 0.07496783137321472, 0.006931261159479618, -0.03645525500178337, 0.04014131799340248, 0.06570720672607422, 0.009626813232898712, -0.06145872548222542, 0.0021147197112441063, -0.058546263724565506, 0.025127766653895378, 0.03802764415740967, 0.013973336666822433, -0.03969109058380127, -0.0358186773955822, -0.028665589168667793, 0.010594828054308891, 0.05407232791185379, 0.016168884932994843, 0.012329502031207085, -0.014350161887705326, 0.05632947385311127, 0.001088953111320734, -0.03320254012942314, 0.0038313164841383696, 0.0039006383158266544, -0.003375445958226919, -0.058455128222703934, 0.002374444156885147, 0.0005932444473728538, -0.024826182052493095, -0.04036839306354523, -0.05633653327822685, -0.036360591650009155, -0.03822881728410721, 0.05515322834253311, 0.03394918888807297, -0.04764675348997116, -0.022420044988393784, -0.05066303908824921, -0.005610177293419838, 0.07811490446329117, 0.03297236189246178, -0.0032090528402477503, 2.3871723463083043e-34, -0.05622956529259682, -0.008593285456299782, 0.012972219847142696, 0.002585223177447915, -0.011008387431502342, 0.010427595116198063, -0.07832837849855423, -0.043449629098176956, 0.0019130920991301537, 0.00048326855176128447, -0.07454323023557663]

['Mete Ozay', 'Ilke Öztekin', 'Uygar Öztekin', 'Fatos T. Yarman Vural']

1205.2382v3

A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of information or cognitive states represented in the brain, based on distributed patterns of neural activity. In the current investigation, we propose a new approach for representation of neural data for pattern analysis, namely a Mesh Learning Model. In this approach, at each time instant, a star mesh is formed around each voxel, such that the voxel corresponding to the center node is surrounded by its p-nearest neighbors. The arc weights of each mesh are estimated from the voxel intensity values by least squares method. The estimated arc weights of all the meshes, called Mesh Arc Descriptors (MADs), are then used to train a classifier, such as Neural Networks, k-Nearest Neighbor, Na\"ive Bayes and Support Vector Machines. The proposed Mesh Model was tested on neuroimaging data acquired via functional magnetic resonance imaging (fMRI) during a recognition memory experiment using categorized word lists, employing a previously established experimental paradigm (\"Oztekin & Badre, 2011). Results suggest that the proposed Mesh Learning approach can provide an effective algorithm for pattern analysis of brain activity during cognitive processing.

Mesh Learning for Classifying Cognitive Processes

http://arxiv.org/pdf/1205.2382v3

Title Mesh Learning Classifying Cognitive Processes Summary relatively recent advance cognitive neuroscience multivoxel pattern analysis MVPA enables researcher decode brain state andor type information represented brain cognitive operation MVPA method utilize machine learning algorithm distinguish among type information cognitive state represented brain based distributed pattern neural activity current investigation propose new approach representation neural data pattern analysis namely Mesh Learning Model approach time instant star mesh formed around voxel voxel corresponding center node surrounded pnearest neighbor arc weight mesh estimated voxel intensity value least square method estimated arc weight mesh called Mesh Arc Descriptors MADs used train classifier Neural Networks kNearest Neighbor Naive Bayes Support Vector Machines proposed Mesh Model tested neuroimaging data acquired via functional magnetic resonance imaging fMRI recognition memory experiment using categorized word list employing previously established experimental paradigm Oztekin Badre 2011 Results suggest proposed Mesh Learning approach provide effective algorithm pattern analysis brain activity cognitive processing Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.031485315412282944, 0.019229529425501823, -0.054886896163225174, 0.0016190819442272186, 0.0027205513324588537, 0.006775710731744766, 0.036257434636354446, 0.023961171507835388, 0.04668120667338371, 0.028998807072639465, -0.01394672505557537, 0.017376072704792023, 0.080603688955307, 0.06615357846021652, 0.043615736067295074, -0.02602386847138405, -0.005032430402934551, 0.03030744194984436, 0.03451914340257645, -0.010159572586417198, -0.017039412632584572, -0.01707204058766365, -0.034615546464920044, 0.032288771122694016, -0.01576264016330242, -0.03795994445681572, -0.003097164211794734, -0.050321321934461594, 0.017016449943184853, -0.057551778852939606, 0.007827313616871834, 0.01102251373231411, 0.011782663874328136, 0.004094381351023912, 2.1645867036568234e-06, -0.01822569966316223, -0.02014610357582569, -0.011265979148447514, 0.09104730188846588, -0.00936517771333456, -0.014529407024383545, 0.0019286766182631254, 0.001911905943416059, -0.02110896445810795, -0.004296403843909502, 0.04910839721560478, 0.05533413961529732, 0.0671890452504158, 0.0116097591817379, -0.010796931572258472, -0.02591327577829361, 0.0009950681123882532, 0.07880203425884247, -0.014014569111168385, -0.033753424882888794, 0.07288730889558792, 0.020312804728746414, 0.03607099875807762, -0.0024954574182629585, -0.0873458981513977, -0.007841728627681732, 0.02934900112450123, -0.02532275766134262, 0.05294301360845566, 0.04141336679458618, 0.05369476601481438, 0.04258273169398308, 0.003086925484240055, -0.004937573801726103, 0.037431128323078156, -0.040763624012470245, -0.022883929312229156, 0.03459637984633446, -0.009250955656170845, -0.011530626565217972, 0.06152959167957306, -0.04988805949687958, 0.02104625292122364, -0.016785651445388794, -0.010308384895324707, 0.01522157248109579, 0.009858652949333191, 0.022697051987051964, -0.04908784478902817, 0.005270705092698336, 0.004151514265686274, -0.011649088002741337, -0.007593293208628893, 0.006706863176077604, -0.0503508485853672, -0.08639252185821533, -0.00687598017975688, 0.024337163195014, -0.00154537009075284, -0.016872689127922058, -0.005758856423199177, 0.023921912536025047, -0.07627797871828079, 0.05609862133860588, -0.04873337596654892, 0.06519652903079987, 0.012804357334971428, 0.03325018286705017, -0.021127095445990562, -0.057052843272686005, 0.021217932924628258, -0.04583197087049484, 0.05501866340637207, -0.027605824172496796, 0.01676979288458824, -0.05279158800840378, 0.01419519167393446, 0.014181842096149921, 0.07973647117614746, 0.033398523926734924, -0.04640515148639679, -0.03171765059232712, 0.023620476946234703, 0.006257498636841774, -0.043831080198287964, 0.004991359077394009, 0.02746378257870674, 0.06383495777845383, 0.03141620010137558, -0.02171248383820057, -0.02433408983051777, -0.024926409125328064, 0.04778895154595375, -0.0455312542617321, 0.03541754558682442, 0.019427236169576645, -0.012082578614354134, -0.0343005396425724, 0.008751648478209972, -0.025633493438363075, 0.013103228062391281, -0.01463745255023241, 0.010767878964543343, -0.07849008589982986, -0.025693414732813835, 0.023205628618597984, 0.002372953575104475, 0.07222466170787811, -0.032009661197662354, -0.015620526857674122, -0.008924685418605804, -0.002926462097093463, 0.0129020344465971, 0.001381410751491785, -0.04071402922272682, -0.011717061512172222, -0.008311476558446884, -0.03537026792764664, -0.0038967495784163475, 0.111547090113163, -0.013771933503448963, 0.03934689983725548, -0.018118225038051605, 0.04183077812194824, 0.0028521253261715174, -0.029329493641853333, -0.018072592094540596, -0.04682976007461548, 0.002315270947292447, -0.015090220607817173, -0.06186505779623985, -0.08795259892940521, -0.06153035908937454, 0.0175457913428545, 0.03659113124012947, -0.00032831443240866065, 0.00892804004251957, -0.016569901257753372, -0.005741829983890057, 0.0030732634477317333, 0.1025797501206398, -0.009768599644303322, 0.00805413257330656, -0.02591252513229847, 0.007101444993168116, 0.030864493921399117, 0.004758872091770172, 0.05840105935931206, 0.05691307410597801, -0.029793962836265564, -0.025715870782732964, -0.03078456036746502, -0.017314676195383072, -0.017781535163521767, -0.03671083599328995, 0.03141537308692932, -0.05458870902657509, 0.02018505148589611, -0.013496954925358295, 0.026426488533616066, -0.03286902606487274, 0.028500983491539955, -0.020555725321173668, 0.02522658184170723, 0.07066638767719269, -0.08930569887161255, -0.05458175763487816, 0.02267356403172016, -0.0705396756529808, -0.005532463546842337, -0.03465946391224861, -0.030753327533602715, -0.014343006536364555, 0.014800607226788998, -0.03441528230905533, -0.028921574354171753, 3.241159356548451e-05, -0.007484134286642075, -0.01962006650865078, 0.02169225923717022, 0.03751559555530548, 0.013615000993013382, 0.00911540538072586, -0.04358428716659546, -0.021595530211925507, -0.03436526283621788, 0.07036685943603516, -0.05641172453761101, 0.02559608221054077, -0.062493953853845596, 0.03137361258268356, 0.01966824382543564, -0.0116150276735425, 0.03945380821824074, -0.025737931951880455, 0.039751872420310974, 0.0075929113663733006, 0.03955730050802231, -0.01581084541976452, -0.007516662124544382, -0.013173242099583149, -0.020732061937451363, 0.022362450137734413, 0.002708022017031908, 0.038598500192165375, 0.019950829446315765, 0.03561348840594292, 0.02356518805027008, -0.04961713030934334, 0.03298250585794449, -0.03389272093772888, 0.0053532784804701805, 0.0017502481350675225, 0.01651708409190178, -0.02879074215888977, 0.021217482164502144, -0.026027144864201546, 0.04131610319018364, -0.011835324577987194, 0.04064405709505081, -0.026032114401459694, 0.01174120418727398, 0.05295287445187569, -0.04170546308159828, 0.006430544890463352, 0.024715255945920944, -0.05876346305012703, -0.0016254449728876352, -0.033653855323791504, 0.014034392312169075, -0.013625025749206543, -0.03475525975227356, -0.03325584530830383, -0.02978457883000374, 0.04551006853580475, -0.025987252593040466, -0.003027579514309764, -0.04647773131728172, -0.0008534439257346094, -0.015544802881777287, 0.007112177088856697, 0.09836184978485107, 0.045650601387023926, -0.014459660276770592, 0.02603165991604328, -0.009206852875649929, -0.025454865768551826, -0.0138099929317832, -0.029131723567843437, -0.05505434051156044, 0.061762485653162, 0.05750591680407524, -0.11242067068815231, -0.02631145529448986, 0.009757664985954762, -0.029700186103582382, 0.047175388783216476, 0.010764404200017452, 0.005290715489536524, 0.012053513899445534, -0.014153246767818928, 0.04922923073172569, 0.11144664883613586, 0.012612441554665565, -0.005631021223962307, 0.02816755697131157, 0.038207631558179855, -0.004623629152774811, -0.0030065167229622602, -0.0165718924254179, 0.05583891645073891, 0.014461207203567028, -0.01582571119070053, 0.060102466493844986, 0.012472543865442276, 0.09468822926282883, 0.022382384166121483, -0.016278253868222237, 0.03850323334336281, 0.029062334448099136, -0.0032706079073250294, -0.0343574583530426, -0.00667217094451189, -0.015109897591173649, 0.004742450546473265, -0.012506872415542603, 0.005822306498885155, 0.027878401800990105, 0.018209481611847878, 0.017902839928865433, -0.030547697097063065, -0.03735671937465668, 0.012499005533754826, -0.03890825808048248, 0.020315470173954964, 0.02200407348573208, 0.012201027013361454, -0.023213109001517296, -0.007676620967686176, 0.035742972046136856, -0.05194461718201637, -0.010128195397555828, -0.05166802927851677, -0.052492886781692505, 0.0030578002333641052, 0.017627732828259468, 0.007864825427532196, -0.05392197147011757, 0.036626577377319336, 0.0004195170185994357, 0.017477326095104218, -0.026394451037049294, -0.010570826940238476, 6.48634959361516e-05, 0.0014088148018345237, 0.03380191698670387, -0.0008986179600469768, -0.06077165901660919, -0.01069195382297039, -0.01008683256804943, 0.05598360300064087, 0.01285562850534916, 0.04845259711146355, -0.03895515203475952, -0.008020542562007904, -0.023807045072317123, 0.01739400252699852, -0.05347766354680061, 0.030479274690151215, -0.04968640208244324, 0.045145902782678604, -0.015976306051015854, 0.013934692367911339, -0.029211288318037987, 0.0008904128917492926, -0.0007473736186511815, -0.030419817194342613, 0.039910294115543365, 0.04145747050642967, 0.03404921665787697, -0.08357670158147812, -0.009528832510113716, -0.048792872577905655, -0.008783306926488876, 0.006827997975051403, 0.0032105816062539816, 0.08323562890291214, 0.02454250119626522, -0.06671756505966187, -0.015966355800628662, -0.018528252840042114, -0.027572927996516228, 0.04216378554701805, -0.006419231649488211, 0.006005194038152695, -0.00011679307499434799, -0.05934133753180504, -0.012857826426625252, -0.021733270958065987, 0.007452929858118296, 0.013955168426036835, -0.04272737354040146, -0.05158967152237892, 0.021030256524682045, -0.024629447609186172, 0.059206873178482056, -0.0015900987200438976, -0.0020975300576537848, 0.06307758390903473, -0.022124985232949257, 0.05827164649963379, -0.021366022527217865, 0.022450299933552742, -0.0605023130774498, -0.12519319355487823, -0.02813449688255787, 0.023447468876838684, 0.03402530774474144, -0.051296498626470566, 0.0018096375279128551, 0.06188362091779709, 0.011147151701152325, -0.017547596246004105, 0.0419095903635025, -0.01188701018691063, -0.01790919527411461, 0.007578253746032715, 0.09757070988416672, -0.02779761329293251, 0.044275928288698196, -0.02437802217900753, 0.026096653193235397, 0.014325841329991817, -0.034424666315317154, -0.0008788975537754595, -0.0015546864597126842, -0.025846775621175766, 0.008722473867237568, 0.039452191442251205, 0.0020421806257218122, -0.03228665143251419, 0.005529098212718964, 0.04670201241970062, -0.03305130824446678, -0.047586582601070404, 0.05745482072234154, -0.014199694618582726, 0.0388462096452713, 0.03291044384241104, 0.027439774945378304, 0.0362141989171505, -0.03760785609483719, -0.06508558243513107, -0.009120920673012733, 0.045639242976903915, -0.007800194434821606, -0.041048090904951096, -0.01482174638658762, -0.012478666380047798, -0.039871882647275925, -0.01971343159675598, -0.02823115698993206, -0.023472771048545837, -0.008939665742218494, 0.012625515460968018, 0.007228734437376261, -0.000627626315690577, 0.0005783822853118181, -0.0339445099234581, -0.015984809026122093, -0.003030642168596387, -0.062154628336429596, -0.018100306391716003, 0.01097066793590784, 0.004243044648319483, 0.014662285335361958, -0.03797221556305885, -0.017545519396662712, 0.049800459295511246, 0.031695906072854996, -0.01877029426395893, -0.03415706008672714, -0.06427264958620071, -0.00671146297827363, 0.0005439578671939671, 0.05044485256075859, 0.061913423240184784, 0.03980555385351181, 0.0011399890063330531, -0.045017071068286896, -0.01661190390586853, 0.018100058659911156, 0.04666579142212868, 0.011904260143637657, -0.020798929035663605, 0.03267005831003189, 0.020269185304641724, -0.013581525534391403, -0.017783191055059433, 0.04216008260846138, -0.01554115954786539, 0.037341684103012085, -0.006584692280739546, -0.0097845159471035, 0.029359715059399605, -0.06464361399412155, 0.040857527405023575, -0.022746233269572258, -0.028455279767513275, 0.01185624673962593, 0.032037392258644104, 0.00660607498139143, 0.06468136608600616, 0.015239114873111248, -0.01974150910973549, -0.07394056022167206, 0.02653157152235508, 0.008494840934872627, -0.04333114996552467, -0.013180858455598354, -0.016182566061615944, 0.016184700652956963, 0.029677821323275566, -0.00868445448577404, 0.01385851763188839, 0.019369911402463913, -0.03757993131875992, 0.050291359424591064, -0.06858830899000168, 0.026696063578128815, 0.052637387067079544, -0.009769732132554054, 0.008233381435275078, -0.053005218505859375, 0.02566072903573513, 0.02028288133442402, -0.057320479303598404, -0.003650176338851452, -0.04448508843779564, -0.04821746423840523, 0.04507532715797424, 0.03446754068136215, 0.04149740934371948, -0.04501140117645264, 0.02001883089542389, -0.02034296654164791, 0.01466101873666048, 0.03688304126262665, -0.012224896810948849, 0.042190056294202805, -0.01777130737900734, 0.0025794520042836666, 0.033401165157556534, -0.007224019151180983, 0.010942913591861725, -0.008178109303116798, -0.019095728173851967, -0.030047714710235596, -0.04070077836513519, -0.05061818286776543, -5.9021721965000755e-33, 0.006491910666227341, -0.015886396169662476, 0.024683615192770958, -0.0033241589553654194, -0.036822110414505005, -0.02062344178557396, -0.03528651222586632, 0.004815298598259687, -0.0051923939026892185, -0.046246666461229324, -0.001531691406853497, -0.01970437541604042, -0.0035714164841920137, -0.017887545749545097, 0.05913270637392998, 0.04515723139047623, -0.023991161957383156, -0.02064145915210247, 0.03631492331624031, -0.0068024867214262486, 0.04689023643732071, 0.007027989719063044, 0.054082054644823074, -0.08323599398136139, -0.067172572016716, 0.038030389696359634, 0.031198009848594666, -0.018499216064810753, -0.09369352459907532, -0.004371278919279575, -0.045983362942934036, -0.010021131485700607, 0.024844907224178314, 0.028593726456165314, 0.013709629885852337, -0.00016370868252124637, -0.006377073470503092, -0.03319542482495308, -0.0038472602609544992, -0.020566577091813087, -0.054269276559352875, 0.019080260768532753, 0.042336538434028625, -0.0011938471579924226, 0.02860954776406288, 0.028200892731547356, 0.08331780135631561, -0.06117838993668556, -0.01628095470368862, 0.04275721311569214, -0.0027180598117411137, -0.005010117311030626, -0.0004883695510216057, 0.029115259647369385, 0.051482584327459335, -0.0027178970631211996, -0.0679360181093216, 0.060371365398168564, -0.07015001028776169, 0.021811744198203087, 0.0017275778809562325, 0.019043391570448875, -0.01309110689908266, 0.020953837782144547, 0.0707833468914032, 0.04059448093175888, 0.07208303362131119, -0.015770399942994118, 0.006655949633568525, 0.08623431622982025, 0.030313590541481972, 0.058377865701913834, 0.028184959664940834, -0.018070565536618233, 0.038871441036462784, -0.05405314266681671, -0.06545764207839966, 0.029391491785645485, -0.0509597510099411, 0.023003017529845238, -0.0220490675419569, -0.03917659446597099, -0.027928350493311882, 0.012962153181433678, 0.03844472020864487, -0.03428677096962929, -0.02635403536260128, 0.026571709662675858, -0.012088922783732414, -0.061571989208459854, 0.0037734059151262045, 0.0008863011025823653, -0.028004683554172516, 0.007587796542793512, 0.061191707849502563, -0.038203563541173935, 0.00037336614332161844, 0.0370204783976078, 0.06240122392773628, -0.0039001156110316515, -0.09371300041675568, -0.01141255535185337, -0.03041987121105194, -0.011347649618983269, 0.06583696603775024, -0.009747357107698917, 0.005952127743512392, 0.00906175747513771, 0.04482872411608696, -0.02329687401652336, 0.041080132126808167, -0.056153371930122375, 0.010407057590782642, 0.032816387712955475, -0.02272387221455574, -0.043834391981363297, -0.013324877247214317, -0.029539376497268677, -0.004817652516067028, -0.031807560473680496, -0.03250570967793465, -0.01334863156080246, -0.02607581950724125, 0.05410971865057945, 0.0011549334740266204, -0.005077969282865524, -0.05073587968945503, 0.026187848299741745, 0.07664952427148819, -0.038922302424907684, -0.0019109540153294802, 0.02443740703165531, 2.865737371848809e-07, -0.019856344908475876, 0.03260611370205879, -0.044556986540555954, -0.010715911164879799, 0.02679772488772869, 0.0008635124540887773, -0.03948662430047989, 0.03336894512176514, 0.0376666821539402, -0.03506500646471977, 0.0014542058343067765, -0.004091278184205294, 0.0062292953953146935, 0.009272194467484951, -0.042138710618019104, -0.08793504536151886, -0.0186349805444479, 0.055387746542692184, -0.014778157696127892, -0.003800108330324292, 0.035941217094659805, -0.027689078822731972, 0.029845204204320908, -0.048098012804985046, 0.02265811152756214, 0.05029168352484703, 0.014587705954909325, 0.051411762833595276, 0.02445375733077526, -0.014435507357120514, -0.026251373812556267, -0.05937648564577103, -0.00910640973597765, 0.04802875220775604, 0.02230076678097248, 0.0319548062980175, -0.008199025876820087, -0.021197978407144547, 0.004148019943386316, 0.041020236909389496, 0.05030323937535286, 0.03223058208823204, 0.029236719012260437, 0.02885877899825573, 0.012603485956788063, -0.05931983143091202, -0.06606346368789673, 0.060556571930646896, 0.03516146540641785, 0.038945142179727554, 0.0794307142496109, -0.016332251951098442, -0.06322836130857468, -0.03150169178843498, -0.02801726944744587, -0.022576041519641876, 0.0692429468035698, -0.007332460954785347, 0.0054847681894898415, 0.056209489703178406, -0.05714372172951698, 0.013315732590854168, 0.015114400535821915, -0.0546858049929142, 0.04176394268870354, -0.030985180288553238, -0.0033207018859684467, 2.698704292803875e-34, -0.06495275348424911, 0.005177704151719809, 0.015302525833249092, 0.009426096454262733, -0.03788871690630913, -0.015462870709598064, -0.010908729396760464, 0.010644686408340931, -0.015549774281680584, -0.029332397505640984, -0.023074524477124214]

['A. H. Karimi', 'M. J. Shafiee', 'A. Ghodsi', 'A. Wong']

1707.00081v1

In this work, we perform an exploratory study on synthesizing deep neural networks using biological synaptic strength distributions, and the potential influence of different distributions on modelling performance particularly for the scenario associated with small data sets. Surprisingly, a CNN with convolutional layer synaptic strengths drawn from biologically-inspired distributions such as log-normal or correlated center-surround distributions performed relatively well suggesting a possibility for designing deep neural network architectures that do not require many data samples to learn, and can sidestep current training procedures while maintaining or boosting modelling performance.

Synthesizing Deep Neural Network Architectures using Biological Synaptic Strength Distributions

http://arxiv.org/pdf/1707.00081v1

Title Synthesizing Deep Neural Network Architectures using Biological Synaptic Strength Distributions Summary work perform exploratory study synthesizing deep neural network using biological synaptic strength distribution potential influence different distribution modelling performance particularly scenario associated small data set Surprisingly CNN convolutional layer synaptic strength drawn biologicallyinspired distribution lognormal correlated centersurround distribution performed relatively well suggesting possibility designing deep neural network architecture require many data sample learn sidestep current training procedure maintaining boosting modelling performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.010573148727416992, -0.008800351992249489, -0.02899429388344288, 0.0047276862896978855, -0.000527168158441782, -0.030559904873371124, 0.014191307127475739, -0.027332350611686707, -0.02529105916619301, 0.03455287218093872, -0.05245533585548401, -0.017583083361387253, 0.025366928428411484, 0.03453656658530235, 0.030218835920095444, -0.014279011636972427, -0.0025927869137376547, 0.03601573407649994, -0.04111184552311897, -0.06047210469841957, 0.021320560947060585, -0.041892752051353455, 0.007795075885951519, 0.03693452104926109, -0.03687824308872223, 0.01238639559596777, 0.015700194984674454, 0.02870655059814453, 0.03713812306523323, -0.026110557839274406, 0.015892356634140015, -0.031518906354904175, 0.020530246198177338, -0.006676246877759695, 2.166505055356538e-06, 0.0015044859610497952, 0.05158325284719467, 0.007001642603427172, -0.007902550511062145, -0.004512349609285593, 0.014077076688408852, -0.018214227631688118, -0.046595774590969086, -0.019244687631726265, 0.0064669460989534855, -0.024804063141345978, 0.056053511798381805, 0.0404793880879879, -0.01250522956252098, 0.05165214091539383, -0.003537923563271761, -0.0672474354505539, 0.09647398442029953, -0.004036299418658018, -0.02310667559504509, -0.007662859745323658, -0.010734345763921738, 0.03722130507230759, 0.04232761263847351, -0.021619975566864014, -0.024141261354088783, 0.033536676317453384, 0.09638527780771255, 0.0053522465750575066, 0.05245243385434151, 0.020146964117884636, -0.010600417852401733, -0.014458815567195415, -0.0005963052390143275, 0.04173111915588379, -0.06302731484174728, 0.020546335726976395, -0.03029017522931099, -0.016714733093976974, 0.0029099024832248688, -0.018643703311681747, -0.05690360441803932, 0.03699612244963646, -0.016792047768831253, 0.036550480872392654, -0.039281003177165985, 0.039932508021593094, 0.07383669167757034, -0.0017746281810104847, 0.011495078913867474, 0.0075895702466368675, -0.004032536409795284, 0.013870663940906525, -0.033085137605667114, -0.04952119290828705, -0.03540750592947006, 0.031244153156876564, 0.005311671644449234, 0.007174055557698011, 0.03960977494716644, -0.01861865259706974, 0.0019827857613563538, -0.08288469910621643, 0.018107526004314423, -0.03038647584617138, 0.030437516048550606, -0.007261374965310097, -0.04872863367199898, -0.05195625498890877, -0.052501097321510315, 0.043583109974861145, -0.05588417500257492, 0.09318938851356506, -0.018852505832910538, -0.004752028733491898, -0.04440724849700928, 0.01692495308816433, 0.0354161374270916, 0.043933603912591934, 0.03881550952792168, -0.03163696825504303, -0.08251667767763138, 0.0157646331936121, -0.00017426905105821788, -0.07900690287351608, -0.020689181983470917, 0.07821742445230484, -0.003251141868531704, 0.026539862155914307, 0.005308551713824272, -0.023583248257637024, -0.02360311895608902, 0.03376984968781471, 0.02852127142250538, -0.012087643146514893, 0.030605826526880264, -0.0012285485863685608, -0.03363760560750961, 0.007032918278127909, 0.012620797380805016, 0.04486610367894173, -0.002728719962760806, -0.007026933133602142, -0.06699148565530777, 0.029578743502497673, -0.018561718985438347, -0.010021300055086613, 0.0078784991055727, -0.05049307271838188, 0.02589065581560135, -0.019077040255069733, -0.050433289259672165, 0.011272242292761803, -0.01882939413189888, -0.01688731089234352, -0.01945030689239502, 0.013533009216189384, -0.014002669602632523, 0.003805479733273387, 0.10969790816307068, -0.0047271037474274635, -0.024107232689857483, 0.016346752643585205, 0.056691672652959824, 0.026917271316051483, -0.0032702009193599224, 0.00986265204846859, 0.003808068810030818, -0.023974016308784485, -0.01477114949375391, -0.060565195977687836, -0.03614702448248863, -0.06169365718960762, -0.05838329717516899, 0.01722576655447483, 0.021863281726837158, 0.013507436960935593, -0.021030627191066742, -0.01576739177107811, 0.007465737406164408, 0.07452444732189178, 0.059882890433073044, 0.033766742795705795, 0.0015154862776398659, -0.04857783019542694, 0.02989567629992962, -0.036922670900821686, -0.01198445726186037, 0.061685316264629364, 0.018916938453912735, -0.028140876442193985, -0.058720991015434265, 0.03957627713680267, -0.046580057591199875, -0.037788160145282745, 0.027151010930538177, -0.029568491503596306, -0.0028808775823563337, -0.04127882793545723, 0.04167173430323601, -0.02210882678627968, 0.00948947761207819, -0.023735877126455307, 0.012406516820192337, 0.01491889264434576, 0.02738688699901104, -0.0673302486538887, -0.049687471240758896, -0.022413400933146477, -0.002749498700723052, -0.022473040968179703, 0.02223498374223709, 0.02941972389817238, -0.03972508758306503, -0.007874853909015656, 0.005490568000823259, 0.006979071069508791, 0.015198023058474064, -0.01677548885345459, -0.01335449144244194, -0.0344853512942791, -0.011771656572818756, 0.02567111700773239, -0.02110852114856243, 0.03335750848054886, 0.04264061897993088, -0.011756906285881996, -0.02903771959245205, -0.007556823082268238, 0.009015819989144802, 0.012630130164325237, 0.04304524511098862, -0.014045031741261482, 0.01821216754615307, -8.019706729101017e-05, -0.016808493062853813, -0.014376817271113396, 0.006036114878952503, -0.06281660497188568, -0.0031511997804045677, -0.023214086890220642, -0.016502927988767624, 0.009928649291396141, 0.00846621859818697, 0.04404822364449501, 0.07109296321868896, 0.050735026597976685, -0.00022615653870161623, -0.05259984731674194, 0.07042323052883148, 0.03410172834992409, 0.04047875851392746, 0.013227622956037521, 0.035447441041469574, -0.0022777188569307327, 0.06018679589033127, -0.020496392622590065, 0.011727358214557171, 0.04131126031279564, -0.01545021217316389, -0.019022146239876747, 0.05287627503275871, 0.047965314239263535, -0.03186846151947975, 0.014498363249003887, -0.04128623381257057, -0.04785594716668129, 0.027804667130112648, 0.01674363575875759, -0.007734197657555342, 0.030050916597247124, 0.0047814021818339825, -0.005357032176107168, 0.04607570543885231, -0.020510172471404076, 0.004134838003665209, -0.01371053233742714, -0.013681337237358093, 0.010568685829639435, 0.02291553094983101, -0.030099114403128624, 0.09814208000898361, -0.010439256206154823, -0.044186294078826904, 0.05356942489743233, 0.011539752595126629, 0.023245351389050484, -0.02756764367222786, -0.0645628497004509, -0.023981932550668716, 0.04889548569917679, 0.05621206760406494, -0.05022075027227402, 0.01365332305431366, 0.03709040954709053, -0.0011660769814625382, 0.04276658594608307, -0.008982428349554539, -0.07559218257665634, 0.02174954302608967, 0.013194967992603779, 0.034803539514541626, 0.10881204903125763, 0.027102695778012276, -0.03844381123781204, 0.015345933847129345, 0.06603019684553146, 0.008185962215065956, 0.021639510989189148, -0.01178076770156622, 0.025499913841485977, -0.005348969716578722, -0.007974916137754917, -0.05352436751127243, 0.014208911918103695, 0.0444234199821949, 0.0011325633386150002, -0.027679558843374252, -0.008465112186968327, 0.031836122274398804, -0.005159306339919567, 0.02319904789328575, 0.0058111888356506824, -0.008609906770288944, -0.014321533963084221, -0.01409077551215887, -0.017777204513549805, -0.008347278460860252, 0.030248921364545822, 0.055817753076553345, -0.014718213118612766, -0.054646510630846024, 1.0741106052591931e-05, -0.002607885980978608, 0.03487260267138481, 0.03512540087103844, -0.01940302923321724, -0.008856169879436493, -0.02598360739648342, -0.018391570076346397, -0.047333549708127975, 0.01154271885752678, 0.005235389806330204, 0.017041394487023354, -0.048003677278757095, -0.02407904528081417, -0.028491556644439697, -0.04420473426580429, 0.039106033742427826, -0.009870450012385845, 0.06362788379192352, 0.03326229751110077, -0.05456451699137688, 0.026866573840379715, -0.012813991867005825, 0.03838206082582474, 0.030429130420088768, -0.06021092087030411, -0.030205054208636284, -0.01228469517081976, 0.011449751444160938, -0.0039728484116494656, 0.0047872052527964115, 0.022815167903900146, 0.03008543699979782, 0.010888791643083096, -0.0193625520914793, -0.02904380112886429, 0.05925504118204117, -0.08907803148031235, 0.017593933269381523, -0.04371170699596405, 0.04190792888402939, -0.011806229129433632, 0.01445282343775034, 0.04542052000761032, -0.02399400994181633, 0.03717639669775963, -0.0072401403449475765, -0.022696470841765404, -0.07752092182636261, -0.014145172201097012, -0.03883029520511627, -0.04314164072275162, -0.006729867309331894, 0.0364447757601738, -0.015846386551856995, -0.023802179843187332, -0.05591610446572304, -0.014121434651315212, -0.026263419538736343, 0.0102300476282835, 0.04368752986192703, -0.007937673479318619, -0.0036314327735453844, -0.0008378343773074448, -0.02506283111870289, -0.02361106500029564, -0.022657062858343124, -0.02104194462299347, -0.02490270510315895, 0.020952807739377022, 0.018578821793198586, 0.052558545023202896, -0.017722927033901215, 0.041143160313367844, -0.023902375251054764, -0.04780180752277374, 0.03567270562052727, -0.10713161528110504, 0.017190806567668915, 0.09097111970186234, -0.0056845094077289104, -0.057189568877220154, 0.029844507575035095, 0.006955950986593962, -0.01586996577680111, 0.026417721062898636, 0.001955583458766341, 0.05654716491699219, 0.06583584100008011, -0.043256811797618866, -0.043752431869506836, 0.05422259867191315, -0.03391818702220917, 0.011296122334897518, -0.023501461371779442, 0.022661076858639717, 0.023085664957761765, -0.011072365567088127, -0.06009305268526077, -0.02381030283868313, -0.014439201913774014, 0.0059117465279996395, 0.007455072365701199, -0.021701080724596977, -0.04219604656100273, -0.02051762491464615, 0.014166498556733131, -0.06411460787057877, 0.004452020861208439, 0.033407896757125854, 0.057836297899484634, -0.07518919557332993, -0.050263501703739166, 0.012910314835608006, -0.03909464552998543, 0.030656909570097923, 0.028288908302783966, -0.043827615678310394, 0.004602121189236641, -0.021531859412789345, -0.003466178895905614, -0.0018580250907689333, 0.0759916603565216, -0.008250532671809196, -0.053766120225191116, -0.0035998786333948374, 0.04178433492779732, -0.03847675025463104, 0.0050234319642186165, -0.011906192637979984, -0.0262737013399601, -0.028728285804390907, -0.015626022592186928, 0.0685594230890274, -0.004676768556237221, -0.021309781819581985, -0.0266279187053442, -0.045283425599336624, 0.05811123177409172, 0.08667556941509247, -0.001709237229079008, 0.0036903033033013344, 0.0278789009898901, -0.026780910789966583, -0.03330923244357109, 0.00664890743792057, -0.013543283566832542, 0.09376930445432663, 0.056711595505476, 0.009697371162474155, -0.006189442239701748, -0.0002741660864558071, -0.013883251696825027, 0.00960620865225792, 0.021504376083612442, 0.043089400976896286, 0.006413787137717009, -0.024846410378813744, 0.012380613014101982, 0.02823551557958126, 0.0422375351190567, -0.026582496240735054, -0.0206341240555048, 0.06891060620546341, 0.029462279751896858, 0.01797829382121563, -0.05069785192608833, 0.088188037276268, -0.039126601070165634, 0.01877988502383232, 0.0331980399787426, 0.005962747149169445, -0.0005335164023563266, -0.0199457798153162, 0.021106457337737083, -0.0003481826570350677, -0.02325662039220333, -0.02879898063838482, 0.00063996174139902, -0.004178488627076149, -0.0063431174494326115, -0.013997308909893036, -0.03718419000506401, -0.04928835853934288, 0.019605642184615135, -0.028610078617930412, -0.03080584667623043, -0.025753118097782135, 0.012256637215614319, 0.036058928817510605, 0.0010409391252323985, -0.01846928894519806, -0.018812475726008415, 0.008449404500424862, -0.05982457473874092, -0.021323690190911293, -0.03444785624742508, 0.06053902953863144, 0.012152942828834057, 0.04910272732377052, -0.0019022600026801229, -0.0608195923268795, -0.00012423332373145968, 0.008215502835810184, -0.014918546192348003, -0.02573234587907791, 0.016753138974308968, 0.03659852594137192, 0.04599935561418533, -0.0049217804335057735, 0.009010146372020245, -0.01746775582432747, -0.024168720468878746, -0.0020211567170917988, -0.02503410540521145, 0.05820668861269951, 0.030280163511633873, 0.06822037696838379, 0.017113013193011284, -0.03202644735574722, 0.01742967776954174, 0.0016622764524072409, -0.05347936600446701, 0.021919917315244675, -0.04031765088438988, 0.050379522144794464, 0.007670280523598194, -0.02968602627515793, -5.467444263523254e-33, 0.04991685599088669, 0.033974308520555496, -0.0008313973667100072, -0.007884283550083637, -0.0003091355611104518, 0.03474074602127075, -0.03384625166654587, -0.016423270106315613, -0.061214007437229156, 0.0002428000298095867, -0.030962515622377396, 0.04840455949306488, 0.014590425416827202, 0.010598113760352135, -0.0022134596947580576, -0.02045898512005806, -0.030543508008122444, -0.014232351444661617, 0.07907391339540482, -0.004251888953149319, 0.036514028906822205, 0.05030263215303421, 0.026852330192923546, -0.027706699445843697, -0.09966085851192474, 0.017283489927649498, 0.001973913749679923, -0.031199892982840538, -0.00543004646897316, 0.0032757108565419912, -0.01226722076535225, 0.05394625663757324, -0.006399586331099272, -0.013341768644750118, 0.018249427899718285, -0.0555400475859642, -0.011524321511387825, 0.02503073401749134, -0.042594585567712784, -0.021088505163788795, -0.02102232165634632, 0.014025283977389336, 0.10930992662906647, -0.022934822365641594, -0.040650852024555206, 0.016274480149149895, 0.04197527840733528, -0.055402908474206924, 0.0053674932569265366, -0.03160571679472923, -0.028379829600453377, 0.011686183512210846, 0.03237418457865715, -0.025251854211091995, -0.009872019290924072, -0.03383500501513481, -0.03469732776284218, 0.03672150522470474, -0.014957990497350693, 0.008494250476360321, 0.03182099387049675, 0.032910771667957306, -0.01213959138840437, 0.07748249173164368, 0.10053304582834244, 0.028012534603476524, 0.0297078974545002, 0.02020273171365261, -0.04543494060635567, -0.04884938523173332, 0.023512572050094604, 0.02729976177215576, 0.07495114952325821, 0.04176850989460945, 0.09031475335359573, -0.06765785068273544, -0.11004409939050674, 0.036095332354307175, 0.06628485769033432, -0.03924376145005226, 0.00045033791684545577, -0.0016751637449488044, -0.031006408855319023, -0.019109705463051796, 0.07288791239261627, -0.0041115740314126015, -0.0302125234156847, -0.05707120522856712, 0.013119344599545002, -0.0435461662709713, 0.025832902640104294, 0.03164592385292053, -0.018509618937969208, -0.052138082683086395, 0.06262164562940598, 0.03317615017294884, -0.006450894754379988, 0.03697691857814789, 0.020313186571002007, -0.02690560184419155, -0.031678132712841034, -0.03813663870096207, -0.04147923365235329, 0.04201792553067207, 0.02676229737699032, 0.03443334251642227, 0.004005874507129192, 0.04518895223736763, 0.05525357276201248, -0.037901632487773895, -0.023144427686929703, -0.03217247873544693, 0.06039051339030266, 0.040890783071517944, -0.015337849967181683, -0.05051181837916374, -0.02145644836127758, 0.030712611973285675, -0.0006802574498578906, 0.013300635851919651, -0.026203233748674393, 0.03028145059943199, 0.0019751929212361574, 0.021786577999591827, -0.033450715243816376, 0.013024434447288513, -0.049755536019802094, 0.052936654537916183, -0.04918179288506508, -0.09798502177000046, -0.04437055438756943, -0.005851876921951771, 2.800239826683537e-07, 0.00368439476005733, -0.035772353410720825, -0.009509018622338772, -0.028867430984973907, -0.004807431250810623, -0.023891951888799667, 0.001560645061545074, 0.0007860359037294984, -0.035010263323783875, -0.08963557332754135, 0.026594243943691254, 0.03556391969323158, -0.01771826110780239, 0.0075966729782521725, -0.05865849182009697, 0.033893510699272156, -0.03070000931620598, 0.032890431582927704, 0.05365963652729988, -0.010812113992869854, -0.02091125212609768, 0.07800082117319107, 0.027124540880322456, -0.0662870928645134, 0.0708080381155014, -0.014107140712440014, -0.0036090801004320383, 0.03375013917684555, 0.06278064846992493, 0.0133268553763628, -0.008104169741272926, -0.01880563236773014, 0.007844381034374237, 0.052925076335668564, 0.036843352019786835, -0.007600749377161264, -0.013350195251405239, -0.04707467183470726, -0.03436216339468956, -0.014449616894125938, 0.03757353499531746, -0.0010297728003934026, 0.022371450439095497, -0.016193874180316925, 0.02072276547551155, -0.07113850861787796, -0.04838680848479271, -0.010450947098433971, -0.0025267740711569786, 0.011546649970114231, 0.02191438525915146, -0.04877026379108429, 0.019849924370646477, -0.02879854291677475, -0.038840796798467636, -0.03348561003804207, 0.027407348155975342, -0.03919929265975952, -0.0022913357242941856, 0.07448005676269531, -0.0019175135530531406, -0.012286273762583733, -0.08165011554956436, -0.03542416915297508, 0.08037952333688736, 0.027068592607975006, -0.0039700050838291645, 2.0599020916586578e-34, -0.014943969435989857, -0.009110859595239162, -0.0048960428684949875, -0.005819110665470362, -0.028747625648975372, 0.001930512604303658, -0.02935311384499073, -0.047097817063331604, -0.024632245302200317, -0.007363094948232174, -0.06183752417564392]

['Yukun Bao', 'Zhongyi Hu', 'Tao Xiong']

1401.1926v1

Addressing the issue of SVMs parameters optimization, this study proposes an efficient memetic algorithm based on Particle Swarm Optimization algorithm (PSO) and Pattern Search (PS). In the proposed memetic algorithm, PSO is responsible for exploration of the search space and the detection of the potential regions with optimum solutions, while pattern search (PS) is used to produce an effective exploitation on the potential regions obtained by PSO. Moreover, a novel probabilistic selection strategy is proposed to select the appropriate individuals among the current population to undergo local refinement, keeping a well balance between exploration and exploitation. Experimental results confirm that the local refinement with PS and our proposed selection strategy are effective, and finally demonstrate effectiveness and robustness of the proposed PSO-PS based MA for SVMs parameters optimization.

A PSO and Pattern Search based Memetic Algorithm for SVMs Parameters Optimization

http://arxiv.org/pdf/1401.1926v1

Title PSO Pattern Search based Memetic Algorithm SVMs Parameters Optimization Summary Addressing issue SVMs parameter optimization study proposes efficient memetic algorithm based Particle Swarm Optimization algorithm PSO Pattern Search PS proposed memetic algorithm PSO responsible exploration search space detection potential region optimum solution pattern search PS used produce effective exploitation potential region obtained PSO Moreover novel probabilistic selection strategy proposed select appropriate individual among current population undergo local refinement keeping well balance exploration exploitation Experimental result confirm local refinement PS proposed selection strategy effective finally demonstrate effectiveness robustness proposed PSOPS based SVMs parameter optimization Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.003677141619846225, -0.035738736391067505, -0.04013725370168686, -0.03242357820272446, 0.030800711363554, -0.039950333535671234, -0.01886816881597042, 0.005230278708040714, -0.042481835931539536, 0.024726781994104385, 0.012441267259418964, 0.03372093662619591, 0.02127053588628769, 0.031095923855900764, 0.004369962494820356, -0.022394470870494843, 0.020802423357963562, 0.02872377820312977, -0.024639282375574112, -0.015320093370974064, 0.010774748399853706, -0.05783988907933235, 0.04203600436449051, 0.014674242585897446, 0.01602581888437271, 0.058635413646698, 0.006723678670823574, -0.015436884947121143, 0.06322726607322693, -0.08951087296009064, -0.003759145736694336, -0.024501057341694832, 0.028123676776885986, 0.02793862670660019, 2.2616532078245655e-06, -0.036963921040296555, -0.032476793974637985, 0.0032623892184346914, 0.026409732177853584, 0.03917929157614708, 0.002073109382763505, 0.03084416687488556, -0.006864043418318033, -0.021254749968647957, -0.005016466602683067, 0.04610675573348999, 0.006996175739914179, -0.005163429770618677, 0.013850786723196507, 0.049966830760240555, 0.007034222595393658, -0.01077267061918974, -0.0055515761487185955, -0.005961314309388399, 0.0049150362610816956, -0.029194096103310585, 0.010065233334898949, -0.04453019052743912, 0.03081720694899559, 0.033118076622486115, 0.005480745807290077, 0.022903041914105415, -0.028572145849466324, -0.010755067691206932, 0.005171436816453934, -0.023038821294903755, 0.028927749022841454, 0.001220251084305346, 0.03976190835237503, -0.03837075084447861, -0.01207458321005106, 0.027661114931106567, 0.04790668189525604, -0.03404846414923668, -0.044478338211774826, 0.004322148393839598, -0.011043783277273178, -0.006818997673690319, -0.03986704349517822, 0.021853957325220108, -0.024631114676594734, 0.04021928459405899, -0.026827029883861542, -0.014711967669427395, 0.03977760672569275, 0.03946291655302048, -0.046823784708976746, 2.6331184926675633e-05, 0.013845368288457394, -0.04849924147129059, -0.04791396111249924, 0.07287142425775528, 0.030747124925255775, -0.010249597951769829, -0.11397520452737808, 0.008140258491039276, 0.04176026210188866, -0.06973940879106522, 0.04634816572070122, -0.003153870115056634, 0.06837436556816101, -0.02545064501464367, 0.079568050801754, -0.01883280649781227, 0.0324615016579628, -0.020405225455760956, -0.014496776275336742, 0.00917659979313612, -0.02453886903822422, 0.020419694483280182, -0.015960251912474632, 0.006689108442515135, 0.000592039548791945, 0.04904790595173836, 0.039669547230005264, -0.012207607738673687, -0.05336661636829376, 0.008851108141243458, 0.005773353856056929, -0.08753803372383118, -0.00592151889577508, -0.010708723217248917, 0.046298831701278687, 0.03143148869276047, -0.041090257465839386, -0.024879753589630127, -0.011879729107022285, -0.019868776202201843, -0.06079072505235672, 0.05876893550157547, 0.015579299069941044, 0.016668248921632767, -0.011215792037546635, 0.04482512176036835, -0.03675244003534317, 0.002441456075757742, -0.005092583131045103, 0.011115124449133873, -0.061317455023527145, 0.01819661445915699, 0.031145736575126648, 0.008254305459558964, 0.017648853361606598, 0.014926595613360405, -0.007066081743687391, -0.04160340502858162, -0.06267282366752625, 0.0510798841714859, 0.02852947823703289, 0.01220077183097601, 0.0015731266466900706, 0.0019528173143044114, -0.00385532109066844, 0.037689436227083206, 0.04513508826494217, -0.013316062279045582, 0.005556254647672176, 0.039995696395635605, -0.030353102833032608, 0.024603955447673798, -0.024406835436820984, -0.02410191483795643, -0.0074059488251805305, -0.021635213866829872, -0.04286428913474083, -0.00022230813920032233, 0.01678432710468769, -0.04647410288453102, -0.018872296437621117, 0.04422963410615921, -0.00714170653373003, -0.03455179184675217, -0.014838485978543758, -0.017196187749505043, -0.018737126141786575, -0.009008611552417278, 0.0099612632766366, 0.025899605825543404, 0.0076784975826740265, 0.08975937217473984, -0.014930125325918198, -0.08478620648384094, 0.0854603722691536, 0.014383108355104923, -0.11916803568601608, -0.02971193939447403, -0.040287163108587265, -0.009607029147446156, -0.0031536074820905924, -0.022763287648558617, -0.00095268280711025, 0.01993132382631302, -0.019903723150491714, 0.02921059913933277, 0.03179725632071495, -0.009835685603320599, -0.028085334226489067, 0.02557881362736225, 0.0070360880345106125, 0.043047111481428146, -0.059091974049806595, 0.011170136742293835, 0.057266660034656525, -0.06873846799135208, 0.013537530787289143, -0.06366901844739914, -0.02204342931509018, 0.0415157824754715, -0.05688927322626114, -0.019338279962539673, 0.009087278507649899, 0.049104612320661545, -0.04214935749769211, 0.0018240561475977302, -0.024262724444270134, 0.05794036015868187, -0.011303325183689594, 0.013150150887668133, 0.01798458956182003, -0.026291243731975555, -0.0025248525198549032, 0.04103310406208038, -0.010072187520563602, 0.0471162311732769, 0.04732349514961243, 0.06147848069667816, 0.029258472844958305, 0.005802573636174202, 0.022217629477381706, -0.00349768390879035, 0.06660081446170807, -0.03727759048342705, 0.02554694563150406, -0.01923183538019657, -0.03530440852046013, -0.04421129450201988, 0.00034627271816134453, -0.020201511681079865, -0.0016784374602138996, -0.009883537888526917, 0.030242126435041428, 0.006886009126901627, -0.021420078352093697, 0.009157838299870491, 0.004820864647626877, -0.05298547074198723, -0.06239103153347969, -0.021907765418291092, 0.01115189678966999, -0.03484298661351204, 0.06259624660015106, -0.03468991443514824, 0.03765132650732994, 0.027334481477737427, -0.025112157687544823, 0.021298693493008614, 0.08607489615678787, 0.04333405941724777, -0.08463340252637863, -0.011440347880125046, -0.03714009374380112, -0.033234912902116776, -0.018300646916031837, 0.012797861360013485, 0.062186069786548615, -0.0007351968088187277, -0.009989459067583084, -0.01610920950770378, 0.03344639018177986, 0.03118065372109413, -0.044449836015701294, -0.009669619612395763, -0.041665151715278625, -0.0027058254927396774, -0.0011745274532586336, 0.028318680822849274, 0.11918363720178604, -0.04176497831940651, -0.0894327238202095, 0.028543928638100624, -0.024264570325613022, -0.001089047291316092, 0.001568520674481988, 0.033416926860809326, -0.01840732991695404, 0.0019027249654754996, 0.0120028555393219, 0.02202434279024601, -0.08201244473457336, 0.11987313628196716, -0.028154954314231873, -0.035358887165784836, 0.0034880698658525944, -0.02871515601873398, -0.030676420778036118, -0.010925199836492538, -0.032237082719802856, 0.030475551262497902, 0.050625015050172806, -0.0019755875691771507, 0.0064444043673574924, 0.0515131838619709, -0.012416989542543888, 0.007408302277326584, -0.023126613348722458, 0.09003005921840668, 0.06744924932718277, 0.014335541985929012, 0.093263640999794, -0.01776057854294777, -0.009624870494008064, 0.0035482461098581553, 0.0008196597918868065, 0.03162013366818428, 0.040032677352428436, 0.035838544368743896, -0.004287630319595337, 0.015800338238477707, -0.05351509898900986, -0.013064744882285595, -0.024345114827156067, 0.019189773127436638, 0.009048542007803917, 0.03239990025758743, 0.001705415197648108, -0.025089425966143608, 0.01069995854049921, -0.009333017282187939, -0.04096091166138649, 0.05016300454735756, 0.016308145597577095, -0.021641673520207405, 0.04903427138924599, 0.057407982647418976, -0.0001289107312913984, -0.003312689019367099, -0.011407759971916676, -0.07664722204208374, 0.03712521493434906, -0.019781092181801796, -0.028802745044231415, 0.002073433017358184, -0.05746717378497124, 0.020490916445851326, 0.03765731677412987, 0.002116265008226037, 0.02666889689862728, -0.0002957706747110933, -0.013676801696419716, 0.03651527687907219, -0.00787924975156784, 0.008799919858574867, -0.045342471450567245, 0.011369438841938972, -0.001579580595716834, -0.03943187743425369, 0.0024808545131236315, -0.0015171439154073596, 0.024220764636993408, 0.055655308067798615, 0.02435479685664177, 0.0051905014552176, 0.006097646430134773, -0.025582561269402504, -0.044561728835105896, 0.029162218794226646, -0.014901774004101753, -0.0026459575165063143, -0.020925480872392654, -0.0008647575741633773, -0.010679846629500389, -0.0506327860057354, 0.06936202198266983, -0.0009426738251931965, 0.008563662879168987, -0.007784075569361448, -0.020542994141578674, -0.05044274777173996, -0.055437859147787094, -0.003883837489411235, 0.06517762690782547, 0.04914268106222153, 0.03659336641430855, -0.007245396729558706, 0.03768044337630272, -0.04388798773288727, -0.013917751610279083, -0.02601510100066662, -0.024600185453891754, 0.04894952103495598, -0.0013682869030162692, -0.13367421925067902, 0.0004059697675984353, -0.018817488104104996, -0.00416740495711565, -0.05248893052339554, -0.03703877329826355, 0.06296925991773605, 0.009855581447482109, -0.06706518679857254, -0.021979782730340958, -0.05914877727627754, -0.012524552643299103, 0.03144872188568115, -0.058651845902204514, -0.04369201883673668, 0.045233625918626785, 0.03854402154684067, 0.023051129654049873, -0.048302482813596725, -0.048287469893693924, 0.01657227613031864, 0.017751852050423622, -0.07982781529426575, -0.008849028497934341, 0.04052353650331497, -0.006703249644488096, 0.01977488398551941, 0.021823905408382416, 0.0016473435098305345, -0.0013807151699438691, 0.018481826409697533, 0.008892552927136421, -0.025116657838225365, 0.0016670671757310629, -0.028164079412817955, 0.02393549494445324, 0.004943820182234049, -0.023494191467761993, -0.02149377204477787, -0.004574220161885023, -0.026671957224607468, -0.00032590649789199233, -0.03249523416161537, 0.009270030073821545, 0.01347107533365488, -0.017817236483097076, -0.00406629778444767, -0.040393371134996414, -0.06584537029266357, 0.05217879265546799, -0.007641511503607035, 0.08077394217252731, 0.005353801883757114, 0.06900671124458313, -0.003750591306015849, 0.0030992808751761913, 0.03819998726248741, -0.03861285001039505, 0.01869237795472145, -0.0012033147504553199, -0.030450895428657532, 0.021175825968384743, 0.010533014312386513, -0.057135872542858124, 0.002688395557925105, -0.11135266721248627, -0.008138187229633331, -0.02204001508653164, 0.031107570976018906, 0.0462365485727787, -0.004587844479829073, -0.011678778566420078, -0.03731125593185425, -0.03741229698061943, 0.08040200173854828, -0.03415926173329353, 0.08005005121231079, -0.06271100044250488, -0.0013046541716903448, 0.0015743133844807744, 0.0019094955641776323, -0.018674153834581375, 0.04574893042445183, 0.0450948067009449, 0.005147186573594809, -0.020565129816532135, -0.0335010401904583, 0.007336647715419531, -0.028592834249138832, 0.03571534901857376, 0.05651430785655975, 0.06159026175737381, -0.009918775409460068, -0.029449602589011192, 0.007073886226862669, -0.0013438411988317966, 0.02989714778959751, 0.004144066944718361, 0.03440772742033005, -0.029080357402563095, -0.03958253934979439, 0.036960288882255554, 0.01696677692234516, 0.04721353203058243, -0.02623136155307293, 0.05952969193458557, 0.03958997502923012, -0.0019402789184823632, -0.00305762211792171, -0.033766601234674454, -0.0004512969171628356, 0.02387985959649086, -0.007367850746959448, 0.03369324281811714, 0.034655939787626266, 0.008566596545279026, 0.04479549452662468, -0.012523750774562359, 0.013629987835884094, -0.01829555816948414, -0.014997454360127449, 0.016316557303071022, -0.010724063031375408, -0.048878103494644165, 0.02181735448539257, 0.04495875909924507, -0.01549496129155159, -0.01540263183414936, -0.021670816466212273, 0.023586992174386978, -0.020646726712584496, -0.016795042902231216, -0.020890867337584496, 0.04235156625509262, 0.006491153035312891, 0.009671837091445923, -0.031000282615423203, 0.042541325092315674, 0.002838327083736658, 0.00845387578010559, -0.02852548286318779, -0.04085118696093559, -0.015915466472506523, -0.024139882996678352, 0.10152598470449448, 0.03782924264669418, 0.035163119435310364, -0.02058461122214794, -0.009828801266849041, 0.007376357913017273, 0.05036572739481926, 0.02962961047887802, -0.015699142590165138, 0.021507684141397476, -0.015335154719650745, 0.0025190787855535746, 0.0017965136794373393, -0.059257425367832184, 0.06016925722360611, -0.025930175557732582, -0.08120293915271759, -0.004395098891109228, 0.06745308637619019, -0.024255143478512764, -6.192918601890475e-33, -0.009222880005836487, -0.04663950577378273, -0.053477369248867035, 0.02306111343204975, -0.05047270283102989, -0.08049900829792023, 0.014203631319105625, 0.015723831951618195, 0.04731672257184982, -0.07010576128959656, -0.06456442177295685, -0.05366639792919159, -0.004192302003502846, 0.01318455021828413, -0.019602380692958832, 0.06959869712591171, -0.006651621777564287, 0.026247510686516762, 0.005900494288653135, -0.07600120455026627, -0.0019656738732010126, 0.04743985831737518, -0.028353441506624222, 0.021123547106981277, -0.0886029303073883, 0.03852927312254906, 0.011892816983163357, 0.009246678091585636, -0.025705447420477867, -0.004343856126070023, 0.03988131508231163, -0.013791992329061031, -0.031447023153305054, 0.0026791016571223736, -0.008992588147521019, -0.015400269068777561, 0.05707656592130661, -0.03747499734163284, -0.041943635791540146, 0.04203520342707634, 0.04330809786915779, -0.03718211129307747, 0.08159410953521729, -0.002525739371776581, -0.03270081430673599, 0.050045840442180634, 0.030946718528866768, -0.033762428909540176, 0.013488619588315487, -0.025113729760050774, 0.010883520357310772, -0.011920261196792126, 0.019000427797436714, -0.002549233613535762, 0.005992483347654343, -0.060648418962955475, -0.02743850275874138, 0.012064299546182156, -0.00048546743346378207, 0.048494961112737656, 0.01767856627702713, 0.04204831272363663, -0.04055476561188698, 0.04985217750072479, 0.06110791862010956, -0.001213215058669448, -0.025972094386816025, 0.0009546834626235068, 0.043821848928928375, -0.0469416007399559, -0.0006152671412564814, 0.015762627124786377, 0.0195525623857975, -0.016566216945648193, 0.04441902041435242, -0.05328324809670448, -0.0009608797845430672, 0.053897883743047714, -0.008520171046257019, 0.007240633014589548, 0.02951621077954769, 0.006125189829617739, 0.015943944454193115, -0.02397451549768448, 0.04564089700579643, -0.04422081261873245, -0.005264434963464737, -0.0444292351603508, -0.005483691114932299, -0.026676444336771965, -0.06101590022444725, -0.01587848737835884, -0.02647404372692108, -0.018906129524111748, 0.10368521511554718, -0.024616600945591927, 0.004948911257088184, -0.055279698222875595, 0.021780546754598618, -0.06913622468709946, -0.04757006838917732, -0.052517373114824295, 0.03624347969889641, -0.06447933614253998, -0.03815852478146553, 0.022798718884587288, -0.042237065732479095, -0.017114609479904175, 0.03467613831162453, 0.03244677558541298, 0.03761095181107521, -0.058519601821899414, -0.01645851507782936, 0.03952516242861748, 0.005809157155454159, -0.06250282377004623, -0.005655666813254356, 0.03209630772471428, 0.017287198454141617, -0.030893458053469658, -0.04521682858467102, 0.033400487154722214, -0.012313352897763252, 0.028440168127417564, 0.013344609178602695, 0.01846763677895069, 0.004711077082902193, -0.01737368106842041, -0.03636620193719864, -0.002342432737350464, -0.01707209274172783, -0.007879070937633514, 2.9309347837624955e-07, -0.01041074562817812, 0.05428820848464966, -0.07770206779241562, -0.024935301393270493, 0.005889451131224632, 0.010647010989487171, 0.02286149561405182, -0.03643760830163956, -0.008768513798713684, 0.038649216294288635, 0.04306253418326378, -0.029859323054552078, 0.024316778406500816, -0.02844705805182457, -0.06732888519763947, 0.021138476207852364, 0.027266571298241615, 0.05150364339351654, -0.007648668251931667, 0.03865012899041176, 0.017075911164283752, 0.03868316486477852, 0.05676823481917381, -0.017145678400993347, 0.0222234595566988, 0.011993185617029667, 0.012692654505372047, 0.0059907883405685425, -0.006957013159990311, 0.03344378247857094, -0.036548350006341934, -0.001607273006811738, -0.04083544388413429, 0.006122227292507887, 0.009802973829209805, 0.0808316171169281, -0.00916336104273796, -0.015508219599723816, 0.01333964429795742, -0.036939915269613266, 0.07590460032224655, 0.054831113666296005, 0.016939517110586166, 0.019477875903248787, -0.021192118525505066, -0.04727575555443764, -0.032562341541051865, -0.0077344682067632675, 0.04953298345208168, -0.011095291003584862, 0.0390411838889122, -0.04330747574567795, -0.021488331258296967, -0.023884281516075134, -0.06007685139775276, -0.04788508266210556, 0.015195824205875397, 0.03280103579163551, -0.029618799686431885, -0.0011353706941008568, -0.013907797634601593, -0.00018552466644905508, 0.00025308915064670146, -0.026062242686748505, 0.03388327732682228, 0.07733666151762009, 0.0021139977034181356, 2.8949271311459914e-34, 0.026833826676011086, -0.01702634058892727, -0.026147445663809776, 0.01295970194041729, -0.04653386399149895, 0.056297238916158676, -0.01437375694513321, 0.04207147657871246, -0.013778366148471832, 0.054939866065979004, 0.0016376040875911713]

['Laurent Dinh', 'Jascha Sohl-Dickstein', 'Samy Bengio']

1605.08803v3

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

Density estimation using Real NVP

http://arxiv.org/pdf/1605.08803v3

Title Density estimation using Real NVP Summary Unsupervised learning probabilistic model central yet challenging problem machine learning Specifically designing model tractable learning sampling inference evaluation crucial solving task extend space model using realvalued nonvolume preserving real NVP transformation set powerful invertible learnable transformation resulting unsupervised learning algorithm exact loglikelihood computation exact sampling exact inference latent variable interpretable latent space demonstrate ability model natural image four datasets sampling loglikelihood evaluation latent variable manipulation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.010649830102920532, 0.02311602793633938, -0.020355718210339546, -0.005554623901844025, 0.0006417612312361598, -0.028737174347043037, -0.010901322588324547, -0.01590411737561226, -0.1122327521443367, 0.03075490891933441, 0.037034448236227036, 0.010051854886114597, -0.011723372153937817, 0.07618006318807602, 0.03141924738883972, -0.053763486444950104, -0.03253723308444023, -0.03481411933898926, -0.002702742349356413, -0.015392945148050785, -0.010877312161028385, -0.04691161960363388, -0.0022866632789373398, -0.005943214520812035, -0.050516411662101746, 0.03401336073875427, -0.032526787370443344, 0.00789625570178032, -0.007631155662238598, -0.010761920362710953, 0.038475681096315384, 0.003875394118949771, 0.036349259316921234, 0.0011104156728833914, 2.2003926005709218e-06, -0.009628217667341232, -0.06573694944381714, -0.001562722260132432, 0.014251703396439552, -0.018286028876900673, 0.056330300867557526, -0.03087347000837326, -0.010104950517416, -0.036110393702983856, 0.010928073897957802, -0.043912239372730255, 0.03971060737967491, 0.03208854794502258, 0.004468249157071114, 0.02489420212805271, -0.013020123355090618, -0.02878211811184883, -0.026115087792277336, -0.03821719065308571, 0.02270023338496685, 0.01526643242686987, 0.03172875940799713, 0.08737664669752121, -0.0033838676754385233, -0.013362876139581203, -0.06270113587379456, 0.03501931577920914, 0.03922010585665703, -0.01136148814111948, 0.05493024364113808, 0.05089964717626572, -0.008463502861559391, 0.002855163998901844, -0.0037736191879957914, 0.05889538675546646, -0.04003172367811203, -0.023408574983477592, 0.021420015022158623, -0.010112285614013672, -0.028182625770568848, 0.01535558421164751, -0.029412399977445602, 0.00022403427283279598, 0.014020279049873352, -0.005953972693532705, -0.0651131197810173, 0.06388892978429794, -0.004973533097654581, -0.0372430682182312, -0.01904982700943947, 0.03239607438445091, 0.018035590648651123, 0.026453478261828423, -0.003989831078797579, 0.011344771832227707, -0.07550116628408432, 0.003910334315150976, 0.052219610661268234, -0.01516471616923809, -0.009265275672078133, -0.00013690338528249413, 0.01323720719665289, -0.01991141401231289, -0.003407789394259453, -0.019302811473608017, 0.01645573601126671, -0.016897888854146004, -0.027540946379303932, 0.02366347424685955, -0.0271059051156044, 0.013538961298763752, -0.037882838398218155, 0.05146782845258713, -0.02636655420064926, 0.003981068264693022, 0.014980736188590527, 0.010038052685558796, 0.021465808153152466, -0.013755719177424908, -0.042797744274139404, 0.029272625222802162, -0.04460911080241203, -0.011200972832739353, 0.0022670463658869267, -0.02765447273850441, 0.0048254383727908134, 0.05300246179103851, -0.022495094686746597, -0.0130784772336483, 0.0004081222286913544, 0.05092325061559677, -0.004301030188798904, 0.009587946347892284, -0.0020570328924804926, 0.014571290463209152, 0.010478978045284748, 0.04112740978598595, -0.0036102631129324436, 0.02427060902118683, 0.05826350301504135, 0.0329047329723835, -0.0011298913741484284, 0.011419476009905338, -0.025536512956023216, 0.03419099375605583, -0.04022182896733284, -0.024700386449694633, 0.01759188622236252, -0.0996844619512558, -0.0015581946354359388, -0.022319894284009933, -0.009967698715627193, 0.008913420140743256, -0.002470556413754821, -0.021445652469992638, 0.007652417290955782, 0.06288086622953415, 0.0005462969420477748, 0.01910991407930851, 0.09172536432743073, -0.04226336255669594, 0.027800245210528374, 0.05447080731391907, 0.026610011234879494, -0.007319944445043802, 0.011734085157513618, -0.020244652405381203, 0.030244702473282814, -0.0023794674780219793, 0.011528469622135162, 0.02208157442510128, -0.08298255503177643, -0.035038940608501434, -0.03125761076807976, 0.013485992327332497, 0.0594177320599556, -0.0051813810132443905, -0.011391252279281616, -0.0860612690448761, 0.018680598586797714, 0.0346805639564991, -0.030389977619051933, -0.03474942967295647, 0.03280140087008476, -0.0015850740019232035, -0.018067391589283943, -0.011742761358618736, 0.0021383243147283792, 0.05925469845533371, -0.06055235117673874, -0.0042679524049162865, 0.011101914569735527, -0.00016513756418135017, -0.022749442607164383, -0.08336728811264038, 0.01772402971982956, -0.013356980867683887, -0.018818765878677368, -0.06530267745256424, 0.07467612624168396, 0.001767632202245295, 0.04988868907094002, -0.03110351972281933, 0.002070755697786808, 0.03057403862476349, -0.01628143899142742, 0.028329160064458847, 0.03982521593570709, -0.10013280808925629, -0.036805201321840286, -0.055660828948020935, -0.004115090239793062, -0.032668862491846085, -0.04110625013709068, -0.011410728096961975, -0.01727079227566719, 0.0061016143299639225, 0.030498499050736427, 0.0019429570529609919, -0.005586742889136076, -0.007047377992421389, 0.022210396826267242, -0.018289292231202126, -0.0009321554098278284, -0.01852666400372982, 0.014552906155586243, -0.08806540071964264, -0.009087537415325642, 0.0175443384796381, -0.050853975117206573, 0.02839195728302002, 0.0622074119746685, 0.006134950555860996, 0.03610248491168022, -0.0164769496768713, 0.012480534613132477, -0.0005450441385619342, 0.026424352079629898, -0.023745015263557434, -0.061654701828956604, 0.042415060102939606, 0.04277745261788368, 0.02622140757739544, 0.000644337444100529, -0.06678236275911331, 0.022591805085539818, -0.03615241497755051, -0.0153742590919137, -0.01686926931142807, 0.0009431696962565184, -0.03246311470866203, 0.04243976250290871, -0.017091821879148483, 0.004176161251962185, 0.03078451193869114, 0.017333058640360832, -0.06577140092849731, 0.028276285156607628, 0.011105488985776901, 0.03992597386240959, 0.00491581903770566, 0.029202355071902275, 0.01545617263764143, -0.004111316986382008, -0.0016908448887988925, -0.04319053143262863, -0.03390529379248619, -0.00792075414210558, 0.03916841745376587, 0.010911816731095314, 0.013821640983223915, 0.04355299845337868, -0.005744686350226402, 0.018366754055023193, -0.002830742858350277, -0.0013830405659973621, 0.04280416667461395, -0.0012844335287809372, -0.03598383069038391, 0.02094946801662445, -0.01657905988395214, 0.034387681633234024, 0.02542286552488804, -0.029142752289772034, 0.0266385767608881, -0.027484338730573654, 0.052461784332990646, 0.0016043236246332526, -0.017410418018698692, -0.017343251034617424, 0.018353557214140892, 0.013698505237698555, -0.06702005863189697, 0.00781296193599701, 0.06254797428846359, 0.017182186245918274, 0.030021684244275093, 0.0010438847821205854, -0.06260251998901367, -0.022610321640968323, -0.03555336967110634, 0.09749814867973328, 0.05328864976763725, 0.02248813398182392, -0.004445554688572884, -0.009257427416741848, 0.04422260448336601, -0.019743165001273155, 0.012856983579695225, -0.05308947712182999, -0.006304504815489054, 0.06813588738441467, -0.0122982207685709, 0.012470263987779617, 0.008772098459303379, 0.0002033537020906806, 0.008100972510874271, 0.004462329670786858, -0.0021042623557150364, -0.019550098106265068, -0.012331974692642689, -0.010804083198308945, 0.0777839943766594, -0.01423706579953432, 0.03165833279490471, 0.02188299596309662, -0.047326911240816116, 0.005283399485051632, -0.008395816199481487, -0.03744632750749588, -0.036302801221609116, -0.057150427252054214, 0.053408339619636536, -0.02878793329000473, 0.07904554158449173, 0.004445851314812899, 0.025705931708216667, 0.0035479243379086256, -0.02649879641830921, 0.03338601440191269, -0.0032560224644839764, -0.021714020520448685, -0.0194871723651886, -0.046870846301317215, -0.0075970608741045, 0.031686075031757355, 0.0031535474117845297, -0.03167720139026642, -0.02889399416744709, 0.04366684705018997, -0.040086906403303146, -0.06360219419002533, -0.06839509308338165, -0.031773120164871216, 0.0034782986622303724, 0.050119899213314056, 0.07639975100755692, -0.012372884899377823, -0.04611487686634064, -0.023170096799731255, 0.0467417947947979, 0.053241923451423645, 0.009385610930621624, 0.0033471703063696623, -0.036890286952257156, -0.004398579243570566, 0.04957781732082367, -0.08063633739948273, 0.06978652626276016, -0.07369917631149292, 0.005778034217655659, -0.012358009815216064, 0.06491713970899582, 0.00025715812807902694, 0.01769673265516758, 0.07721643894910812, 0.04162262752652168, -0.017800282686948776, 0.026264064013957977, -0.028728552162647247, -0.04106852039694786, 0.027396194636821747, 0.02229125425219536, 0.0045221415348351, 0.029316475614905357, 0.027921533212065697, -0.0031548591796308756, 0.02222481742501259, -0.018913205713033676, 0.011159290559589863, -0.012569655664265156, -0.04444238543510437, -0.016916774213314056, -0.08872319757938385, 0.03406905382871628, 0.012388709932565689, 0.0046469345688819885, 0.007771320175379515, -0.09487202763557434, 0.0238933302462101, -0.07748374342918396, -0.04287145659327507, -0.03680549934506416, 0.011060566641390324, -0.005171754397451878, 0.02064565196633339, -0.04089170694351196, -0.02180882915854454, 0.00932925846427679, -0.08708182722330093, -0.003363543888553977, 0.0363331064581871, 0.035078614950180054, -0.08491148054599762, 0.01847919262945652, -0.0030068669002503157, -0.008462478406727314, -0.01915394328534603, -0.00335623137652874, 0.09026826173067093, 0.061597175896167755, 0.021306784823536873, -0.04032563045620918, 0.09136228263378143, -0.04213899374008179, 0.0025344309397041798, 0.012159631587564945, 0.04703045263886452, -0.012535708025097847, -0.020036347210407257, -0.03565507009625435, 0.023898350074887276, -0.00015539216110482812, 0.021151823922991753, -0.033775556832551956, -0.024503909051418304, 0.023098962381482124, -0.05677582323551178, 0.04170898348093033, 0.08149544894695282, -0.009269041940569878, 0.007007308304309845, -0.024353506043553352, -0.0552067831158638, -0.05103768780827522, 0.08423064649105072, 0.0007236955570988357, 0.09818831831216812, 0.02335144206881523, 0.0026916484348475933, 0.02990013360977173, -0.04195044934749603, -0.0317305251955986, -0.01695268601179123, 0.025916917249560356, 0.003962941467761993, -0.022056976333260536, 0.0038259103894233704, 0.04377766698598862, -0.008339069783687592, -0.024795375764369965, -0.009912398643791676, -0.037039656192064285, -0.05588063597679138, -0.0238515492528677, 0.06827756017446518, 0.0268669743090868, 0.04298333451151848, -0.020001986995339394, -0.011308237910270691, 0.028642602264881134, -0.014729824848473072, 0.008444046601653099, 0.012346682138741016, -0.028960615396499634, 0.014755208976566792, 0.02343752793967724, -0.015299895778298378, 0.04772576689720154, 0.019425014033913612, 0.009628545492887497, -0.04727387800812721, -0.06458356231451035, -0.07016406208276749, 0.018504425883293152, 0.0010480608325451612, 0.06524240970611572, 0.046055812388658524, 0.01793270744383335, -0.026608800515532494, -0.021602604538202286, -0.014660840854048729, 0.017300739884376526, -0.044854920357465744, -0.007417050655931234, 0.03422209620475769, 0.08317054063081741, -0.03900470957159996, 0.0023988012690097094, 0.06439872831106186, -0.01340567972511053, -0.026806959882378578, -0.02995026484131813, 0.07521253824234009, 0.006717605050653219, -0.07688982039690018, 0.012655952014029026, 0.041336964815855026, -0.04469034820795059, 0.013953079469501972, 0.09484159201383591, 0.04170418903231621, 0.0027574102859944105, 0.003219963749870658, 0.007615366019308567, -0.023746291175484657, -0.0010086398106068373, -0.04278485104441643, 0.007034330628812313, -0.0447411984205246, 0.049755748361349106, 0.025678427889943123, -0.06327534466981888, -0.020280124619603157, -0.0671764463186264, 0.03063284233212471, -0.06764308363199234, 0.07081471383571625, 0.02719103917479515, 0.02712959609925747, 0.006813554558902979, 0.005580221768468618, -0.01762222871184349, 0.01878983899950981, 0.006080413702875376, 0.06828100234270096, -0.025552188977599144, -0.05436090752482414, -0.006586718838661909, -0.02879769541323185, 0.07943236082792282, -0.015379167161881924, 0.007160235196352005, -0.0071761514991521835, 0.05836505815386772, -0.00993296317756176, 0.018364811316132545, 0.015509143471717834, -0.025860974565148354, 0.02196734957396984, 0.002323104301467538, -0.06493540853261948, 0.006830958183854818, -0.05472486838698387, -0.03231729194521904, -0.03084253892302513, -0.008079295046627522, 0.012890188954770565, 0.009460312314331532, -0.008178036659955978, -5.9604961854260464e-33, -0.018971489742398262, -0.06584259122610092, -0.07015916705131531, -0.04645419120788574, -0.005203710403293371, 0.04628501459956169, 0.004966117441654205, 0.0009582216734997928, 0.038813747465610504, -0.005212066229432821, 0.0033010246697813272, -0.016250580549240112, 0.00955180823802948, -0.0032770687248557806, 0.01601174660027027, 0.024943402037024498, -0.010523471049964428, -0.016930563375353813, 0.021720875054597855, -0.026260340586304665, 0.05911374092102051, 0.012552740052342415, 0.058738626539707184, -0.04724355414509773, -0.0382128469645977, 0.05084439367055893, -0.009296251460909843, 0.008790440857410431, -0.01086942944675684, -0.018238773569464684, -0.006053648889064789, 0.005104726646095514, 0.000376410927856341, -0.002202857518568635, -0.041362158954143524, -0.02210375666618347, -0.025006351992487907, -0.03273395821452141, -0.0169017743319273, 0.037684377282857895, -0.030591582879424095, 0.019302494823932648, 0.0951518639922142, -0.015211377292871475, 0.004781591240316629, -0.01744915544986725, 0.04835636913776398, -0.08158497512340546, 0.01949826255440712, -0.027756154537200928, -0.000519462104421109, 0.012808368541300297, -0.023824062198400497, 0.03548337519168854, 0.03832806646823883, -0.011896129697561264, -0.004583317786455154, -0.03483440354466438, -0.053852468729019165, -0.0035186181776225567, 0.03076566569507122, 0.03245420381426811, 0.018723992630839348, -0.01380581222474575, 0.056270577013492584, 0.03468693792819977, 0.028709635138511658, -0.0416753813624382, -0.008040527813136578, -0.10184377431869507, 0.03178522363305092, 0.014999667182564735, -0.007266285829246044, 0.03542017191648483, 0.06051762029528618, -0.030281223356723785, -0.03831816092133522, 0.05456576868891716, -0.0039031333290040493, -0.03436404466629028, -0.01648486778140068, -0.0033270472194999456, -0.020293589681386948, 0.024431627243757248, 0.02938733622431755, -0.059190113097429276, 0.040662623941898346, -0.009722812101244926, -0.019358595833182335, -0.021765314042568207, -0.02466856874525547, -0.012996300123631954, 0.014022727496922016, -0.03608400747179985, 0.05056583881378174, -0.058448340743780136, 0.021653272211551666, 0.035815201699733734, 0.017786283046007156, -0.028541676700115204, -0.008968811482191086, -0.026330458000302315, 0.003169627860188484, 0.004955329466611147, 0.011676871217787266, 0.02788151614367962, -0.0005668480298481882, 0.02189040742814541, 0.007071499712765217, -0.0022531813010573387, -0.010018737986683846, -0.029080260545015335, 0.016870949417352676, 0.06610100716352463, 0.032552629709243774, -0.05833089351654053, -0.02015562728047371, 0.04463272541761398, 0.03226799517869949, 0.009641813114285469, -0.0002682415070012212, 0.04967760667204857, 0.01973719522356987, -0.00383964111097157, -0.07542604953050613, -0.03108001872897148, -0.028752842918038368, -0.07413706928491592, 0.017530888319015503, -0.020465653389692307, -0.026766635477542877, -0.017400462180376053, 2.8517479222500697e-07, -0.00044458688353188336, -0.02756710723042488, 0.04978560656309128, -0.058846231549978256, -0.008194489404559135, 0.0013152387691661716, -0.04197196289896965, 0.001034432789310813, -0.016674308106303215, -0.13716544210910797, 0.007053903769701719, -0.047729749232530594, -0.0012088624062016606, -0.02740277722477913, -0.04440278932452202, -0.014283962547779083, 0.04559166356921196, 0.010107001289725304, 0.012961123138666153, -0.015638556331396103, 0.039089906960725784, 0.09781671315431595, 0.022442009299993515, -0.007892626337707043, 0.06074938550591469, 0.06087226793169975, 0.024520957842469215, -0.022745801135897636, 0.030443526804447174, -0.026782257482409477, 0.018000781536102295, -0.016747716814279556, 0.02072114124894142, 0.0345451645553112, -0.032948657870292664, 0.03593244031071663, 0.06571822613477707, 0.06702256947755814, -0.014948250725865364, 0.02493453212082386, 0.012436517514288425, 0.028022628277540207, -0.002595571568235755, -0.04919673502445221, 0.04108378291130066, -0.021201735362410545, 0.0009745479910634458, -0.009278434328734875, -0.0917138084769249, 0.057656724005937576, 0.07526659965515137, 0.012008881196379662, 0.02019045688211918, -0.0007373227854259312, -0.01684580184519291, 0.015313133597373962, 0.0036278327461332083, 0.05571644753217697, 0.0228611808270216, -0.027559058740735054, -0.0002413691981928423, 0.009088759310543537, -0.025400003418326378, 0.027406057342886925, 0.059615932404994965, 0.028942061588168144, -0.01301523670554161, 2.958527574421468e-34, -0.007337640039622784, 0.05104650929570198, 0.014015091583132744, -0.046967312693595886, -0.05296701565384865, 0.01702713593840599, -0.010052100755274296, 0.016366759315133095, -0.025969862937927246, -0.007252396550029516, -0.032608382403850555]

['Tim Salimans', 'Jonathan Ho', 'Xi Chen', 'Szymon Sidor', 'Ilya Sutskever']

1703.03864v2

We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a viable solution strategy that scales extremely well with the number of CPUs available: By using a novel communication strategy based on common random numbers, our ES implementation only needs to communicate scalars, making it possible to scale to over a thousand parallel workers. This allows us to solve 3D humanoid walking in 10 minutes and obtain competitive results on most Atari games after one hour of training. In addition, we highlight several advantages of ES as a black box optimization technique: it is invariant to action frequency and delayed rewards, tolerant of extremely long horizons, and does not need temporal discounting or value function approximation.

Evolution Strategies as a Scalable Alternative to Reinforcement Learning

http://arxiv.org/pdf/1703.03864v2

Title Evolution Strategies Scalable Alternative Reinforcement Learning Summary explore use Evolution Strategies ES class black box optimization algorithm alternative popular MDPbased RL technique Qlearning Policy Gradients Experiments MuJoCo Atari show ES viable solution strategy scale extremely well number CPUs available using novel communication strategy based common random number ES implementation need communicate scalar making possible scale thousand parallel worker allows u solve 3D humanoid walking 10 minute obtain competitive result Atari game one hour training addition highlight several advantage ES black box optimization technique invariant action frequency delayed reward tolerant extremely long horizon need temporal discounting value function approximation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.010028883814811707, -0.013128409162163734, -0.026057640090584755, -0.030221175402402878, 0.004878659266978502, -0.014877968467772007, -0.030878612771630287, -0.0016068447148427367, -0.03687499091029167, 0.013204746879637241, -0.025796733796596527, 0.041408758610486984, -0.018586693331599236, 0.0671517550945282, 0.026066899299621582, -0.046991750597953796, 0.03483828529715538, 0.02150040864944458, 0.027106795459985733, -0.021359805017709732, 0.03828122466802597, -0.055856071412563324, 0.01979007013142109, 0.03843805193901062, -0.015974676236510277, 0.05443720892071724, -0.05283265560865402, -0.0191878080368042, 0.05992041155695915, -0.05865510180592537, 0.06399223208427429, -0.020726079121232033, 0.0633535385131836, 0.07328445464372635, 2.10949497159163e-06, -0.031426772475242615, -0.04287101700901985, -0.05255860462784767, 0.013506189920008183, -0.05363984405994415, -0.005646675359457731, -0.007612558547407389, -0.03274733945727348, 0.0269639790058136, -0.014742285013198853, -0.057817697525024414, 0.03558387607336044, 0.0720294788479805, 0.030441764742136, 0.05954684689640999, 0.01101240050047636, -0.030404595658183098, 0.012276296503841877, -0.010167576372623444, 0.004066468682140112, -0.015025134198367596, 0.02657054364681244, 0.050452686846256256, 0.03207598999142647, -0.0014031532919034362, -0.03445456549525261, 0.002568034455180168, 0.036261651664972305, -0.0063331578858196735, 0.022249143570661545, 0.04405801743268967, 0.04869062826037407, -0.020321885123848915, -0.005653799045830965, 0.02698940970003605, -0.08161929249763489, 0.022444723173975945, 0.018153415992856026, 0.010154066607356071, 0.04773460701107979, -0.054447807371616364, 0.026789696887135506, 0.022396352142095566, -0.045277196913957596, -0.014573980122804642, -0.03851654753088951, 0.01607932150363922, -0.008331972174346447, 0.02173185534775257, 0.01672307215631008, 0.06474046409130096, -0.015735363587737083, -0.015333334915339947, 0.03165540471673012, -0.01898333989083767, 0.017821315675973892, 0.0005474862409755588, 0.031732141971588135, 0.02687392197549343, -0.020033469423651695, -0.005140138324350119, -0.008643722161650658, 0.005428913049399853, 0.002399782184511423, -0.04165777936577797, 0.040924422442913055, 0.004369278904050589, 0.07294194400310516, 0.0008557176915928721, -0.04806003347039223, 0.02095821127295494, -0.059605807065963745, -0.009159456938505173, 0.0006190522108227015, 0.07130775600671768, -0.04529561847448349, 0.03301046043634415, -0.046228669583797455, 0.04537353292107582, -0.014000599272549152, -0.040571149438619614, -0.02696555107831955, 0.004788064863532782, 0.007030936889350414, -0.07378073036670685, -0.011121234856545925, 0.0662880539894104, 0.017299136146903038, 0.02846861071884632, -0.05856674909591675, -0.027069665491580963, -0.032031964510679245, 0.015279430896043777, 0.009350497275590897, 0.03980491682887077, 0.0009182990179397166, 0.009684242308139801, -0.029650501906871796, 0.03237231820821762, 0.02012120746076107, 0.07251841574907303, 0.017319541424512863, 0.04553365334868431, 0.013163012452423573, 0.035012394189834595, -0.0005119525594636798, -0.01836876943707466, 0.013387046754360199, -0.05580149218440056, -0.023380771279335022, -0.05675634741783142, -0.05220526456832886, 0.03525989130139351, 0.025333808735013008, -0.051769472658634186, 0.024740057066082954, 0.051491059362888336, -0.00529465964064002, 0.011211296543478966, 0.08663155138492584, -0.017197260633111, -0.034882448613643646, 0.04070843756198883, 0.01558446791023016, -0.012904749251902103, -0.05151975154876709, 0.00771212438121438, -0.02759432978928089, 0.0073857298120856285, -0.04037606716156006, -0.023183241486549377, 0.041214942932128906, -0.07301031053066254, 0.046987466514110565, 0.10803361237049103, 0.008241532370448112, -0.013620108366012573, -0.07170960307121277, -0.01333396602421999, 0.011437390930950642, -0.014894076623022556, -0.007690149825066328, 0.022912675514817238, -0.004326249938458204, -0.022517455741763115, -0.011772166937589645, -0.059269361197948456, 0.04781134054064751, 0.06620072573423386, 0.01934150420129299, -0.02707235887646675, -0.04831712692975998, 0.02522076852619648, -0.022249098867177963, -0.03197338804602623, 0.03707364946603775, -0.017536133527755737, 0.02821708656847477, 0.003172866767272353, 0.002118441741913557, 0.0332864485681057, -0.05928865447640419, -0.02764708921313286, 0.023579536005854607, 0.030403265729546547, -0.07398143410682678, -0.047512635588645935, 0.03045695088803768, -0.04314548522233963, -0.03057374805212021, 0.002589751733466983, -0.07309523969888687, -0.025677815079689026, -0.04504965990781784, 0.02566571533679962, 0.012766562402248383, -0.00013553316239267588, -0.004956026095896959, -0.014592759311199188, -0.04540063068270683, 0.012618894688785076, 0.005091773346066475, 0.08621421456336975, 0.02646690420806408, -0.015375512652099133, -0.014835406094789505, 0.06624825298786163, -0.018333638086915016, 0.02513435110449791, -0.07496988028287888, 0.015351131558418274, 0.041954003274440765, -0.0048937746323645115, 0.02803332731127739, -0.0443735271692276, 0.0245869942009449, -0.03939568251371384, 0.0004902056534774601, 0.005478097125887871, -0.06804861128330231, -0.0015435278182849288, -0.03346964344382286, -0.0005431779427453876, 0.07336284220218658, -0.0342644602060318, 0.020443132147192955, 0.022830652073025703, 0.030443601310253143, -0.037495870143175125, -0.011601168662309647, -0.07041975110769272, 0.056841377168893814, -0.006738506723195314, 0.0351397730410099, -0.009246239438652992, 0.0017259003361687064, -0.051981501281261444, 0.030674083158373833, -0.0025566001422703266, -0.033009108155965805, -0.002844335976988077, 0.008058037608861923, 0.05154356360435486, -0.08173820376396179, -0.003892401233315468, 0.050796691328287125, 0.012488667853176594, 0.00045014775241725147, 0.03684617206454277, 0.07074961811304092, 0.0007145696436055005, 0.03583862632513046, -0.004850586876273155, -0.006940427236258984, 0.004524896387010813, -0.004761216230690479, 0.013165079057216644, -0.01539677381515503, -0.009110493585467339, 0.00554990628734231, 0.013705740682780743, 0.0721498355269432, -0.03184125944972038, -0.07630708068609238, 0.03815344348549843, 0.016481665894389153, -0.004437259864062071, -0.00024628546088933945, -0.008270133286714554, -0.021400541067123413, 0.006582342088222504, 0.003459132742136717, 0.02443838119506836, -0.013400516472756863, 0.000747887184843421, -0.048308681696653366, 0.06543107330799103, 0.006796697620302439, -0.021804146468639374, 0.006535166408866644, -0.010373018682003021, 0.02206168696284294, 0.043683186173439026, 0.01859140768647194, 0.008455577306449413, 0.024466563016176224, 0.08608192205429077, -0.06375376135110855, 0.05343639478087425, -0.015149638056755066, 0.01217131782323122, -0.014446516521275043, -0.003278987016528845, 0.03385842218995094, 0.03475243225693703, -0.04072221741080284, 0.0022230492904782295, -0.04856008663773537, -0.014496786519885063, 0.020685527473688126, -0.06797021627426147, -0.00024166620278265327, 0.0253959558904171, -0.06890059262514114, -0.06543243676424026, -0.04430815577507019, 0.024542100727558136, 0.04308832809329033, 0.04978666454553604, -0.012348241172730923, -0.00016219167446251959, -0.0077836480922997, -0.01735883206129074, -0.0024915500544011593, -0.005603641737252474, 0.014912114478647709, -0.075831338763237, -0.010113279335200787, 0.020246079191565514, 0.004040026571601629, 0.025599852204322815, -0.006524939090013504, -0.04150718078017235, 0.03431634604930878, 0.005308352876454592, -0.01265634037554264, -0.07125993072986603, -0.054034989327192307, 0.05759930983185768, -0.018354641273617744, -0.0007662392454221845, -0.038294218480587006, -0.03453749418258667, -0.0457497201859951, -0.02958260476589203, 0.020281393080949783, 0.04673561453819275, -0.0785394012928009, 0.0022406617645174265, -0.003559370758011937, -0.03699129819869995, 0.03566018119454384, 0.024775084108114243, 0.024203190580010414, -0.008607029914855957, 0.08048536628484726, 0.016247736290097237, 0.02119877003133297, -0.04823530092835426, -0.07285361737012863, 0.019710758700966835, -0.0042642345651984215, -0.03725656121969223, -0.0022623881231993437, -0.002631197217851877, -0.012806574814021587, -0.059759434312582016, -0.03664582222700119, 0.038749612867832184, -0.028958478942513466, -0.006846417207270861, -0.02290896698832512, -0.05053621158003807, 0.05655045434832573, -0.004755139816552401, 0.015695225447416306, 0.03350067138671875, -0.016925577074289322, -0.024715587496757507, 0.0366206169128418, -0.0032813253346830606, -0.02006758749485016, 0.027816304937005043, -0.08725222200155258, -0.02313634753227234, 0.0023515617940574884, -0.08209440857172012, -0.043649252504110336, -0.0007692735525779426, -0.013446908444166183, -0.05060892552137375, -0.008925258181989193, 0.07864062488079071, -0.0023655297700315714, -0.02395194210112095, 0.04262702167034149, 0.032300692051649094, 0.0384184829890728, -0.005206918343901634, -0.05841347947716713, -0.020141875371336937, 0.07482018321752548, 0.012408589012920856, -0.023683160543441772, -0.03524043411016464, -0.006024234462529421, 0.03306121379137039, 0.02178916521370411, -0.005307073704898357, -0.007208087481558323, -0.016687888652086258, 0.0020409899298101664, 0.016697393730282784, 0.03857358545064926, 0.04595150426030159, 0.021073730662465096, 0.029686719179153442, 0.00927240401506424, -0.04584571719169617, -0.032261695712804794, -0.044065210968256, -0.022868365049362183, 0.016921009868383408, 0.02340967021882534, -0.04520782455801964, -0.05899151787161827, -0.05268178507685661, -0.0023413347080349922, -0.03245081752538681, -0.0520230270922184, -0.00976510625332594, -0.03668022155761719, -0.006155462469905615, -0.06338202953338623, -0.07593964040279388, 0.024372471496462822, -0.02422279678285122, 0.08335399627685547, -0.010772110894322395, -0.029987137764692307, 0.014222015626728535, 0.04063132032752037, -0.03388727083802223, -0.06753987073898315, 0.019541924819350243, -0.024768903851509094, -0.024571089074015617, 0.05037974938750267, -0.005217744968831539, -0.043118666857481, 0.013726030476391315, -0.050730131566524506, -0.026715412735939026, -0.026873070746660233, 0.013525948859751225, 0.06799875199794769, -0.0031965910457074642, -0.007153648417443037, -0.01978149265050888, 0.018100827932357788, 0.04254106432199478, 0.0028374330140650272, 0.07809945195913315, 0.0073562245815992355, 0.04675498604774475, 0.03960340842604637, -0.0035523478873074055, 0.03789423406124115, -0.02717050351202488, 0.03318379446864128, 0.0007704957388341427, 0.005266736261546612, -0.01349576748907566, 0.023500865325331688, -0.009722062386572361, -0.0023799831978976727, 0.02441062405705452, -0.03290645033121109, -0.029104014858603477, 0.025602096691727638, 0.012728055939078331, 0.0022671539336442947, 0.009488819167017937, -0.04468286782503128, 0.02797081135213375, 0.00953145232051611, 0.030195707455277443, 0.048017166554927826, -0.018063083291053772, 0.07236265391111374, -0.03622095659375191, -0.0006392730283550918, 0.06180991604924202, 0.030241239815950394, 0.029625732451677322, -0.04714517667889595, -0.002249358920380473, 0.02589530125260353, 0.04073112830519676, 0.028665099292993546, 0.01968972571194172, -1.190534658235265e-05, 0.031913675367832184, 0.023565830662846565, 0.023361941799521446, -0.010266832076013088, 0.0012491486268118024, -0.013736872002482414, -0.04073024168610573, 0.007575188297778368, 0.04711553081870079, 0.04247700050473213, 0.01648649573326111, -7.335551345022395e-05, -0.02221723459661007, -0.044435299932956696, -0.019337372854351997, -0.021706514060497284, -0.05082261934876442, 0.02105940878391266, 0.05883591249585152, 0.008502565324306488, -0.02217007614672184, 0.029996413737535477, 0.01181469764560461, 0.005468759685754776, 0.07407355308532715, -0.019316287711262703, 0.0033606800716370344, -0.015802251175045967, 0.016834115609526634, -0.002177424728870392, -0.003629564307630062, 0.013050742447376251, -0.015136339701712132, -0.012127643451094627, 0.010074267163872719, -0.017813831567764282, 0.03895828127861023, 0.005962096620351076, 0.03174077719449997, 0.08313071727752686, -0.05113835260272026, -0.03673003613948822, -0.03517962619662285, -0.004036185797303915, -0.04520895704627037, 0.008634553290903568, -0.005346701014786959, -0.043724387884140015, -5.4640878598096715e-33, 0.02393949218094349, -0.0033822667319327593, -0.019140195101499557, -0.06719667464494705, -0.06944720447063446, 0.012355802580714226, -0.0030107388738542795, -0.0014912518672645092, 0.005683625116944313, -0.017862936481833458, 0.021482013165950775, -0.026174910366535187, -0.005954023916274309, 0.012873978354036808, 0.03158979490399361, -0.0031511292327195406, -0.039329756051301956, -0.006676971446722746, 0.004549031145870686, -0.0313158743083477, 0.018243690952658653, 0.0543697252869606, -0.0005400745430961251, -0.009478691965341568, -0.026257377117872238, 0.061904728412628174, -0.02122356742620468, -0.0024509557988494635, -0.05328267067670822, 0.027038386091589928, 0.006039354018867016, -0.0514957532286644, -0.04726869612932205, -0.07029420137405396, -0.024267569184303284, -0.025234680622816086, -0.03255375847220421, -0.012338182888925076, -0.058017004281282425, 0.0026418594643473625, -0.047309018671512604, -0.03278769180178642, 0.061648495495319366, -0.000531713361851871, -0.060943689197301865, 0.04214692860841751, 0.0005390757578425109, -0.007532502058893442, 0.02432926557958126, 0.011129097081720829, 0.01208470854908228, -0.0029268364887684584, 0.01902983896434307, -0.009493688121438026, -0.014491059817373753, 0.019878942519426346, -0.04538680240511894, -0.0448133759200573, 0.03924085199832916, 0.014221170917153358, -0.05501618608832359, -0.06809551268815994, -0.029253406450152397, 0.09044352918863297, 0.11937612295150757, 0.008289351128041744, 0.011285975575447083, -0.041026365011930466, 0.019485123455524445, -0.03382208198308945, 0.012618333101272583, 0.023692304268479347, 0.05806157737970352, -0.00966129545122385, 0.022839993238449097, -0.0214796494692564, -0.034045059233903885, 0.051473215222358704, 0.029283417388796806, 0.05046182498335838, -0.01623181626200676, -0.01198064535856247, -0.03645433112978935, 0.02241334691643715, 0.04809179529547691, -0.04054144397377968, 0.04670083895325661, -0.04199296608567238, 0.003003341844305396, 0.012308023869991302, 0.025738803669810295, -0.052916597574949265, 0.01367516815662384, -0.00561865046620369, 0.06120054051280022, -0.006652430165559053, -0.000595302612055093, 0.0016934527084231377, 0.05051064118742943, -0.012392120435833931, -0.029675843194127083, -0.06164642423391342, -0.016470972448587418, -0.017103178426623344, -0.016502372920513153, 0.027386924251914024, -0.03086429461836815, 0.007415604777634144, -0.0009661635849624872, 0.02332228235900402, 0.014371088705956936, 0.009569667279720306, 0.04597388580441475, 0.027360476553440094, 0.06334416568279266, -0.06574442982673645, 0.015723230317234993, 0.024458689615130424, 0.04308784008026123, -0.024151429533958435, -0.03305929899215698, 0.002143839607015252, -0.016004472970962524, 0.03833451867103577, -0.01773407869040966, 0.029183655977249146, -0.021092647686600685, 0.04176228865981102, -0.09146922081708908, -0.08143795281648636, -0.006567269563674927, 0.004714713431894779, 2.7069776820098923e-07, -0.026268761605024338, 0.02047555521130562, 0.006717321462929249, -0.01487700641155243, 0.00902810599654913, 0.03794422745704651, -0.014935845509171486, 0.04114226624369621, -0.008513941429555416, 0.023739993572235107, 0.04320208728313446, 0.025708170607686043, 0.016560465097427368, -0.06632949411869049, -0.06001119688153267, -0.0754329115152359, -0.05252646282315254, 0.027718573808670044, 0.00801265612244606, -0.015177748166024685, -0.03473735973238945, 0.047811295837163925, 0.06360714137554169, -0.016232876107096672, 0.061522576957941055, 0.04183311015367508, -0.008679497987031937, 0.007645577657967806, 0.046094950288534164, -0.04698779433965683, -0.04953943192958832, 0.06620509177446365, -0.0379088930785656, -0.02946663089096546, 0.007152171339839697, 0.07426988333463669, -0.0006517922738566995, 0.04437480494379997, -0.009362393990159035, -0.008779866620898247, 0.06284713745117188, 0.08898007869720459, 0.03032078966498375, 0.014978205785155296, 0.04563545063138008, 0.006644275970757008, 0.0002923626743722707, -0.03731872886419296, 0.015083259902894497, 0.010599644854664803, 0.022779643535614014, -0.00950675830245018, -0.026245122775435448, -0.013698762282729149, -0.04905729740858078, -0.020203886553645134, -0.007980882190167904, -0.015154254622757435, 0.050430260598659515, 0.05396832153201103, -0.03908819705247879, -0.032669346779584885, -0.02110878936946392, 0.06322375684976578, 0.03761816397309303, -0.01813502423465252, -0.017743214964866638, 2.4781985421564033e-34, -0.04242511838674545, -0.046644095331430435, 0.015080584213137627, -0.007065840996801853, -0.012716246768832207, 0.03349680081009865, 0.053410887718200684, -0.04048994556069374, 0.061773575842380524, 0.03218645602464676, -0.037695109844207764]

['Peter Karkus', 'David Hsu', 'Wee Sun Lee']

1703.06692v3

This paper introduces the QMDP-net, a neural network architecture for planning under partial observability. The QMDP-net combines the strengths of model-free learning and model-based planning. It is a recurrent policy network, but it represents a policy for a parameterized set of tasks by connecting a model with a planning algorithm that solves the model, thus embedding the solution structure of planning in a network learning architecture. The QMDP-net is fully differentiable and allows for end-to-end training. We train a QMDP-net on different tasks so that it can generalize to new ones in the parameterized task set and "transfer" to other similar tasks beyond the set. In preliminary experiments, QMDP-net showed strong performance on several robotic tasks in simulation. Interestingly, while QMDP-net encodes the QMDP algorithm, it sometimes outperforms the QMDP algorithm in the experiments, as a result of end-to-end learning.

QMDP-Net: Deep Learning for Planning under Partial Observability

http://arxiv.org/pdf/1703.06692v3

Title QMDPNet Deep Learning Planning Partial Observability Summary paper introduces QMDPnet neural network architecture planning partial observability QMDPnet combine strength modelfree learning modelbased planning recurrent policy network represents policy parameterized set task connecting model planning algorithm solves model thus embedding solution structure planning network learning architecture QMDPnet fully differentiable allows endtoend training train QMDPnet different task generalize new one parameterized task set transfer similar task beyond set preliminary experiment QMDPnet showed strong performance several robotic task simulation Interestingly QMDPnet encodes QMDP algorithm sometimes outperforms QMDP algorithm experiment result endtoend learning Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.031025972217321396, 0.02668103389441967, 0.021649088710546494, -0.015323212370276451, -0.0014813239686191082, -0.016121603548526764, 0.00402535405009985, -0.032107558101415634, -0.03283702954649925, 0.008134311065077782, -0.0023769207764416933, 0.04723343253135681, -0.0532427579164505, 0.05191734433174133, -0.0011134858941659331, -0.03782499209046364, 0.028332935646176338, 0.02613283321261406, -0.04944739490747452, 0.01441149041056633, -0.019188864156603813, -0.02939177118241787, -0.03360304236412048, 0.046875327825546265, -0.00989626720547676, 0.0059198797680437565, -0.07208975404500961, 0.004919957835227251, 0.01780499890446663, -0.060133568942546844, 0.031804732978343964, -0.023796945810317993, 0.025053849443793297, 0.05941818654537201, 2.1138284864719026e-06, -0.01858232170343399, -0.02044820599257946, -0.04848087951540947, -0.017992977052927017, -0.061153754591941833, -0.00011194974649697542, 0.016113387420773506, 0.0006772365886718035, 0.051967039704322815, -0.018765481188893318, -0.0043318686075508595, 0.036675840616226196, 0.11373875290155411, 0.029003644362092018, 0.06579627096652985, 0.013206016272306442, 0.005761952139437199, -0.006273479200899601, -0.00613773288205266, -0.02691192552447319, -0.08043517917394638, 0.04667407274246216, -0.002621792024001479, 0.01325912680476904, -0.01594838686287403, 0.00668476615101099, -0.02813080884516239, 0.024899892508983612, 0.0015015132958069444, -0.014787954278290272, 0.020480016246438026, 0.05562844127416611, -0.03551187738776207, 0.007709511090070009, 0.027892742305994034, -0.055867087095975876, -0.011390318162739277, 0.05261988565325737, -0.01584886573255062, -0.0038745058700442314, 0.0019222937989979982, -0.014954100362956524, 0.026994317770004272, 0.010876722633838654, -0.008574151434004307, -0.061828527599573135, 0.019952287897467613, 0.012919433414936066, 0.009781984612345695, -0.03137483447790146, 0.09409020096063614, -0.03255153447389603, 0.0034966750536113977, -0.004945752676576376, -0.03453666344285011, 0.01744168810546398, -0.05564747005701065, 0.019959338009357452, 0.05224480479955673, -0.03689974546432495, -0.015759220346808434, -0.024898920208215714, -0.02103315480053425, -0.004129241220653057, -0.01788974553346634, 0.021750617772340775, 0.012814035639166832, 0.003343235934153199, -0.005483077839016914, -0.03295985981822014, 0.07429784536361694, -0.08450855314731598, 0.031090259552001953, -0.03294629231095314, 0.030161399394273758, -0.07682159543037415, 0.04591049253940582, -0.04471530392765999, 0.05690654739737511, -0.004295337479561567, -0.0015008030459284782, 0.0003051023231819272, -0.00014239917800296098, -0.02475285902619362, -0.007182059809565544, 0.012254990637302399, 0.058413438498973846, -0.042622342705726624, -0.0007290702778846025, -0.05104498192667961, -0.02009933814406395, -0.05714922770857811, 0.04941367730498314, 0.008298489265143871, -0.0009516914724372327, -0.0029290211386978626, -0.000962698832154274, 0.01263232808560133, -0.00936858355998993, -0.0005180638981983066, 0.09378392994403839, 0.0009130481048487127, 0.026409942656755447, -0.002874745288863778, -0.013908186927437782, 0.05055607110261917, -0.041183825582265854, 0.06646643579006195, -0.04589851200580597, -0.006213030777871609, -0.06043104827404022, -0.01015190314501524, 0.02262885309755802, 0.003660062327980995, 0.022585248574614525, 0.02166733331978321, 0.06567391753196716, 0.015607836656272411, 0.009166115894913673, 0.021286681294441223, -0.01206413097679615, -0.03391915559768677, 0.04767339304089546, 0.022239631041884422, 0.0186676736921072, -0.027258355170488358, 0.027732208371162415, -0.006523631978780031, -0.018439652398228645, -0.049396391957998276, -0.03163345903158188, 0.009031427092850208, -0.04531993344426155, 0.04168481379747391, 0.07369372248649597, -0.0213736854493618, -0.06286493688821793, -0.019804954528808594, 0.0014777041506022215, -0.04594047740101814, -0.006110127083957195, 0.014001572504639626, 0.003166917013004422, -0.004344311077147722, 0.01979881152510643, -0.02204635739326477, -0.04010356217622757, -0.00598213030025363, 0.04344548285007477, -0.008878751657903194, -0.049643758684396744, -0.12176612764596939, -0.013272139243781567, -0.024608999490737915, -0.04617917537689209, 0.007150623481720686, -0.04449775815010071, 0.030607590451836586, -0.037487372756004333, 0.08241700381040573, 0.052748166024684906, -0.062068864703178406, -0.045863743871450424, -0.040851738303899765, 0.02802382968366146, -0.03433741256594658, -0.028436236083507538, 0.019226612523198128, -0.04660359025001526, -0.00861297082155943, -0.07961571216583252, -0.06419836729764938, -0.0017733493587002158, -0.0024086127523332834, -0.028222322463989258, -0.03761179372668266, -0.0056339590810239315, 0.053131889551877975, -0.016182225197553635, -0.04607883468270302, -0.04324328526854515, 0.005347989499568939, 0.0649358406662941, 0.0009943322511389852, -0.007174686994403601, -0.020931679755449295, 0.011352763511240482, 0.04135260730981827, 0.029331574216485023, -0.026871591806411743, -0.017917409539222717, 0.0375029481947422, -0.0021428177133202553, 0.0722382441163063, 0.0012903449824079871, 0.003621121635660529, 0.009250099770724773, 0.04360689967870712, -0.0004525354306679219, -0.026668500155210495, -0.0063553438521921635, -0.03523262217640877, -0.018314581364393234, 0.016804806888103485, -0.04284052550792694, 0.03887270390987396, 0.06928262859582901, -0.027617676183581352, -0.10786374658346176, 0.0022246602457016706, 0.01628844067454338, 0.005994969978928566, 0.04595674201846123, -0.03378388658165932, 0.012190754525363445, -0.014088700525462627, -0.0038656063843518496, -0.012746523134410381, 0.004772924352437258, -0.01987532339990139, 0.02828678861260414, 0.060366518795490265, 0.005043551791459322, -0.039259184151887894, -0.027922209352254868, 0.02970755472779274, -0.023631654679775238, -0.00954422540962696, 0.025764225050807, 0.04885553568601608, 0.037445127964019775, -0.0011454552877694368, -0.015926145017147064, 0.029688909649848938, -0.008911470882594585, -0.04962291941046715, 0.016011876985430717, -0.012713124975562096, 0.027596820145845413, -0.03301067650318146, 0.0005410274607129395, 0.07092736661434174, -0.016704566776752472, -0.04941552132368088, 0.009818286634981632, 0.08277123421430588, 0.016212688758969307, -0.014320585876703262, -0.025358226150274277, -0.003031875006854534, -0.02729410119354725, 0.0028493229765444994, -0.02208692580461502, -0.011122229509055614, 0.04459688812494278, -0.02409716323018074, 0.03255293890833855, -0.0264740027487278, -0.05542784556746483, 0.017819587141275406, -0.034359391778707504, -0.03919408842921257, 0.05442915856838226, -0.058804042637348175, 0.001469647977501154, 0.0570610836148262, 0.030694959685206413, -0.04063422977924347, 0.03859672322869301, -0.0763273686170578, -0.0443585142493248, 0.017886603251099586, 0.015854395925998688, 0.003494731616228819, 0.0357714481651783, -0.030667729675769806, 0.0063279601745307446, -0.06202559918165207, 0.03590754419565201, 0.010697461664676666, -0.05234412103891373, -0.009641476906836033, 0.023142045363783836, -0.04669557139277458, 0.011542044579982758, -0.025386996567249298, 0.012827594764530659, -0.007248125039041042, 0.034703753888607025, -0.0013127867132425308, 0.05688684061169624, -0.03601109981536865, 0.02383345551788807, -0.009845543652772903, 0.0350886732339859, 0.011417228728532791, -0.0014797114999964833, -0.04290356487035751, -0.0334707647562027, 0.016143249347805977, -0.026454344391822815, 0.008267376571893692, -0.053665634244680405, -0.002933894284069538, 0.012691647745668888, -0.02310340851545334, -0.006941626779735088, -0.05089915543794632, 0.09037233144044876, -0.0065603978000581264, 0.04493512958288193, -0.058815762400627136, -0.06275878101587296, 0.06932301819324493, -0.04177314043045044, 0.0044350759126245975, 0.031222134828567505, -0.037791669368743896, 0.02285340428352356, -0.047255922108888626, -0.034897658973932266, 0.005082149989902973, 0.04391913115978241, 0.01819455809891224, 0.02554125152528286, 0.02231878973543644, -0.0024250776041299105, 0.048491254448890686, -0.032984837889671326, -0.05577395111322403, 0.009850767441093922, -0.016014227643609047, 0.0017598061822354794, -0.017990969121456146, 0.03427090123295784, 0.036032646894454956, -0.05121183767914772, -0.018013935536146164, 0.006699871737509966, 0.0073770093731582165, -0.0218514334410429, -0.0035433080047369003, -0.02773512527346611, -0.034308530390262604, 0.03936833143234253, 0.0459124930202961, -0.0038101437967270613, -0.017106836661696434, 0.0464002825319767, 0.025758806616067886, -0.02805270627140999, -0.0821443498134613, 0.0009772724006325006, -0.06815565377473831, 0.01786160096526146, -0.008745912462472916, -0.01831016130745411, -0.03959822654724121, -0.01883023791015148, -0.03075465001165867, -0.055347174406051636, -0.03698970749974251, 0.03563212230801582, 0.04072649031877518, -0.04875189810991287, 0.022670865058898926, -0.021019969135522842, -0.010380429215729237, 0.0032992837950587273, -0.0008157404372468591, 0.021133383736014366, 0.06369426846504211, 0.036101482808589935, -0.04737597331404686, 0.009926458820700645, -0.03407502919435501, -0.013923990540206432, -0.018282920122146606, -0.016134388744831085, -0.02609286643564701, 0.008430047892034054, 0.0012859416892752051, 0.03309497609734535, 0.026349587365984917, -0.014123116619884968, -0.027783386409282684, -0.0031335277017205954, 0.07756909728050232, -0.03193631023168564, -0.0012227962724864483, -0.030870255082845688, -0.02540774829685688, -0.005681248381733894, 0.011821446940302849, -0.048775408416986465, 0.04101497679948807, -0.06980302184820175, -0.006557516288012266, -0.041456691920757294, -0.049805622547864914, 0.03763201832771301, -0.02295357547700405, -0.024317195639014244, -0.018052643164992332, -0.06321826577186584, -0.008339756168425083, 0.025818495079874992, 0.0377872996032238, 0.008055119775235653, -0.030959224328398705, 0.0512482114136219, 0.054326534271240234, -0.04799927398562431, -0.03474155068397522, 0.039714135229587555, 0.00020064043928869069, -0.02751145511865616, 0.014705010689795017, 0.04436548799276352, -0.03441131114959717, -0.0006974104908294976, -0.06099732220172882, -0.0011395395267754793, -0.024425199255347252, 0.017809320241212845, 0.0682615339756012, 0.006278422195464373, -0.005536058451980352, -0.03892596811056137, -0.007607805076986551, 0.026427416130900383, -0.03608522564172745, 0.023636488243937492, 0.0010004752548411489, 0.07728713750839233, 0.006507700774818659, 0.025295114144682884, 0.01393660344183445, -0.07014460861682892, 0.02731880359351635, -0.008106821216642857, -0.027721358463168144, -0.04097050428390503, 0.02042279578745365, -0.0001301504671573639, -0.01604572869837284, 0.016972996294498444, 0.04183869808912277, 0.002969579305499792, -0.08002778887748718, -0.011472366750240326, -0.016507120802998543, 0.014678262174129486, -0.09378670156002045, 0.10686591267585754, 0.019167684018611908, 0.008125516586005688, 0.07120081782341003, 0.0063572833314538, 0.05445697531104088, -0.035041917115449905, 0.06541293114423752, 0.05347122624516487, -0.0035065640695393085, 0.0063226670026779175, 0.00930878147482872, 0.03725201636552811, -0.005343790166079998, -0.01453916821628809, 0.030412936583161354, 0.02048139087855816, 0.004663878120481968, 0.029983118176460266, 0.014337757602334023, 0.017108993604779243, -0.02503165230154991, -0.0027128676883876324, -0.017389319837093353, -0.08910822123289108, -0.002539682202041149, 0.07829706370830536, 0.042996153235435486, 0.0036338481586426497, -0.03884261101484299, -0.05961665138602257, 0.02163298800587654, -0.014872854575514793, 0.0263366661965847, 0.0022052626591175795, 0.023446304723620415, 0.061649173498153687, 0.021652406081557274, 0.0004595612990669906, 0.010551340878009796, 0.023884981870651245, 0.023547640070319176, 0.052516721189022064, 0.009748345240950584, 0.0278931874781847, -0.05228012427687645, 0.0008628853247500956, 0.04806758463382721, 0.06053340062499046, 0.01101086288690567, -0.012554828077554703, 0.041264377534389496, -0.01862582191824913, 0.0307808518409729, 0.03245437890291214, 0.00282341823913157, -0.03008037805557251, 0.03860868141055107, -0.036432694643735886, -0.012255443260073662, -0.039731498807668686, -0.03840527683496475, -0.06067325174808502, 0.037480514496564865, 0.028192726895213127, 0.005396051798015833, -5.003115178740819e-33, 0.010722163133323193, -0.03259165585041046, -0.006273624021559954, -0.08918527513742447, -0.03324686363339424, 0.0030429475009441376, 0.00054752646246925, -0.02656550705432892, -0.007906848564743996, 0.025134682655334473, -0.030206356197595596, -0.005920012015849352, 0.007332062814384699, 0.006834874395281076, 0.02750365622341633, -0.024280574172735214, 0.048210352659225464, -0.04875638335943222, 0.035375673323869705, 0.01573428139090538, 0.023103320971131325, 0.02743484452366829, 0.015757963061332703, 0.029744800180196762, -0.01379105169326067, 0.009569303132593632, -0.006949546746909618, 0.06331077218055725, -0.037901345640420914, 0.014172988012433052, -0.01947951503098011, -0.039250295609235764, 0.008363299071788788, -0.03349324315786362, -0.058490924537181854, 0.03646927699446678, -0.01920388638973236, -0.056710511445999146, -0.06381646543741226, 0.04239600896835327, -0.08881110697984695, -0.016469808295369148, 0.06598399579524994, 0.034241098910570145, -0.04505929723381996, 0.029633644968271255, 0.003475896781310439, 0.008114593103528023, 0.027010608464479446, -0.015964778140187263, 0.04697022587060928, 0.015998883172869682, 0.010799961164593697, -0.045944035053253174, 0.06906472146511078, 0.044477637857198715, -0.030068522319197655, -0.0057773529551923275, -0.015405857004225254, -0.06728868931531906, -0.02828642539680004, 3.894592009601183e-05, -0.01468399167060852, 0.04729524254798889, 0.06435845047235489, 0.010722845792770386, 0.031480394303798676, -0.021602829918265343, 0.01502608135342598, 0.029401017352938652, -0.018944313749670982, 0.11074341833591461, 0.04818100482225418, -0.0051386295817792416, 0.05132691562175751, 0.011079778894782066, -0.0069597079418599606, 0.006111462134867907, -0.037714045494794846, 0.08854199945926666, 0.011480214074254036, 0.009904191829264164, -0.009288047440350056, 0.02569129690527916, 0.04201187193393707, -0.027525857090950012, 0.025070277974009514, 0.013911563903093338, 0.014919277280569077, 0.008783564902842045, 0.014094389043748379, -0.0217483788728714, 0.04001228138804436, -0.0687326043844223, 0.08574974536895752, 0.0010564684635028243, 0.002362537197768688, 0.042676251381635666, 0.0031926806550472975, 0.0036502720322459936, -0.07282224297523499, -0.027197521179914474, -0.00032457595807500184, -0.026658110320568085, -0.0030520956497639418, 0.039992786943912506, -0.039790283888578415, 0.022003700956702232, 0.029749883338809013, -0.007031372748315334, -0.007289055269211531, 0.009961115196347237, 0.03884746506810188, 0.040705177932977676, 0.057540878653526306, -0.03556229546666145, 0.0008252557599917054, 0.06424592435359955, 0.0029569249600172043, -0.05697249248623848, 0.007697191089391708, -0.024796079844236374, 0.017826324328780174, 0.01250778790563345, -0.034486912190914154, -0.02627432346343994, -0.0604347363114357, 0.04117339104413986, -0.007352007087320089, -0.03819713369011879, 0.0006346976151689887, 0.03225114569067955, 2.7790633794211317e-07, -0.04472324252128601, -0.013202408328652382, 0.0589902438223362, 0.018691081553697586, 0.002460326999425888, 0.026849182322621346, 0.017111491411924362, 0.06403344869613647, -0.073707215487957, -0.02267640270292759, 0.04460536316037178, -0.008394409902393818, -0.013927068561315536, -0.03163570165634155, -0.08372540026903152, -0.031178388744592667, -0.010887952521443367, 0.027277257293462753, -0.029721850529313087, -0.03165503218770027, 0.03180249407887459, 0.05446795001626015, 0.03014783002436161, 0.04146294295787811, 0.06168484687805176, 0.030944863334298134, -0.005538485944271088, -0.014211725443601608, 0.05186088755726814, -0.016235211864113808, 0.06828709691762924, 0.02437274158000946, 0.00780212739482522, -0.030521947890520096, -0.014385264366865158, 0.06530220061540604, 0.0047454191371798515, 0.08142571151256561, 0.013205974362790585, -0.07339560240507126, 0.009949847124516964, -0.0011912191985175014, 0.022568969056010246, 0.013574413023889065, 0.05545604228973389, -0.03825885057449341, -0.004953957162797451, -0.015775201842188835, 0.009857309982180595, -0.00220827991142869, 0.00034870594390667975, 0.04600288346409798, 0.018649980425834656, -0.027277441695332527, -0.0012657264014706016, -0.028593052178621292, -0.025362566113471985, -0.05006631463766098, 0.024558035656809807, 0.015409376472234726, -0.06256429105997086, -0.023114047944545746, 0.00794497225433588, -0.027645450085401535, 0.0185255017131567, -0.03229302540421486, -0.06264863163232803, 2.3531169892680365e-34, -0.043301500380039215, -0.001660670037381351, 0.0011766229290515184, 0.05661686137318611, -0.028562935069203377, 0.007220553699880838, 0.013859227299690247, 0.02527056820690632, 0.03660977631807327, -0.0009444690076634288, -0.05147132650017738]

['Gregory Farquhar', 'Tim Rocktäschel', 'Maximilian Igl', 'Shimon Whiteson']

1710.11417v2

Combining deep model-free reinforcement learning with on-line planning is a promising approach to building on the successes of deep RL. On-line planning with look-ahead trees has proven successful in environments where transition models are known a priori. However, in complex environments where transition models need to be learned from data, the deficiencies of learned models have limited their utility for planning. To address these challenges, we propose TreeQN, a differentiable, recursive, tree-structured model that serves as a drop-in replacement for any value function network in deep RL with discrete actions. TreeQN dynamically constructs a tree by recursively applying a transition model in a learned abstract state space and then aggregating predicted rewards and state-values using a tree backup to estimate Q-values. We also propose ATreeC, an actor-critic variant that augments TreeQN with a softmax layer to form a stochastic policy network. Both approaches are trained end-to-end, such that the learned model is optimised for its actual use in the tree. We show that TreeQN and ATreeC outperform n-step DQN and A2C on a box-pushing task, as well as n-step DQN and value prediction networks (Oh et al. 2017) on multiple Atari games. Furthermore, we present ablation studies that demonstrate the effect of different auxiliary losses on learning transition models.

TreeQN and ATreeC: Differentiable Tree-Structured Models for Deep Reinforcement Learning

http://arxiv.org/pdf/1710.11417v2

Title TreeQN ATreeC Differentiable TreeStructured Models Deep Reinforcement Learning Summary Combining deep modelfree reinforcement learning online planning promising approach building success deep RL Online planning lookahead tree proven successful environment transition model known priori However complex environment transition model need learned data deficiency learned model limited utility planning address challenge propose TreeQN differentiable recursive treestructured model serf dropin replacement value function network deep RL discrete action TreeQN dynamically construct tree recursively applying transition model learned abstract state space aggregating predicted reward statevalues using tree backup estimate Qvalues also propose ATreeC actorcritic variant augments TreeQN softmax layer form stochastic policy network approach trained endtoend learned model optimised actual use tree show TreeQN ATreeC outperform nstep DQN A2C boxpushing task well nstep DQN value prediction network Oh et al 2017 multiple Atari game Furthermore present ablation study demonstrate effect different auxiliary loss learning transition model Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01316402293741703, 0.05500173568725586, -0.01709579862654209, -0.011896061711013317, 0.011172867380082607, -0.028798716142773628, -0.027678873389959335, -0.033178865909576416, -0.0897672027349472, 0.03314647823572159, -0.01905691996216774, 0.04594454914331436, -0.013976276852190495, 0.09259748458862305, -0.02823040634393692, -0.04811405390501022, 0.014418493025004864, -0.020454393699765205, 0.009714450687170029, 0.00665325578302145, 0.006376389879733324, -0.02524893544614315, 0.011220214888453484, 0.024400651454925537, -0.017069872468709946, -0.028975829482078552, -0.07300082594156265, 0.009559551253914833, 0.02669318951666355, -0.10974527150392532, 0.06187072768807411, -0.04063085839152336, 0.02688501961529255, 0.037311844527721405, 2.499215042917058e-06, -0.014352608472108841, -0.04441729560494423, -0.04387463256716728, -0.02660377509891987, -0.06379099935293198, -0.021189361810684204, 0.008499334566295147, -0.02366100437939167, 0.02870815619826317, -0.034925058484077454, -0.060933202505111694, 0.05658379942178726, 0.053683556616306305, 0.024348057806491852, 0.06436561048030853, 0.007132934872061014, -0.05201410502195358, 0.02186226285994053, -0.016609609127044678, -0.014238082803785801, -0.060841504484415054, 0.026247963309288025, 0.0054502785205841064, -0.0198858380317688, -0.022903643548488617, -0.03703626990318298, -0.023633791133761406, 0.045094046741724014, -0.0329861156642437, -0.0006519826129078865, 0.03430164232850075, 0.011379961855709553, -0.02396611124277115, -0.025257349014282227, 0.024091629311442375, -0.10133696347475052, 0.014571270905435085, 0.05606049299240112, -0.032175227999687195, -0.004909995477646589, -0.056844670325517654, -0.014463036321103573, 0.07220830768346786, -0.006125079933553934, -0.004694508388638496, 0.0020430898293852806, 0.04154488444328308, -0.013677175156772137, 0.015342826955020428, 0.028810987249016762, 0.057707350701093674, -0.05552862212061882, -0.015328849665820599, 0.0147025715559721, -0.012862683273851871, 0.00914211105555296, -0.03952938690781593, -0.01426597498357296, 0.01796196959912777, -0.0776386708021164, 0.002510853810235858, -0.0077051701955497265, 0.02287413738667965, -0.021712010726332664, -0.015246293507516384, 0.06991683691740036, -0.021991193294525146, 0.016262179240584373, 0.017219670116901398, -0.0384330116212368, 0.0702858567237854, -0.023915618658065796, -0.00796933937817812, -0.008287429809570312, 0.04511446878314018, -0.06853482127189636, -0.004689872730523348, -0.05632670968770981, 0.07560078054666519, -0.04569074511528015, -0.036409892141819, 0.0005086914752610028, 0.003863157005980611, -0.03483925387263298, -0.006154460366815329, 0.026594379916787148, 0.07929013669490814, -0.04181882366538048, 0.0012778369709849358, -0.04112203046679497, -0.012676914222538471, -0.056427501142024994, 0.018074212595820427, 0.019909676164388657, 0.025474989786744118, 0.020029360428452492, 0.01450286339968443, -0.019962556660175323, 0.00789528526365757, 0.016663461923599243, 0.09282171726226807, -0.004265087656676769, 0.07223895937204361, -0.02007296308875084, -0.028516285121440887, 0.0166032575070858, 0.002551053185015917, 0.05244666710495949, -0.051536887884140015, -0.037243086844682693, -0.07910723239183426, -0.009100109338760376, 0.047550834715366364, 0.021538322791457176, 0.010174350813031197, 0.038866378366947174, 0.029880885034799576, 0.016976257786154747, 0.024329373612999916, 0.02587384730577469, -0.014804191887378693, -0.032722506672143936, 0.06155375763773918, 0.06212633475661278, 0.050039272755384445, -0.017834415659308434, 0.02737872675061226, 0.0059295236133039, -0.0064169252291321754, -0.03610096871852875, -0.024588119238615036, 0.014264359138906002, -0.03450183570384979, -0.03597240149974823, 0.07958179712295532, 0.009674587287008762, -0.04459352046251297, -0.03559575602412224, -0.010440846905112267, 0.023000266402959824, -0.03031240403652191, 0.0596296489238739, 0.02167091891169548, -0.003814785275608301, 0.003238838165998459, -0.05925632268190384, -0.079142726957798, -0.02335129678249359, 0.07346136122941971, 0.0028070404659956694, -0.008032725192606449, -0.12160138040781021, -0.001841897377744317, -0.01026308722794056, -0.031034626066684723, 0.04375842958688736, -0.014394223690032959, 0.02140290103852749, -0.024908166378736496, 0.01902209222316742, 0.04241795465350151, -0.05894653499126434, -0.0609307698905468, -0.037542425096035004, 0.05539131909608841, -0.04162150248885155, -0.0663742944598198, 0.0214383527636528, -0.05128220468759537, -0.01642371341586113, -0.03940753638744354, -0.04436315968632698, -0.028235409408807755, -0.04120747745037079, 0.03190353140234947, -0.0009059980511665344, -0.047170110046863556, 0.04838511347770691, -0.014643228612840176, -0.028171159327030182, -0.02289263717830181, 0.01852118782699108, 0.06980464607477188, -0.00899962242692709, -0.007172089070081711, -0.025921985507011414, 0.04595009237527847, 0.0025169358123093843, 0.034662339836359024, -0.05000634491443634, -0.024454953148961067, 0.055390939116477966, -0.00984534714370966, 0.03759882599115372, -0.04780988022685051, 0.020028352737426758, -0.002742352895438671, 0.009053748100996017, -0.009543577209115028, -0.059807874262332916, -0.02286306582391262, -0.0603104867041111, -0.037120215594768524, 0.008898700587451458, -0.02038470096886158, 0.04564504325389862, 0.04997383430600166, -0.017934590578079224, -0.05183480679988861, -0.01900642178952694, -0.020569438114762306, 0.005763157270848751, 0.023688247427344322, 0.027202876284718513, 0.02263050340116024, -0.03185243159532547, -0.01111034769564867, 0.05001882463693619, 0.0030720094218850136, -0.04062027484178543, -0.020051274448633194, -0.0014086754526942968, 0.03393758833408356, -0.041078630834817886, 0.014895714819431305, 0.0056129577569663525, -0.05838862061500549, -0.035208698362112045, 0.03492922708392143, 0.07725794613361359, -0.037994347512722015, 0.012019893154501915, 0.006768384482711554, 0.01756744086742401, -0.03182165324687958, -0.008668825961649418, 0.011467773467302322, -0.014426618814468384, -0.004237170796841383, -0.02341623790562153, -0.02301912009716034, 0.0355258546769619, -0.032399363815784454, -0.010531212203204632, 0.03226470574736595, 0.017379967495799065, 0.013024462386965752, -0.02770061604678631, -0.015550399199128151, -0.009622326120734215, -0.011275564320385456, -0.009333336725831032, -0.07468956708908081, 0.00251016509719193, -0.006177074741572142, -0.0058136857114732265, 0.029635537415742874, -0.010472684167325497, -0.019471798092126846, -0.0014920830726623535, -0.021901480853557587, 0.011193052865564823, 0.06040969491004944, -0.012046808376908302, 0.020518314093351364, 0.011776706203818321, 0.004512947052717209, -0.039598867297172546, 0.05826956033706665, -0.008948986418545246, -0.033504027873277664, -0.00948317814618349, 0.011506550014019012, 0.026767786592245102, 0.07237767428159714, -0.03485419973731041, 0.04868980124592781, -0.0653553456068039, -0.006213682238012552, 0.0200777817517519, -0.03574823588132858, 0.0005518480320461094, 0.007267207372933626, -0.022659985348582268, 0.006821202579885721, -0.039931584149599075, -0.023261886090040207, 0.03905526176095009, 0.045223087072372437, -0.036639925092458725, -0.0007733213133178651, -0.012295483611524105, -0.008385402150452137, 0.05428558588027954, 0.02981412783265114, 0.012485170736908913, -0.0021296702325344086, -0.028421659022569656, -0.04755517095327377, 0.0022994226310402155, 0.010126732289791107, -0.01448359340429306, -0.047723788768053055, -0.028088312596082687, -0.018093837425112724, -0.020208705216646194, -0.03567880764603615, -0.016048088669776917, 0.02501513808965683, -0.006256448570638895, 0.023405613377690315, -0.032206255942583084, -0.0372297503054142, 0.013355927541851997, -0.034424688667058945, 0.007326791994273663, 0.06413647532463074, -0.04491189122200012, -0.007023884914815426, -0.003070665756240487, 0.017621057108044624, 0.06986453384160995, 0.017089026048779488, 0.004970645997673273, -0.012732317671179771, 0.08859480172395706, -0.010946390219032764, 0.0040741912089288235, -0.007413859013468027, -0.05837944522500038, 0.01910327933728695, -0.0052605485543608665, -0.012832260690629482, -0.04492548853158951, 0.05296711623668671, 0.006515756715089083, -0.06745260953903198, -0.03447894752025604, -0.005689391866326332, -0.02010972797870636, -0.03335728868842125, -0.012097044847905636, -0.052853893488645554, 0.04974135011434555, 0.006100945640355349, 0.036654144525527954, -0.05272247642278671, -0.02398809790611267, 0.004043281078338623, -0.0024237600155174732, 0.00032583053689450026, -0.036291949450969696, 0.011699431575834751, -0.12986642122268677, 0.030445531010627747, -0.04344836249947548, -0.07793319225311279, -0.02659136988222599, 0.007854842580854893, -0.016857540234923363, -0.01830390840768814, -0.062375105917453766, 0.03553003817796707, 0.01838156208395958, -0.024904435500502586, 0.039983123540878296, -0.04285662993788719, 0.0597320981323719, 0.009210742078721523, -0.027049057185649872, 0.01990734040737152, 0.13573674857616425, 0.04537865146994591, -0.022018559277057648, 0.020335141569375992, -0.009152759797871113, 0.013451255857944489, 0.004908343777060509, -0.0022120876237750053, 0.015000119805335999, 0.029304979369044304, 0.021123813465237617, 0.039243195205926895, 0.03549472242593765, 0.04196247458457947, 0.007706885226070881, 0.051734913140535355, 0.07011599838733673, 0.003861016593873501, -0.07475899159908295, -0.03664344549179077, -0.020282212644815445, 0.052766475826501846, -0.028283732011914253, -0.0744575783610344, 0.008959558792412281, -0.0883590430021286, -0.01847582869231701, 0.007788846269249916, -0.039775263518095016, 0.0038346927613019943, 0.0013687820173799992, 0.002340615727007389, -0.0010848105885088444, -0.06917113810777664, 0.004070573952049017, -0.008361194282770157, 0.044565409421920776, -0.00678636459633708, -0.03474164381623268, -0.0021079452708363533, 0.04665057733654976, 0.004033355507999659, -0.04332474246621132, 0.00971061922609806, 0.004695062059909105, -0.0024069782812148333, 0.05367521941661835, 0.036735787987709045, -0.026497280225157738, 0.017607025802135468, -0.03988368436694145, -0.013548478484153748, -0.021596180275082588, 0.0027530186343938112, 0.06579362601041794, 0.004735251422971487, 0.0074813771061599255, -0.007385134696960449, 0.0067837475799024105, 0.053234729915857315, -0.029521996155381203, 0.005085580982267857, -0.01864258199930191, 0.08985459059476852, 0.038164976984262466, -0.014893126673996449, 0.04147843271493912, -0.06688182801008224, 0.04505927860736847, -0.008330713026225567, 0.026265984401106834, -0.003211496165022254, 0.0629630982875824, 0.0074106245301663876, -0.0485164076089859, 0.025436852127313614, 0.03469491004943848, -0.04734106734395027, 0.01489491481333971, 0.01919126696884632, 0.028062084689736366, 0.0031530370470136404, -0.044012926518917084, 0.041495248675346375, 0.015184598043560982, 0.020312495529651642, 0.060103364288806915, -0.006276065018028021, 0.09489992260932922, -0.04396171122789383, 0.017740419134497643, 0.01627705805003643, 0.08073120564222336, 0.0519862025976181, -0.008122502826154232, 0.03492666408419609, 0.018205489963293076, 0.0041399369947612286, 0.038407884538173676, 0.05123787745833397, 0.035786911845207214, 0.024377573281526566, 0.020629458129405975, 0.027890615165233612, 0.000665089872200042, -0.03384968265891075, 0.024729924276471138, -0.086114801466465, -0.018698470667004585, 0.02078772708773613, 0.028587287291884422, 0.003410039469599724, 0.00259012239985168, -0.031230106949806213, 0.030011199414730072, -0.0021490748040378094, -0.038742247968912125, -0.012728048488497734, -0.016931086778640747, 0.0329570434987545, 0.015844207257032394, -0.018616177141666412, -0.012594768777489662, 0.029994670301675797, 0.08548951894044876, 0.039737850427627563, -0.03208067640662193, 0.02528829500079155, 0.003298952942714095, 0.0056814635172486305, 0.01809564046561718, 0.04983239248394966, 0.01841123029589653, -0.031851448118686676, 0.014386001974344254, 0.0034671369940042496, 0.011223066598176956, 0.04484691098332405, 0.061216358095407486, -0.0006285856361500919, 0.032320354133844376, -0.04128379002213478, -0.015035883523523808, -0.014832988381385803, -0.03581956773996353, -0.039225924760103226, 0.009177656844258308, 0.011993804946541786, -0.08294077217578888, -6.117760064492791e-33, -0.0009981987532228231, -0.01315875444561243, 0.014048025012016296, -0.043228793889284134, -0.04666291922330856, 0.0002905474102590233, -0.022225337103009224, -0.028109146282076836, 0.015207610093057156, 0.046566396951675415, -0.018499502912163734, 0.0006993931601755321, 0.007308249827474356, 0.05142363905906677, 0.06028496474027634, -0.041918668895959854, 0.00743501540273428, -0.00568219693377614, -0.012388551607728004, 0.024306094273924828, -0.0050884741358459, 0.026888713240623474, 0.044405706226825714, 0.002581444103270769, -0.029878530651330948, 0.04714519530534744, -0.01179488841444254, 0.009406344033777714, -0.03630716726183891, 0.018742728978395462, 0.019830426201224327, -0.029107941314578056, 0.002640385879203677, -0.07173020392656326, -0.028266575187444687, 0.010886471718549728, -0.06112700700759888, -0.04403529316186905, -0.045019328594207764, -0.025820517912507057, -0.06279845535755157, 0.000604043947532773, 0.04684150964021683, 0.0392780676484108, 0.028244350105524063, -0.022598087787628174, 0.03274168819189072, 0.017020702362060547, 0.006821545772254467, -0.05357076972723007, -0.006716867443174124, 0.01090423483401537, -0.0031149869319051504, -0.019420888274908066, 0.01437399722635746, 0.037801407277584076, 0.002245224080979824, 0.01379002071917057, -0.008829254657030106, 0.014509876258671284, -0.04259973391890526, 0.01217851135879755, -0.01202025730162859, 0.06281336396932602, 0.06352335959672928, 0.027726558968424797, -0.012708396650850773, 0.019695326685905457, -0.009257386438548565, 0.0016697796527296305, -0.011582368053495884, 0.07631836831569672, 0.03359769657254219, -0.015857983380556107, 0.08804239332675934, 0.025133322924375534, -0.03337018936872482, 0.02260432206094265, 0.009286493994295597, 0.0887475311756134, -0.007805796805769205, 0.030970517545938492, 0.008966011926531792, 0.004539420362561941, 0.024609578773379326, -0.04117593169212341, 0.017516640946269035, -0.01235138438642025, 0.0347040556371212, 0.016441132873296738, 0.024260099977254868, -0.010060607455670834, 0.015990247949957848, -0.0159807987511158, 0.03769557550549507, 0.020823653787374496, -0.00019560998771339655, 0.040634892880916595, -0.0043410309590399265, 0.02951260842382908, -0.027530910447239876, -0.05577802658081055, -0.031113632023334503, -0.020435916259884834, 0.0038375717122107744, 0.03600049018859863, -0.028691699728369713, 0.03492056578397751, -0.00510324165225029, -0.004172287415713072, 0.015310434624552727, 0.0065925451926887035, -0.005129394121468067, 0.04406684637069702, 0.02605999819934368, -0.07815385609865189, -0.0034627176355570555, 0.060159832239151, 0.013830868527293205, -0.018515978008508682, -0.030045682564377785, -0.028908325359225273, -0.020423851907253265, -0.012345440685749054, -0.030328603461384773, -0.011320404708385468, -0.07820679992437363, -0.012616044841706753, -0.040376339107751846, -0.06361867487430573, 0.0065856254659593105, 0.022642677649855614, 3.136595410069276e-07, -0.05045618861913681, 0.004233001731336117, 0.023112336173653603, -0.014821682125329971, 0.0016848474042490125, 0.01694943569600582, 0.005479471292346716, 0.005728830583393574, -0.012821833603084087, -0.026291243731975555, 0.03411891311407089, -0.030894678086042404, 0.01748802699148655, 0.004229552578181028, -0.07048989087343216, -0.030685249716043472, -0.0857849195599556, 0.055083125829696655, -0.032347921282052994, -0.03799213469028473, -0.01908191107213497, 0.0908849909901619, 0.015139402821660042, 0.004478378687053919, 0.05384828895330429, 0.06900890171527863, -0.02744738571345806, 0.0027571311220526695, 0.04881108179688454, -0.02613026835024357, -0.0013347113272175193, -0.010519679635763168, -0.0321221686899662, -0.024325015023350716, -0.022259416058659554, 0.06373097002506256, -0.010803905315697193, 0.07104288041591644, 0.005731409881263971, -0.04729549214243889, 0.03130010515451431, -0.0078755347058177, 0.050673212856054306, 0.019615625962615013, 0.03356762230396271, -0.05815504863858223, 0.029016632586717606, -0.018356407061219215, -0.01328314933925867, 0.012055863626301289, 0.008443178609013557, -0.004309053532779217, -0.0011130424682050943, -0.025612546131014824, -0.00795400608330965, 0.0076043857261538506, -0.008637052960693836, -0.047707896679639816, -0.01097068190574646, 0.039694346487522125, -0.015173085033893585, 0.01905878446996212, -0.0503481924533844, 0.055934298783540726, -0.005685728508979082, -0.006097410339862108, -0.003133669262751937, 2.9288385360460317e-34, -0.04443735629320145, -0.017259348183870316, -0.029592648148536682, 0.021240370348095894, 0.0011815091129392385, 0.03121531754732132, 0.04339079558849335, 0.03104338049888611, 0.06121138855814934, 0.007710923906415701, -0.049705807119607925]

['Nan Rosemary Ke', 'Anirudh Goyal', 'Olexa Bilaniuk', 'Jonathan Binas', 'Laurent Charlin', 'Chris Pal', 'Yoshua Bengio']

1711.02326v1

A major drawback of backpropagation through time (BPTT) is the difficulty of learning long-term dependencies, coming from having to propagate credit information backwards through every single step of the forward computation. This makes BPTT both computationally impractical and biologically implausible. For this reason, full backpropagation through time is rarely used on long sequences, and truncated backpropagation through time is used as a heuristic. However, this usually leads to biased estimates of the gradient in which longer term dependencies are ignored. Addressing this issue, we propose an alternative algorithm, Sparse Attentive Backtracking, which might also be related to principles used by brains to learn long-term dependencies. Sparse Attentive Backtracking learns an attention mechanism over the hidden states of the past and selectively backpropagates through paths with high attention weights. This allows the model to learn long term dependencies while only backtracking for a small number of time steps, not just from the recent past but also from attended relevant past states.

Sparse Attentive Backtracking: Long-Range Credit Assignment in Recurrent Networks

http://arxiv.org/pdf/1711.02326v1

Title Sparse Attentive Backtracking LongRange Credit Assignment Recurrent Networks Summary major drawback backpropagation time BPTT difficulty learning longterm dependency coming propagate credit information backwards every single step forward computation make BPTT computationally impractical biologically implausible reason full backpropagation time rarely used long sequence truncated backpropagation time used heuristic However usually lead biased estimate gradient longer term dependency ignored Addressing issue propose alternative algorithm Sparse Attentive Backtracking might also related principle used brain learn longterm dependency Sparse Attentive Backtracking learns attention mechanism hidden state past selectively backpropagates path high attention weight allows model learn long term dependency backtracking small number time step recent past also attended relevant past state Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.029247580096125603, 0.01919320784509182, 0.0024480000138282776, 8.124144369503483e-05, 0.0074616107158362865, -0.012341553345322609, -0.01701655425131321, 0.028148027136921883, 0.015285437926650047, -0.01433069258928299, -0.00913965329527855, -0.04621945321559906, 0.04792526364326477, -0.0030442881397902966, 0.04588934779167175, -0.004698378033936024, 0.037145860493183136, 0.026709742844104767, -0.0016523755621165037, 0.027162108570337296, 0.013374784961342812, -0.028132570907473564, 0.012163208797574043, 0.005304956808686256, -0.021360022947192192, 0.009449531324207783, 0.019754812121391296, -0.06331315636634827, 0.08901650458574295, -0.06490975618362427, 0.023099713027477264, 0.0357673354446888, -0.005420570261776447, 0.04956650361418724, 2.418971689621685e-06, -0.015537510626018047, -0.02225945144891739, -0.07426919043064117, 0.008125088177621365, -0.01384198572486639, -0.08253917098045349, 0.06558720767498016, 0.03352351859211922, 0.012672295793890953, -0.05847464129328728, 0.02889617718756199, 0.02028082311153412, 0.04909207299351692, 0.009771314449608326, 0.014929580502212048, -0.010185342282056808, -0.04957325756549835, 0.010539427399635315, -0.053079623728990555, 0.06056114658713341, -0.010637613944709301, 0.040753331035375595, -0.040669381618499756, -0.040680889040231705, -0.039497144520282745, -0.021466875448822975, 0.042156629264354706, 0.030136283487081528, -0.012693899683654308, 0.1075032651424408, 0.07301484048366547, 0.062220197170972824, 0.029727788642048836, -0.032846372574567795, 0.07488199323415756, -0.03702423349022865, -0.0031206165440380573, 0.019612934440374374, -0.017922138795256615, -0.031375396996736526, -0.057292692363262177, -0.013399582356214523, -0.012561806477606297, -0.012033090926706791, 0.002417562296614051, 0.017027972266077995, 0.021733274683356285, 0.04757849872112274, 0.01305318996310234, 0.014408985152840614, 0.0018421128625050187, -0.02699173428118229, -0.03239091858267784, 0.010191967710852623, 0.021524198353290558, -0.0014454054180532694, -0.07657314091920853, 0.06157626211643219, 0.038578666746616364, 0.04641186073422432, -0.011155151762068272, 0.014413783326745033, -0.021293602883815765, 0.017860552296042442, 0.019057337194681168, 0.07533571124076843, -0.004175784066319466, -0.017523720860481262, 0.023720823228359222, -0.04243889078497887, 0.029600640758872032, -0.056358128786087036, -0.05768430605530739, 0.03225021809339523, 0.06557068973779678, -0.051638245582580566, 0.02042781002819538, -0.020213747397065163, 0.05656040832400322, 0.02042843960225582, -0.013982805423438549, -0.030966978520154953, -0.0318123921751976, -0.0370548777282238, -0.030244415625929832, 0.014032475650310516, 0.03200594708323479, -0.012905223295092583, 0.03967241197824478, -0.024636011570692062, 0.04306213557720184, -0.033897992223501205, 0.01057286374270916, -0.01262274757027626, 0.05291217565536499, -0.015478527173399925, -0.0016504874220117927, -0.01424118410795927, -0.04091283306479454, -0.00286150467582047, 0.0346408449113369, 0.042376089841127396, -0.012565838173031807, -0.08863575011491776, -0.031642716377973557, -0.030793268233537674, -0.06677312403917313, 0.026088600978255272, -0.058025479316711426, -0.010351531207561493, -0.00441501522436738, -0.04640904814004898, 0.00500723160803318, 0.018065087497234344, 0.006799329072237015, -0.05524042993783951, 0.0086444653570652, 0.024616986513137817, -0.03607400879263878, -0.007126288954168558, -0.012195232324302197, 0.04877842590212822, -0.02977263554930687, 0.052239615470170975, 0.08540554344654083, -0.04501693323254585, 0.014273806475102901, 0.02444680593907833, 0.006653976626694202, 0.058992329984903336, 0.0050710029900074005, 0.005987722892314196, -0.04097561910748482, -0.0009223868837580085, 0.009504207409918308, -0.0028239223174750805, 0.03635428100824356, -0.003456964623183012, 0.01383215468376875, 0.0540996752679348, -0.011583300307393074, 0.02030462585389614, 0.04768231511116028, -0.012638160027563572, -0.056607380509376526, -0.03172043338418007, -0.013413773849606514, -0.06729143112897873, 0.10707711428403854, -0.006178377661854029, -0.046859581023454666, 0.009395068511366844, -0.014571321196854115, -0.0049538942985236645, -0.0028030648827552795, 0.04635481908917427, -0.008225631900131702, -0.001638724934309721, -0.0036729401908814907, -0.005267815664410591, -0.014862964861094952, -0.05030122026801109, 0.002003180794417858, 0.022919924929738045, 0.007642142474651337, -0.021160680800676346, -0.02609727904200554, 0.051486074924468994, 0.04916595667600632, 0.022126510739326477, 0.02188575640320778, -0.012352466583251953, -0.07665941119194031, 0.009250735864043236, -0.007844997569918633, -0.027702877297997475, 0.011278609745204449, 0.012397919781506062, -0.05217211693525314, -0.03257317841053009, 0.05057387426495552, -0.026325004175305367, 0.07548843324184418, -0.01669386401772499, 0.020845646038651466, 0.016510894522070885, 0.08862392604351044, -0.028934583067893982, 0.0191000085324049, 0.01681515946984291, -0.06225551664829254, 0.03665420040488243, 0.03629251942038536, 0.024255819618701935, 0.04034276679158211, 0.07224141061306, -0.011916511692106724, 0.03525914251804352, -0.05258681997656822, -0.004020191263407469, -0.02814076468348503, -0.0742238238453865, -0.031352728605270386, 0.021213717758655548, -0.010051035322248936, -0.02086350880563259, 0.07077449560165405, 0.01664692535996437, -0.05952548608183861, 0.03570939972996712, -0.045315589755773544, 0.02270674519240856, -0.0013382429024204612, 0.024557901546359062, 0.0227724090218544, 0.02266734279692173, -0.0023155894596129656, 0.02634371630847454, -0.02658703178167343, 0.027443047612905502, -0.03201047703623772, -0.0014631692320108414, 0.020549822598695755, -0.0637451559305191, -0.0590156652033329, -0.05982059985399246, -0.010496124625205994, -0.048283349722623825, -0.01891573891043663, 0.02966989204287529, -0.008014632388949394, 0.018964186310768127, 0.010040458291769028, -0.012323915958404541, -0.001549955690279603, 0.006275290623307228, -0.0243871808052063, -0.02578536793589592, 0.04646407812833786, -0.015119999647140503, -0.04212743043899536, 0.06868233531713486, -0.010352624580264091, 0.0021438777912408113, 0.05792601779103279, 0.02870616316795349, -0.032553475350141525, -0.013725586235523224, -0.032219480723142624, -0.03469839692115784, -6.110942194936797e-05, 0.05831000581383705, -0.07118705660104752, -0.03564181178808212, -0.047535669058561325, 0.007254869677126408, 0.028677228838205338, -0.016231663525104523, -0.01947413757443428, -0.021015983074903488, 0.014432517811655998, 0.017841067165136337, 0.0716981515288353, -0.013508935458958149, -0.016360800713300705, -0.0029515891801565886, 0.007809107657521963, -0.0046139671467244625, 0.016695991158485413, -0.018469853326678276, 0.017039775848388672, -0.011095640249550343, -0.017867689952254295, -0.05375828221440315, 0.06156384199857712, -0.008190752007067204, 0.02515428140759468, -0.020168716087937355, -0.055400386452674866, 0.007392226718366146, -0.00919849518686533, 0.005405053496360779, -0.01714693196117878, -0.02520577982068062, 0.00700770178809762, -0.003292383858934045, -0.0043451241217553616, 0.07497723400592804, 0.027556410059332848, -0.004822573158890009, 0.02699599601328373, 0.009659568779170513, -0.012594174593687057, 0.030187003314495087, 0.017425118014216423, 0.009297667071223259, -0.01930796168744564, -0.039907537400722504, -0.004334204364567995, -0.027562564238905907, -0.01489342749118805, 0.03517613559961319, 0.028369486331939697, 0.04313671588897705, -0.013133962638676167, -0.015385773964226246, -0.039826709777116776, -0.033340707421302795, -0.014535661786794662, 0.0028076888993382454, -0.0016753895906731486, 0.0014953890349715948, -0.0004998535732738674, -0.06334927678108215, 0.006221056915819645, 0.006092398893088102, 0.010422426275908947, -0.03594105318188667, 0.015778597444295883, 0.01624487340450287, 0.008712834678590298, 0.022530965507030487, -0.005317555274814367, 0.016773998737335205, -0.003476288402453065, -0.0439930185675621, 0.03189302235841751, 0.04323352128267288, 0.015026319772005081, -0.015530896373093128, 0.019288918003439903, 0.006287803873419762, -0.03182986378669739, -0.023993758484721184, 0.021815789863467216, -0.01731783337891102, -0.08767350018024445, -0.019064150750637054, 0.04338880628347397, -0.01284244004637003, -0.14006006717681885, 0.0003990309196524322, -0.00043963422649540007, -0.019297784194350243, -0.005507880821824074, -0.0007808535010553896, -0.04439137130975723, -0.024429939687252045, -0.05381350591778755, 0.042500417679548264, -0.0068945265375077724, -0.06345026940107346, -0.011159016750752926, -0.06844677031040192, -0.009299283847212791, -0.017300795763731003, -0.036592818796634674, -0.029101161286234856, -0.07349105179309845, -0.017055021598935127, -0.02979750744998455, -0.06951738148927689, 0.0666961818933487, 0.017384519800543785, -0.012920130044221878, 0.015225449576973915, -0.05325598642230034, 0.06602810323238373, 0.07092059403657913, -0.0357942096889019, 0.014386187307536602, 0.05802574381232262, 0.052721042186021805, -0.02507207915186882, -0.016751009970903397, -0.03702156990766525, -0.027283042669296265, -0.02889181487262249, -0.020890023559331894, 0.042508453130722046, -0.03658837825059891, 0.0042573860846459866, -0.00839752983301878, 0.06182793155312538, -0.029211193323135376, 0.040312089025974274, 0.04495764896273613, 0.085837721824646, 0.009066803380846977, 0.009226098656654358, 2.276599479955621e-05, -0.015059995464980602, 0.047114983201026917, 0.027308577671647072, 0.025180721655488014, -0.022613780573010445, -0.040529876947402954, 0.002037819242104888, -0.036103133112192154, -0.053252942860126495, -0.00885198824107647, 0.003970128018409014, -0.006628416478633881, -0.09843452274799347, -0.07348739355802536, -0.0598038025200367, 0.01146456878632307, 0.04036557301878929, 0.04917775094509125, 0.029054513201117516, 0.04238376393914223, -0.05372842401266098, -0.03406086936593056, 0.01756099797785282, 0.0008135207463055849, 0.04692845046520233, -0.07350035756826401, -0.009041610173881054, -0.004994602873921394, -0.014558173716068268, 0.002230072859674692, -0.014396922662854195, -0.06459816545248032, -0.009492793120443821, 0.05684599280357361, 0.049463093280792236, 0.010284818708896637, 0.018423771485686302, -0.041651297360658646, -0.010579011403024197, 0.02152077667415142, -0.006291963160037994, 0.011120123788714409, 0.008732358925044537, 0.006706605199724436, 0.0200068149715662, 0.002568756230175495, 0.022868158295750618, -0.016371456906199455, 0.0559857152402401, 0.03673602640628815, 0.00014140705752652138, -0.02690832130610943, 0.007059402298182249, 0.00026300782337784767, 0.006993675604462624, 0.05367932841181755, -0.013818667270243168, -0.013829068280756474, -0.031954072415828705, 0.01802094653248787, -0.005327251739799976, 0.03946001082658768, -0.05559675395488739, -0.018953612074255943, 0.05656155198812485, 0.025737930089235306, 0.005549510475248098, -0.09514567255973816, -0.019421840086579323, -0.04906369000673294, -0.04472029581665993, 0.07367424666881561, -0.02248542383313179, 0.02071324922144413, 0.000877212849445641, 0.012031209655106068, -0.008134672418236732, -0.023173507302999496, 0.06679876148700714, 0.029216334223747253, -0.004336690995842218, 0.015454997308552265, 0.029497459530830383, 0.005589290522038937, -0.024596303701400757, 0.005196239799261093, -0.04792533069849014, 0.06178884953260422, -0.03320581465959549, -0.004078239668160677, 0.02796095795929432, -0.018244294449687004, 0.050982967019081116, 0.0015448705526068807, 0.031517304480075836, -0.009545581415295601, 0.047511905431747437, -0.07415953278541565, -0.025655535981059074, 0.021811485290527344, 0.003837242955341935, 0.0018830407643690705, 0.04397137463092804, 0.056388258934020996, 0.051446329802274704, 0.010041521862149239, 0.01842220313847065, 0.0002999921271111816, -0.0017394935712218285, -0.006529750302433968, -0.005297837313264608, 0.013026829808950424, -0.011044382117688656, 0.02137923799455166, -0.03404518589377403, -0.04983745515346527, 0.030176522210240364, -0.02501640096306801, 0.045409318059682846, -0.028995493426918983, 0.03426111489534378, -0.04361601173877716, 0.012742634862661362, -0.013114441186189651, -0.029149042442440987, 0.028359081596136093, 0.007943819276988506, -0.04126236215233803, -0.09758658707141876, -6.500433066853371e-33, -0.009903889149427414, -0.051508061587810516, -0.0012441694270819426, 0.028154592961072922, -0.07538026571273804, -0.015311427414417267, -0.056001927703619, -0.02131965011358261, 0.011103768832981586, -0.005580720491707325, -0.02657642774283886, 0.015252791345119476, 0.003170193638652563, 0.02141750417649746, 0.0726739838719368, 0.011892289854586124, 0.0072221169248223305, 0.017974624410271645, 0.02427179180085659, 0.04434262961149216, 0.04588446393609047, 0.06334986537694931, 0.07916714251041412, -0.06019328907132149, -0.004532790742814541, -0.001221527811139822, 0.0050146509893238544, 0.01504342071712017, 0.0014525841688737273, 0.053919997066259384, -0.0361504890024662, -0.005562848411500454, 0.024965206161141396, -0.06868507713079453, 0.02917415089905262, 0.04319768771529198, -0.07709626853466034, -0.033943820744752884, -0.041052334010601044, -0.026655299589037895, -0.007180334534496069, 0.003264316823333502, 0.03698675334453583, 0.008953766897320747, -0.016961000859737396, -0.0021395068615674973, 0.032587602734565735, -0.007700066082179546, -0.024165857583284378, 0.00880999956279993, -0.008533785119652748, 0.01800856553018093, -0.005548594519495964, -0.0049108583480119705, 0.002347091678529978, 0.008715859614312649, -0.03669070079922676, 0.025805234909057617, -0.06519617140293121, 0.03289059177041054, -0.006204688455909491, 0.04546716809272766, 0.021017488092184067, 0.00926836859434843, 0.005114489700645208, 0.012093017809092999, 0.009546012617647648, -0.007514261640608311, -0.042177461087703705, -0.01153904665261507, -0.04681636393070221, 0.0050393398851156235, 0.0832497701048851, -0.015102914534509182, 0.050883837044239044, -0.03866555914282799, -0.09124856442213058, -0.006478048861026764, 0.060096632689237595, 0.09651464223861694, 0.017978940159082413, 0.013116719201207161, -0.015143794007599354, -0.005338037386536598, 0.01929812878370285, -0.013043471612036228, -0.01357092522084713, -0.02128482051193714, 0.011037146672606468, -0.03057665377855301, 0.01816381886601448, 0.055687058717012405, 0.01645505055785179, -0.045959167182445526, -0.01672695390880108, 0.005937949754297733, 0.046333614736795425, 0.030088501051068306, 0.02743985876441002, 0.019975783303380013, -0.09251496940851212, 0.0008990722126327455, 0.005872116889804602, -0.003837171709164977, 0.034222930669784546, 0.02040226012468338, 0.06563235074281693, -0.006412846501916647, -0.021466517820954323, -0.028858600184321404, 0.00016157345089595765, -0.0008607347845099866, 0.022122221067547798, 0.054651033133268356, 0.02834535576403141, -0.0437002070248127, -0.0012793524656444788, 0.0522313266992569, 0.03315627574920654, 0.05591011419892311, -0.022326314821839333, -0.058575019240379333, 0.01601005531847477, 0.03554040566086769, -0.056801050901412964, -0.02158012054860592, -0.030853377655148506, 0.03376439958810806, -0.01079520769417286, -0.07204329967498779, -0.0062606860883533955, 0.038405027240514755, 3.0715699494976434e-07, -0.06282724440097809, 0.007969876751303673, -0.012487763538956642, -0.04437144845724106, 0.03569483757019043, -0.003389226971194148, -0.006867077201604843, 0.03862832486629486, -0.005715522449463606, 0.007146067451685667, 0.009660495445132256, -0.003867573104798794, 0.028881222009658813, -0.017611978575587273, -0.053252480924129486, -0.048278167843818665, -0.0558880940079689, -0.00538274273276329, -0.014713210053741932, -0.018298225477337837, -0.04108298197388649, 0.06737668067216873, 0.09083965420722961, -0.01506036426872015, 0.045520003885030746, -0.02155880071222782, -0.016807716339826584, 0.042786695063114166, -0.012591668404638767, -0.018340295180678368, 0.08266684412956238, -0.0006041785818524659, -0.05299918353557587, 0.0047755129635334015, -0.037345174700021744, 0.05418204143643379, -0.04496758058667183, 0.0024201511405408382, -0.05243842303752899, -0.06700966507196426, 0.007512073963880539, 0.030231866985559464, 0.04116945341229439, -0.008246741257607937, 0.011836672201752663, -0.06153605505824089, -0.021317144855856895, 0.03821547329425812, -0.011811013333499432, 0.013755794614553452, 0.03371419757604599, 0.0400431789457798, 0.01726650260388851, -0.02968602068722248, 0.00338696944527328, -0.03250734508037567, 0.013634135015308857, -0.0696135014295578, 0.004940396174788475, 0.0016538867494091392, -0.01711628958582878, -0.01351969689130783, 0.0005532627692446113, 0.010595981031656265, 0.03714796155691147, -0.048895463347435, -0.02702265977859497, 2.745498151516218e-34, 0.02801566570997238, -0.05955677852034569, 0.0066246227361261845, 0.011205586604773998, -0.005484992638230324, 0.013765441253781319, -0.004269096069037914, 0.02226710505783558, 0.051556676626205444, -0.05531981959939003, -0.08889651298522949]

['Anakha V Babu', 'Bipin Rajendran']

1711.03640v1

We study the performance of stochastically trained deep neural networks (DNNs) whose synaptic weights are implemented using emerging memristive devices that exhibit limited dynamic range, resolution, and variability in their programming characteristics. We show that a key device parameter to optimize the learning efficiency of DNNs is the variability in its programming characteristics. DNNs with such memristive synapses, even with dynamic range as low as $15$ and only $32$ discrete levels, when trained based on stochastic updates suffer less than $3\%$ loss in accuracy compared to floating point software baseline. We also study the performance of stochastic memristive DNNs when used as inference engines with noise corrupted data and find that if the device variability can be minimized, the relative degradation in performance for the Stochastic DNN is better than that of the software baseline. Hence, our study presents a new optimization corner for memristive devices for building large noise-immune deep learning systems.

Stochastic Deep Learning in Memristive Networks

http://arxiv.org/pdf/1711.03640v1

Title Stochastic Deep Learning Memristive Networks Summary study performance stochastically trained deep neural network DNNs whose synaptic weight implemented using emerging memristive device exhibit limited dynamic range resolution variability programming characteristic show key device parameter optimize learning efficiency DNNs variability programming characteristic DNNs memristive synapsis even dynamic range low 15 32 discrete level trained based stochastic update suffer le 3 loss accuracy compared floating point software baseline also study performance stochastic memristive DNNs used inference engine noise corrupted data find device variability minimized relative degradation performance Stochastic DNN better software baseline Hence study present new optimization corner memristive device building large noiseimmune deep learning system Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.05314948037266731, -0.009155993349850178, -0.050157349556684494, 0.04872630164027214, 0.005095598287880421, -0.02518356591463089, 0.0003099807072430849, -0.05767659470438957, 0.002156688831746578, 0.01658071018755436, -0.03266753628849983, -0.05126240849494934, -0.011261051520705223, 0.06419191509485245, 0.02200341783463955, -0.032919395714998245, 0.07109782099723816, 0.005490906070917845, -0.02134498581290245, -0.0430535227060318, 0.03438249230384827, -0.06872878223657608, -0.04327533394098282, -0.018364327028393745, -0.024112025275826454, 0.0016946790274232626, -0.03805578500032425, -0.00817711278796196, 0.015693094581365585, -0.05313938111066818, 0.0028579465579241514, -0.019088612869381905, -0.015877412632107735, 0.036950577050447464, 1.8801379155775066e-06, 0.016221726313233376, 0.017175475135445595, -0.010094991885125637, -0.0006264086696319282, -0.03319335728883743, -0.007559870835393667, 0.005379247944802046, -0.08483011275529861, 0.0018956575077027082, 0.010440217331051826, -0.03591851145029068, 0.05057434365153313, 0.014670254662632942, -0.04908958077430725, 0.043193504214286804, 0.005937234498560429, -0.021460652351379395, 0.08891589939594269, -0.01632167398929596, 0.018651194870471954, 0.007721512578427792, -0.03733087331056595, 0.018035119399428368, -0.045517612248659134, -0.024087363854050636, -0.029809514060616493, -0.005708449054509401, 0.07130391895771027, 0.001107928459532559, 0.00810286682099104, -0.016869455575942993, -0.005847413092851639, 0.057546112686395645, 0.019734960049390793, 0.048688896000385284, -0.009391577914357185, 0.05681745335459709, -0.02549804002046585, -0.010088917799293995, -0.031337201595306396, -0.045686062425374985, 0.013312739320099354, -0.0033836294896900654, -0.009320785291492939, 0.03419218212366104, -0.06450893729925156, 0.018550559878349304, 0.09374797344207764, 0.014475034549832344, 0.0013979418436065316, 0.03249039873480797, -0.01477118395268917, 0.037617359310388565, -0.025669774040579796, 0.015158496797084808, 0.005648601334542036, 0.01616544835269451, -0.023402182385325432, -0.009421867318451405, -0.012954271398484707, 0.007324493024498224, -0.08146048337221146, -0.0952388346195221, -0.029315976426005363, -0.0673941895365715, -0.031107565388083458, -0.005375958513468504, -0.003090290352702141, 0.0018829901237040758, -0.05384686589241028, -0.02295493148267269, -0.021103311330080032, 0.02708500809967518, -0.010633395053446293, -0.017663724720478058, 0.06258698552846909, 0.013670132495462894, 0.02649928256869316, 0.0794573724269867, 0.06517466902732849, -0.048524342477321625, -0.09330929815769196, 0.008528308011591434, -0.02129824459552765, -0.03862806782126427, -0.033377278596162796, -0.001242935424670577, 0.005317125469446182, -0.008269557729363441, -0.04358569532632828, -0.025857461616396904, 0.0160423181951046, 0.012988114729523659, 0.026195103302598, -0.003927362617105246, 0.013420674949884415, 0.002168084029108286, 0.011450941674411297, 0.02829454094171524, 0.0029111732728779316, 0.07408619672060013, -0.013104108162224293, 0.0061868950724601746, -0.10531572252511978, 0.05341161787509918, 0.012503399513661861, 0.03312240540981293, 0.00210198643617332, -0.06063929945230484, 0.025302141904830933, 0.0064163897186517715, -0.030074430629611015, -0.016140131279826164, 0.04779636859893799, 0.015515318140387535, -0.01956062950193882, 0.039406027644872665, -0.012007099576294422, -0.06090603396296501, 0.052541933953762054, -0.014060398563742638, -0.0182486679404974, 0.03924879804253578, 0.06695083528757095, 0.06612328439950943, 0.05876278132200241, -0.007589313667267561, -0.06904057413339615, -0.048190243542194366, 0.03219836577773094, -0.03568947687745094, -0.01539658010005951, -0.057432033121585846, -0.004856146406382322, 0.0176507867872715, 0.046957310289144516, 0.05358954146504402, -0.030606025829911232, -0.015377204865217209, 0.008228925056755543, -0.014333650469779968, 0.005244355648756027, 0.05306430160999298, -0.009518464095890522, -0.06035376340150833, -0.0010457418393343687, -0.03275994583964348, -0.023039113730192184, 0.07522121071815491, 0.0023572216741740704, -0.028510915115475655, 0.008446762338280678, -0.022558225318789482, -0.04329238086938858, -0.05255027487874031, -0.003936667460948229, -0.038138724863529205, 0.01856948435306549, 0.033227067440748215, 0.041778773069381714, -0.024323731660842896, 0.01953885145485401, 0.057238057255744934, -0.01704060100018978, 0.00926010962575674, -0.008081717416644096, -0.04708755016326904, 0.01766006089746952, -0.04635735601186752, 0.001037132227793336, -0.03329550847411156, -0.007065720856189728, 0.009559144265949726, -0.028913425281643867, -0.014074626378715038, -0.02742210403084755, 0.005640209652483463, 0.012654125690460205, -0.03259750455617905, 0.016046294942498207, -0.05338593199849129, 0.00036229367833584547, 0.03304889798164368, 0.03645789623260498, 0.03417104482650757, 0.030746059492230415, 0.06988140940666199, -0.02714594639837742, -0.02305866777896881, -0.004222692921757698, 0.0183425210416317, 0.06482547521591187, 0.012775507755577564, 0.04840170964598656, -0.030031675472855568, 0.023134874179959297, -0.026372559368610382, -0.027157247066497803, -0.04631783440709114, 0.011628740467131138, -0.007678915746510029, -0.10582710057497025, -0.011640477925539017, 0.019742075353860855, -0.0047205970622599125, 0.07286445796489716, -0.014388013631105423, 0.007371861487627029, -0.07764198631048203, 0.07759837806224823, -0.019448379054665565, 0.002477987902238965, -0.030920470133423805, -0.001142533728852868, 0.06326588988304138, 0.03613719716668129, 0.027000021189451218, 0.026293974369764328, -0.02876817248761654, -0.025615811347961426, 0.0010230564512312412, 0.0695355087518692, 0.04913405328989029, 0.009578624740242958, -0.07232492417097092, -0.04092692211270332, -0.010408511385321617, -0.007413019426167011, -0.05066409707069397, -0.0326261892914772, 0.024438507854938507, -0.008660073392093182, -0.0004912412841804326, 0.009135773405432701, -0.03730880841612816, 0.002822715323418379, -0.010722853243350983, -0.0055412063375115395, 0.034854255616664886, 0.009115010499954224, -0.022907322272658348, 0.0709703266620636, -0.04097652807831764, -0.03252704441547394, 0.015020053833723068, 0.012156185694038868, 0.043439239263534546, 0.011778227984905243, -0.060969315469264984, 0.01659947820007801, -0.0108664371073246, -0.02038576640188694, 0.012016348540782928, 0.00039441094850189984, 0.01934695988893509, 0.014355196617543697, 0.04204899072647095, -0.014718754217028618, -0.007314363960176706, 0.03686995804309845, 0.00780863082036376, -0.005968677811324596, 0.07380838692188263, 0.014112276025116444, 0.024271860718727112, 0.025048358365893364, 0.03168904781341553, 0.011407982558012009, 0.022574253380298615, 0.044786568731069565, 0.0765433982014656, -0.0053725470788776875, 0.02329131029546261, -0.06931354850530624, 0.017951946705579758, -0.024011047556996346, 0.03137120604515076, -0.015423242002725601, -0.006358542945235968, 0.028024926781654358, 0.0030757274944335222, 0.01930742710828781, 0.032378751784563065, 0.006019593682140112, 0.006613684818148613, 0.0016640746034681797, 0.022075703367590904, 0.030235368758440018, 0.018901392817497253, 0.01863512210547924, 0.013247378170490265, -0.03735704347491264, -0.006275638472288847, 0.014513332396745682, 0.03067462146282196, 0.055438801646232605, -0.034610193222761154, 0.011360708624124527, 0.008504261262714863, -0.02900235541164875, -0.0017485759453848004, -0.0023810574784874916, -0.003027246566489339, 0.03327306732535362, -0.00782932061702013, -0.03410567715764046, -0.0009966249344870448, 0.007728774566203356, 0.05667324364185333, -0.009781383909285069, 0.006724958308041096, 0.017402514815330505, -0.05186883732676506, 0.03151722997426987, 0.007247136440128088, 0.00586407957598567, -0.016993721947073936, 0.00529363052919507, -0.02130541019141674, -0.06076042726635933, 0.032088760286569595, 0.030450699850916862, -0.006536457687616348, 0.051713332533836365, 0.027490582317113876, 0.022188261151313782, -0.005076936446130276, -0.00209843460470438, 0.01002530101686716, -0.1190396100282669, -0.007121703587472439, 0.009913690388202667, 0.05891065299510956, 0.021876733750104904, -0.015526696108281612, -0.0030331509187817574, -0.03207094594836235, 0.0054593924432992935, -0.03805110603570938, -0.06129467114806175, -0.028635386377573013, -0.04631740599870682, -0.008684645406901836, -0.004142750520259142, -0.03680085763335228, 0.007330398075282574, -0.007612330839037895, -0.02227240428328514, -0.008569051511585712, 0.02369747683405876, -0.025190353393554688, 0.0047754691913723946, -0.02271682769060135, -0.05997195467352867, -0.003968897741287947, -0.016828065738081932, -0.03482133895158768, -0.004969401750713587, -0.0033171535469591618, -0.021882548928260803, -0.019121630117297173, 0.09512990713119507, 0.012261655181646347, 0.05024753510951996, -0.019764956086874008, -0.01084640808403492, -0.0670635774731636, 0.005473754368722439, 0.015561369247734547, -0.06839524209499359, 0.039085134863853455, 0.05357616767287254, -0.08868063986301422, -0.057262275367975235, -0.0008133779047057033, 0.030234549194574356, -0.0036155511625111103, 0.02579665742814541, 0.014831606298685074, 0.01303093321621418, 0.017898716032505035, -0.10215482860803604, -0.04784424975514412, -0.012300054542720318, 0.011089630424976349, -0.0020695242565125227, -0.05425574630498886, -0.012153279967606068, -0.012734604999423027, 0.01398297306150198, -0.008481751196086407, -0.006294241175055504, 0.014424407854676247, -0.028115853667259216, -0.016896862536668777, -0.036310430616140366, -0.06030918285250664, -0.020837577059864998, -0.010408114641904831, -0.07381686568260193, 0.042341139167547226, -0.010005179792642593, 0.028358139097690582, -0.046312183141708374, 0.017139552161097527, -0.037480924278497696, -0.032402776181697845, 0.032893143594264984, 0.0005393511964939535, 0.01448371633887291, 0.07062096148729324, -0.0009521774481981993, 0.0013535149628296494, 0.002698600525036454, 0.0010981454979628325, 0.02642698399722576, -0.06581565737724304, 0.013769884593784809, 0.035469185560941696, 0.009319414384663105, 0.05440567061305046, -0.019773738458752632, -0.05566216632723808, -0.03491971641778946, 0.002611282980069518, 0.019035227596759796, -0.01791958697140217, 0.018128791823983192, 0.05901603773236275, 0.001548798754811287, 0.008795431815087795, 0.02862788923084736, 0.00569553067907691, 0.011744286864995956, 0.05710507929325104, 0.004374655429273844, -0.035627152770757675, 0.03941413015127182, 0.051239658147096634, 0.024809610098600388, 0.01407203171402216, 0.012037165462970734, -0.06966128200292587, -0.02174580655992031, -0.036389634013175964, -0.002738616429269314, 0.036241911351680756, 0.05606776103377342, 0.027657460421323776, -0.027186332270503044, 0.0557941235601902, 0.017624247819185257, 0.06267672777175903, -0.0313035324215889, 0.019804945215582848, 0.04703965038061142, -0.07600300014019012, -0.028586244210600853, -0.014360212720930576, 0.14213913679122925, -0.05599186569452286, 0.05423947051167488, 0.026252493262290955, 0.010999086312949657, 0.06597977131605148, -0.034347426146268845, -0.012284381315112114, -0.03003980591893196, 0.036552973091602325, -0.004748915322124958, 0.05738915130496025, -0.01614845171570778, -0.002071198308840394, -0.004145885817706585, -0.06459565460681915, -0.011386067606508732, 0.0006377535755746067, 0.04438909515738487, -0.06832513958215714, -0.021415933966636658, 0.02970409393310547, 0.029632633551955223, 0.021652081981301308, -0.022877132520079613, -0.029993919655680656, -0.0004792114777956158, 0.010753033682703972, 0.0034452504478394985, -0.009818630293011665, 0.08229640126228333, 0.018839601427316666, 0.009559308178722858, 0.025218557566404343, 0.0016216582152992487, -0.01332093495875597, 0.007080524228513241, -0.00669397646561265, 0.008840184658765793, 0.03497207164764404, 0.06166337803006172, 0.012346228584647179, -0.02869374305009842, 0.027974259108304977, -0.016598638147115707, -0.0333995446562767, 0.04468728229403496, 0.0020262643229216337, 0.03820563480257988, 0.016544340178370476, 0.04014335945248604, -0.05017172545194626, -0.017437458038330078, 0.0357804000377655, 0.026914644986391068, 0.035094670951366425, -0.0017818338237702847, 0.0039975340478122234, 0.0726742148399353, 0.014676593244075775, 0.01861729845404625, -5.067948834976453e-33, -0.02593240886926651, 0.04286850243806839, 0.05738193541765213, -0.015664393082261086, 0.0007602852419950068, -0.011705677956342697, 0.02438708022236824, 0.031246783211827278, -0.045551881194114685, -0.03468439355492592, -0.03244845196604729, 0.04079823940992355, 0.02422080934047699, 0.013602765277028084, -0.00044231305946595967, -0.025142524391412735, -0.009436187334358692, -0.010523699223995209, 0.09788643568754196, 0.0015541380271315575, 0.03573312982916832, -0.002274696249514818, 0.02241801843047142, -0.043521009385585785, -0.050103362649679184, 0.015541207045316696, 0.026630833745002747, -0.06318310648202896, 0.014911234378814697, -0.021126093342900276, -0.046040188521146774, 0.013119127601385117, -0.029716912657022476, -0.020248351618647575, -0.0009591719135642052, 0.0076214889995753765, -0.07182584702968597, -0.013581481762230396, -0.030436821281909943, 0.01071484386920929, -0.029214873909950256, -0.013098700903356075, 0.0800287052989006, 0.04860233888030052, -0.06586209684610367, 0.04253926873207092, 0.0178025271743536, -0.004926969297230244, -0.0021670765709131956, -0.023906880989670753, 0.024705098941922188, 0.012668132781982422, 0.04446942359209061, 0.0057336618192493916, -0.04546694457530975, -0.04672795534133911, -0.08083123713731766, 0.019633745774626732, -0.0673149824142456, -0.026911314576864243, -0.0235431008040905, 0.06393242627382278, 0.009808900766074657, 0.057904213666915894, 0.06309716403484344, 0.0626019760966301, 0.06099968031048775, 0.06199664622545242, 0.01525199692696333, 0.05430285260081291, -0.0005785544635728002, 0.033834923058748245, 0.013053743168711662, 0.042189475148916245, 0.06895703077316284, -0.04730422422289848, -0.03363944962620735, 0.02992374077439308, 0.04075602814555168, -0.005972641985863447, 0.036722272634506226, 0.012985690496861935, -0.06525015085935593, -0.015881994739174843, 0.031566619873046875, 0.031324975192546844, 0.01750797964632511, -0.04636773094534874, -0.030296435579657555, -0.0008675905410200357, -0.011258631013333797, -0.029780086129903793, -0.0034845536574721336, -0.017625870183110237, 0.029130052775144577, -0.026797782629728317, 0.07938892394304276, -0.0030488858465105295, -0.02976277284324169, 0.023605380207300186, 0.0034229799639433622, -0.05396934598684311, -0.048200443387031555, 0.0038749489467591047, -0.036811552941799164, 0.07634618878364563, 0.005052991211414337, 0.008767721243202686, 0.01849597506225109, -0.017149727791547775, -0.019385559484362602, -0.04068799689412117, 0.011107822880148888, 0.07968059182167053, -0.005500840023159981, -0.047297634184360504, -0.01493225060403347, 0.047814834862947464, -0.046886738389730453, 0.010407918132841587, -0.0032153301872313023, 0.0016186897410079837, 0.010065204463899136, 0.018317531794309616, -0.014976469799876213, -0.006847929675132036, -0.040921736508607864, 0.01981738768517971, -0.043276187032461166, -0.08064454793930054, 0.02121339924633503, 0.026101913303136826, 2.4711292212487024e-07, -0.03420311585068703, -0.06932473182678223, -0.003969753161072731, -0.004151665139943361, 0.04185299947857857, 0.011098192073404789, 0.03177475184202194, -0.03656712546944618, -0.02475045621395111, -0.026523631066083908, 0.05518202483654022, 0.01607835479080677, -0.020370636135339737, 0.03074805997312069, -0.02105429582297802, -0.0006640357314608991, -0.0009723519906401634, 0.09000492841005325, 0.03386685624718666, -0.007672098930925131, -0.021371198818087578, 0.06501550227403641, 0.008798648603260517, -0.043273139744997025, 0.011339141987264156, -0.014750819653272629, 0.018875321373343468, 0.03612981364130974, 0.036196839064359665, -0.008251691237092018, 0.012366224080324173, 0.009076248854398727, -0.04722461476922035, 0.0007441002526320517, 0.02876756154000759, -0.012807394377887249, -0.0425633005797863, -0.014137089252471924, -0.01183856651186943, -0.07569651305675507, 0.011872400529682636, -0.0015125679783523083, -0.004151001572608948, 0.0012853038497269154, 0.06791379302740097, -0.0082458620890975, -0.0746791660785675, -0.05680723115801811, 0.01738293655216694, -0.01630658283829689, 0.03095816820859909, -0.0013184266863390803, -0.0027516144327819347, -0.04224016144871712, -0.015817170962691307, -0.04149327799677849, -0.008653738535940647, -0.06094052270054817, 0.03949848935008049, 0.02070682682096958, 0.005115080624818802, 0.0005323233781382442, -0.06420158594846725, -0.030707696452736855, 0.0520232729613781, 0.03473139554262161, -0.04761578515172005, 1.560988539624841e-34, 0.02598598413169384, 0.03672312945127487, -0.008137982338666916, 0.013999957591295242, -0.023846285417675972, -0.001352093880996108, 0.03364429622888565, -0.062100742012262344, -0.03505842760205269, 0.0021910571958869696, -0.07144109159708023]

['Yukun Bao', 'Tao Xiong', 'Zhongyi Hu']

1401.0104v1

Multi-step-ahead time series prediction is one of the most challenging research topics in the field of time series modeling and prediction, and is continually under research. Recently, the multiple-input several multiple-outputs (MISMO) modeling strategy has been proposed as a promising alternative for multi-step-ahead time series prediction, exhibiting advantages compared with the two currently dominating strategies, the iterated and the direct strategies. Built on the established MISMO strategy, this study proposes a particle swarm optimization (PSO)-based MISMO modeling strategy, which is capable of determining the number of sub-models in a self-adaptive mode, with varying prediction horizons. Rather than deriving crisp divides with equal-size s prediction horizons from the established MISMO, the proposed PSO-MISMO strategy, implemented with neural networks, employs a heuristic to create flexible divides with varying sizes of prediction horizons and to generate corresponding sub-models, providing considerable flexibility in model construction, which has been validated with simulated and real datasets.

PSO-MISMO Modeling Strategy for Multi-Step-Ahead Time Series Prediction

http://arxiv.org/pdf/1401.0104v1

Title PSOMISMO Modeling Strategy MultiStepAhead Time Series Prediction Summary Multistepahead time series prediction one challenging research topic field time series modeling prediction continually research Recently multipleinput several multipleoutputs MISMO modeling strategy proposed promising alternative multistepahead time series prediction exhibiting advantage compared two currently dominating strategy iterated direct strategy Built established MISMO strategy study proposes particle swarm optimization PSObased MISMO modeling strategy capable determining number submodels selfadaptive mode varying prediction horizon Rather deriving crisp divide equalsize prediction horizon established MISMO proposed PSOMISMO strategy implemented neural network employ heuristic create flexible divide varying size prediction horizon generate corresponding submodels providing considerable flexibility model construction validated simulated real datasets Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.03915258124470711, -0.0018047576304525137, -0.037946537137031555, -0.029163600876927376, 0.023922298103570938, -0.010559935122728348, 0.015669895336031914, -0.0034794695675373077, -0.0033809870947152376, 0.021691443398594856, 0.01624354161322117, -0.0034497908782213926, 0.016113724559545517, 0.02761148288846016, 0.03534093126654625, -0.051668234169483185, 0.051391709595918655, 0.008068202994763851, -0.014299766160547733, 0.016710681840777397, 0.04362021014094353, -0.04241078346967697, 0.07169707864522934, 0.03805123269557953, -0.015519268810749054, 0.027965370565652847, -0.008490012027323246, -0.018846118822693825, 0.019404727965593338, -0.07950641959905624, 0.018085330724716187, -0.013710414990782738, 0.03789504989981651, 0.0707944929599762, 2.102576672768919e-06, 0.026005897670984268, -0.03251997008919716, -0.0012418185360729694, 0.03235512599349022, 0.0053711216896772385, -0.02732216753065586, -0.004740250762552023, 0.028869491070508957, 0.018501291051506996, -0.039246294647455215, 0.026364389806985855, -0.017224276438355446, -0.009865387342870235, 0.07743453234434128, 0.07432595640420914, 0.00027607090305536985, -0.010916248895227909, -0.011822042986750603, -0.039401035755872726, -0.016526062041521072, -0.009394883178174496, -0.011243785731494427, -0.02373473532497883, -0.05095831677317619, 0.00524026108905673, -0.024546857923269272, 0.034338295459747314, 0.004920437932014465, 0.024542691186070442, -0.004499648232012987, -0.008153393864631653, 0.07006832212209702, -0.018803834915161133, -0.012230128981173038, 0.007539240177720785, -0.02091563679277897, -0.008576822467148304, 0.049891699105501175, -0.008403030224144459, -0.034337084740400314, 0.01567499339580536, -0.06585749238729477, -0.03615754097700119, -0.017657333984971046, 0.03271196037530899, 0.010214467532932758, 0.0778329074382782, -0.006761787924915552, 0.0042516253888607025, 0.017513692378997803, 0.04049551859498024, -0.03356858715415001, 0.006342525593936443, -0.00247867195867002, -0.055592626333236694, -0.00983470305800438, 0.027488671243190765, -0.0341668538749218, 0.003277673153206706, -0.06371874362230301, 0.01128823310136795, 0.05367080122232437, -0.06224659085273743, 0.02469811402261257, -0.03793741390109062, 0.09172119945287704, 0.005038370843976736, 0.05710703879594803, -0.03600762039422989, 0.021130505949258804, -0.031125633046030998, -0.04498852416872978, -0.029518067836761475, -0.018702013418078423, 0.010514402762055397, -0.029828106984496117, -0.005290273576974869, 0.04136280342936516, 0.027453318238258362, 0.056869860738515854, 0.005648484453558922, -0.06575694680213928, -0.03754996880888939, -0.011580226011574268, -0.060705315321683884, 0.06879886239767075, -0.009981456212699413, -0.00833071768283844, -0.006006863433867693, 0.00354190357029438, 0.06599561125040054, -0.016131220385432243, 0.03911304846405983, -0.020518075674772263, 0.03456377238035202, -0.014393987134099007, -0.017421424388885498, -0.016915349289774895, 0.08635285496711731, -0.020971093326807022, 0.01632203347980976, 0.029767492786049843, 0.03947627544403076, -0.06822893768548965, -0.026673218235373497, 0.0277382992208004, -0.025352949276566505, -0.047135915607213974, 0.02201349474489689, -0.004468167200684547, -0.038225866854190826, -0.019144907593727112, 0.058151111006736755, -0.004372583702206612, -0.018300652503967285, 0.01179812103509903, 0.02258685603737831, -0.011929475702345371, -0.007260104641318321, 0.04782582074403763, 0.006582624278962612, -0.022513512521982193, 0.027173452079296112, 0.01857106015086174, 0.011271234601736069, -0.007792359683662653, -0.01695535145699978, -0.008888271637260914, -0.0010420196922495961, -0.004980150144547224, -0.06673476099967957, -0.049819398671388626, -0.03327057510614395, -0.028439130634069443, -0.0026379041373729706, -0.026101624593138695, -0.03301677107810974, 0.016550177708268166, -0.011871255934238434, 0.026844069361686707, -0.017013423144817352, 0.00861581414937973, 0.013883620500564575, 0.03394570201635361, -0.021242717280983925, 0.013645069673657417, -0.03336179628968239, 0.03507964313030243, 0.0776703953742981, -0.08556180447340012, 0.03859424963593483, -0.02239367365837097, 0.01730775274336338, -0.03602869436144829, -0.03503809869289398, 0.007774834055453539, 0.004510585684329271, -0.010863779112696648, -0.05161430314183235, 0.0063827382400631905, -0.03509156405925751, -0.023275896906852722, 0.027198031544685364, 0.036286234855651855, 0.035480983555316925, -0.029897570610046387, -0.0017001251690089703, 0.040913790464401245, -0.027976516634225845, -0.011222868226468563, -0.01950100064277649, -0.005660625174641609, -0.028721554204821587, 0.005108444485813379, -0.02169034816324711, 0.009320242330431938, 0.012399794533848763, -0.021432271227240562, -0.05022027716040611, -0.0273120254278183, 0.10211089253425598, -0.008300445973873138, -0.019776247441768646, -0.05374283343553543, -0.01355834025889635, 0.04613921046257019, 0.045589324086904526, 0.028133627027273178, 0.005749616771936417, -0.0510299950838089, 0.03689495474100113, 0.004849638789892197, 0.0034064347855746746, 0.030470583587884903, -0.01647311821579933, 0.0477193146944046, 0.0023522789124399424, 0.049978550523519516, -0.05482281744480133, -0.0342634841799736, 0.005909041967242956, -0.05095161497592926, -0.02176756225526333, -0.030936162918806076, 0.07003185898065567, 0.06363226473331451, 0.013523707166314125, -0.04046434909105301, -0.06559412181377411, 0.028008371591567993, -0.04698766767978668, -0.013472136110067368, -0.07410725951194763, -0.006260850001126528, -0.002573124598711729, 0.050922494381666183, 0.015328535810112953, 0.00926639512181282, -0.020402804017066956, -0.016336852684617043, 0.006695483811199665, 0.018310198560357094, 0.018415873870253563, -0.022487521171569824, 0.020506560802459717, -0.017698993906378746, -0.002133009023964405, -0.011047951877117157, 0.014762694016098976, -0.010115576907992363, -0.03817545622587204, 0.018959054723381996, 0.01244337111711502, -0.003279217518866062, 0.0049368841573596, -0.002445680322125554, -0.01997646503150463, -0.05986249819397926, 0.008927068673074245, -0.038715749979019165, 0.027964046224951744, 0.08494223654270172, -0.03476877510547638, -0.07560048997402191, 0.04345446079969406, -0.009738432243466377, -0.03644717112183571, 0.018677672371268272, 0.00559484725818038, -0.026704376563429832, 0.051299870014190674, 0.014899113215506077, -0.021458523347973824, -0.03388980031013489, 0.0004336117999628186, -0.025849634781479836, -0.01071748323738575, -0.00899756420403719, -0.01792747713625431, -0.07434436678886414, -0.04102697595953941, 0.0033772995229810476, -0.017750559374690056, 0.027975309640169144, -0.06986211240291595, -0.01504783146083355, 0.0021883249282836914, -0.0012191787827759981, 0.0161032322794199, 0.002531478414312005, 0.07561211287975311, -0.007749674841761589, 0.022423744201660156, -0.015499099157750607, 0.03417345508933067, 0.06572067737579346, 0.0002410366287222132, 0.00142406125087291, 0.044609636068344116, 0.0052955979481339455, 0.007929026149213314, 0.00960279256105423, -0.014282092452049255, -0.048281099647283554, -0.002578116487711668, 0.003934117034077644, -0.02623467706143856, 0.016981391236186028, 0.0049246144481003284, -0.0023326335940510035, 0.01633189432322979, -0.02110198885202408, -0.03524606674909592, -0.04517240449786186, 0.007758399471640587, 0.007436067331582308, 0.005296618212014437, 0.04230380803346634, -0.006130063906311989, -0.003569220192730427, -0.02611858770251274, -0.014969384297728539, -0.06165922433137894, 0.025385580956935883, 0.0011947214370593429, 0.03745551407337189, 0.04935620352625847, -0.02633366920053959, 0.011576139368116856, 0.01926174946129322, 0.008527692407369614, -0.003372408449649811, 0.01016842108219862, 0.040717970579862595, 0.05689680576324463, -0.04033561423420906, 0.013563724234700203, -0.01446171011775732, -0.014395679347217083, 0.03000633604824543, 0.007212588097900152, 0.0018613407155498862, -0.00574648380279541, -0.01637539081275463, -0.0029521884862333536, 0.07622379809617996, -0.05802188813686371, 0.04296628758311272, 0.03630979359149933, -0.03572981804609299, -0.003079198533669114, -0.04542636126279831, -0.030198998749256134, -0.025477489456534386, 0.03466814011335373, -0.038462765514850616, -0.07570865005254745, 0.06351272761821747, 0.046732354909181595, -0.010122495703399181, -0.008786920458078384, -0.019028542563319206, -0.012249850668013096, -0.03872869908809662, 0.004989619366824627, -0.009500570595264435, 0.03502805531024933, 0.021701419726014137, -0.002871250966563821, 0.016118863597512245, -0.031097013503313065, -0.022121988236904144, -0.03310537338256836, -0.015528654679656029, 0.04829813539981842, 0.007950501516461372, -0.04412534832954407, 0.013453593477606773, -0.08746421337127686, -0.008956694044172764, -0.0814453735947609, -0.012017053551971912, 0.013653603382408619, -0.004836602136492729, -0.009690259583294392, 0.07223110646009445, -0.09751958400011063, -0.0029881063383072615, 0.003190241754055023, -0.02927722968161106, -0.03734049201011658, 0.022091755643486977, 0.017547866329550743, -0.014892471954226494, -0.0402277410030365, -0.0622527077794075, 0.027538206428289413, 0.05832822248339653, -0.067452572286129, 0.01799764111638069, 0.06897507607936859, -0.004753598012030125, -0.0001571734610479325, 0.09142008423805237, 0.0017445243429392576, 0.0798845887184143, 0.03030364215373993, 0.045488934963941574, 0.006386378314346075, -0.054762762039899826, -0.04151783883571625, 0.025445448234677315, -0.019974155351519585, 0.006626641843467951, -0.007021834142506123, -0.003740442916750908, -0.014183918945491314, 0.0658736303448677, 0.00017429571016691625, -0.00532356183975935, 0.018250636756420135, -0.023120401427149773, 0.020001189783215523, -0.04186567664146423, -0.023540325462818146, 0.01438659057021141, -0.030222520232200623, 0.06559985876083374, 0.025183485820889473, 0.13107654452323914, 0.05411478132009506, -0.009786630980670452, 0.015203206799924374, -0.06869690865278244, 0.05626428499817848, 0.02215767093002796, -0.012457059696316719, 0.0330636240541935, 0.06410805881023407, -0.015782250091433525, -0.022123171016573906, -0.024942569434642792, -0.0887429416179657, -0.01713665761053562, 0.039980340749025345, 0.05829857289791107, 0.004173808265477419, -0.026042833924293518, 0.04616135358810425, 0.007666324265301228, 0.07731140404939651, 0.0404655821621418, 0.0641527846455574, -0.0262885931879282, 0.016768192872405052, 0.013139212504029274, -0.011199917644262314, 0.010123797692358494, 0.07555042952299118, 0.0883907899260521, -0.014358868822455406, -0.01306422520428896, -0.025837263092398643, -0.018332863226532936, -0.050307951867580414, 0.023793093860149384, 0.08430997282266617, 0.026371095329523087, 0.010221961885690689, -0.021768569946289062, 0.018881307914853096, -0.0015829401090741158, 0.003871567314490676, 0.001490749535150826, 0.02292650379240513, 0.02597861923277378, -0.006332793738692999, -0.027833931148052216, 0.004461574833840132, 0.09957604855298996, -0.08236117660999298, -0.01027335412800312, 0.05245694890618324, -0.04096710681915283, 0.03043520078063011, -0.06107472628355026, 0.022799905389547348, 0.02665727771818638, -0.00491527421399951, 0.00969021301716566, -0.008182559162378311, -0.0013519912026822567, 0.08924414962530136, -0.04437759891152382, 0.03528173640370369, -0.04270282760262489, -0.023664236068725586, -0.033015020191669464, 0.0010110667208209634, -0.03752078488469124, 0.004966158419847488, 0.013359750621020794, -0.0029440822545439005, -0.011071665212512016, 0.00020685502386186272, 0.030708182603120804, 0.002664553467184305, 0.06505312770605087, -0.04107114300131798, 0.0675843209028244, 0.01145941298455, -0.03915964439511299, -0.09601759910583496, 0.022798873484134674, 0.023068852722644806, 0.006173171568661928, -0.017069581896066666, 0.005514474119991064, -0.045586999505758286, -0.046457428485155106, 0.04062265157699585, 0.02214655466377735, -0.015914518386125565, 0.011440266855061054, -0.03592325374484062, -0.05000218376517296, 0.011567031033337116, 0.046436261385679245, -0.051760245114564896, 0.025535374879837036, 0.0002832651953212917, -0.004193816799670458, -0.004854969680309296, -0.050405073910951614, 0.09498210996389389, 0.027561230584979057, -0.025825031101703644, -0.03061397559940815, 0.021266531199216843, -0.0017891961615532637, -5.748773122453644e-33, -0.017469793558120728, -0.007393695414066315, -0.014607017859816551, -0.029062142595648766, -0.03577070310711861, 0.007681398186832666, -0.013805289752781391, -0.023342857137322426, 0.03951530158519745, -0.07282597571611404, -0.041471388190984726, -0.009202221408486366, -0.0007562229293398559, -0.004506380297243595, 0.08206911385059357, 0.04793629050254822, 0.05470362305641174, -0.023785008117556572, 0.04244883731007576, -0.008769739419221878, 0.05409363657236099, 0.0656127780675888, -0.0006949009257368743, 0.05737491324543953, -0.05576052516698837, 0.0019570200238376856, -0.05395170673727989, -0.0011807178379967809, -0.026633068919181824, -0.007067509461194277, 0.04890928044915199, 0.014851127751171589, -0.005923554301261902, -0.02440164051949978, -0.036235250532627106, 0.0016338195418938994, 0.04273231700062752, -0.05334654450416565, -0.047521550208330154, -0.031913142651319504, 0.036994773894548416, 0.031333502382040024, 0.0471782386302948, -0.016901277005672455, -0.0062779877334833145, 0.05045945569872856, 0.0305709857493639, -0.010003451257944107, 0.006776106543838978, -0.0002846898860298097, 0.040634457021951675, -0.006600119173526764, -0.008763350546360016, -0.0031947919633239508, 0.024324573576450348, 0.04358832165598869, -0.01815023459494114, 0.015262380242347717, -0.04518381878733635, 0.05166337266564369, 0.009726203046739101, 0.02797013521194458, -0.006980812642723322, 0.022358357906341553, 0.0742197185754776, 0.02715766616165638, 0.008285961113870144, -0.019499804824590683, 0.01714867167174816, 0.002533198334276676, 0.013242438435554504, 0.014357173815369606, 0.022737037390470505, -0.0006830920465290546, 0.0674385353922844, -0.11131861060857773, -0.014355665072798729, 0.06476233154535294, 0.0794578567147255, 0.01013123244047165, 0.022681303322315216, -0.006028446368873119, 0.0014945711009204388, -0.003756842575967312, 0.042869292199611664, -0.0766744464635849, 0.014801351353526115, -0.05851660668849945, 0.008637111634016037, 0.012609646655619144, 0.007903852500021458, 0.037979867309331894, -0.010356985032558441, -0.049171339720487595, 0.06392665952444077, 0.03814055025577545, -0.011594301089644432, -0.02688383124768734, 0.03706661984324455, -0.03569644317030907, -0.03221471607685089, -0.05930880457162857, 0.014957698062062263, -0.023800870403647423, -0.02723407931625843, -0.04228493943810463, 0.008254218846559525, 0.01808609813451767, 0.016371451318264008, -0.029301295056939125, 0.02800694666802883, -0.04471534490585327, 0.012937324121594429, -0.0007728789933025837, 0.01329052448272705, -0.05661773309111595, -0.05046602711081505, -0.015118610113859177, 0.03157103434205055, -0.0022679492831230164, 0.006361175328493118, 0.03160878270864487, 0.0008679050370119512, 0.014951547607779503, -0.013249030336737633, -0.009444069117307663, 0.004245278425514698, -0.0684361383318901, -0.004269628785550594, -0.03556042164564133, -0.03452887013554573, 0.01019961852580309, 2.8106509830649884e-07, 0.0037267303559929132, 0.044014401733875275, -0.06834174692630768, 0.015861542895436287, 0.029480958357453346, -0.004510176833719015, -0.0641777291893959, -0.013950606808066368, -0.03240131586790085, 0.04631141945719719, 0.05281461402773857, -0.04698656126856804, 0.021725555881857872, 0.007185411173850298, -0.044237636029720306, -0.050765350461006165, -0.02788665145635605, 0.06607937812805176, -0.01932951994240284, 0.011919070035219193, -0.0025498908944427967, 0.040595605969429016, 0.03253304585814476, -0.03587889298796654, 0.040641024708747864, 0.023437373340129852, 0.004779788665473461, 0.025380179286003113, -0.03124489262700081, 0.034704163670539856, -0.006664464250206947, 0.03101685829460621, -0.04378189146518707, -0.004973482806235552, -0.009589780122041702, 0.08490581065416336, 0.0034446443896740675, -0.02935759723186493, 0.01770998165011406, -0.0203434806317091, 0.06911011040210724, 0.07380305230617523, 0.013594403862953186, 0.0006279130466282368, -0.008691515773534775, -0.005569173488765955, -0.0640486478805542, -0.06883066892623901, 0.008569315075874329, 0.06392417103052139, 0.05796981230378151, -0.016275838017463684, 0.003092448692768812, -0.005576568190008402, -0.05667910352349281, -0.06402210891246796, 0.027606341987848282, 0.007569913752377033, -0.07129167765378952, 0.021973824128508568, -0.016797946766018867, -0.04216492548584938, -0.054832443594932556, -0.039919834583997726, 0.037871405482292175, 0.0003774019714910537, -0.02083977498114109, 2.6109061146457296e-34, 0.018201002851128578, -0.040275249630212784, -0.054120417684316635, 0.01668165624141693, -0.049412161111831665, -0.025443321093916893, -0.04014503210783005, 0.0382259301841259, -0.010593900457024574, -0.011046867817640305, -0.01949661783874035]

['Behnam Neyshabur', 'Ryota Tomioka', 'Nathan Srebro']

1503.00036v2

We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.

Norm-Based Capacity Control in Neural Networks

http://arxiv.org/pdf/1503.00036v2

Title NormBased Capacity Control Neural Networks Summary investigate capacity convexity characterization general family normconstrained feedforward network Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02022957056760788, 0.012715630233287811, -0.04774617776274681, 0.01465693674981594, -0.021458376199007034, -0.05353955924510956, 0.008180944249033928, -0.01536419428884983, -0.03482271730899811, 0.057900186628103256, -0.042462870478630066, -0.06971564888954163, -0.030261939391493797, 0.09634757786989212, 0.030706822872161865, 0.0094125522300601, 0.01840970665216446, 0.01445678249001503, -0.007378820795565844, 0.00012911630619782954, 0.016605796292424202, -0.0535566546022892, 0.01574763096868992, 0.031846679747104645, -0.026028934866189957, 0.035579342395067215, 0.04200657457113266, -0.0055363536812365055, 0.009592840448021889, -0.02675439417362213, 0.09641909599304199, 0.03074304573237896, 0.028574751690030098, 0.0057159969583153725, 2.0836944258917356e-06, -0.022517116740345955, 0.0031302401330322027, -0.04464348778128624, 0.03947426751255989, 0.01876130886375904, 0.05311483517289162, -0.07856960594654083, -0.00153453613165766, -0.026840150356292725, 0.04443707317113876, 0.03918275237083435, 0.016343295574188232, 0.06102863326668739, 0.00020925819990225136, 0.06024119257926941, 0.002806625794619322, -0.06246504932641983, 0.052300825715065, -0.040376365184783936, -0.05364159122109413, -0.06436370313167572, 0.012958427891135216, 0.017824312672019005, -0.01903333142399788, -0.027934083715081215, -0.02049288898706436, 0.052403103560209274, 0.06895540654659271, -0.03519083559513092, 0.046655770391225815, 0.0174954105168581, 0.04956624284386635, -0.004389702808111906, -0.008545147255063057, 0.041237372905015945, -0.023585589602589607, -0.020118001848459244, 0.021477555856108665, -0.04333634302020073, -0.016805488616228104, -0.012762813828885555, -0.005789532791823149, 0.02107434906065464, 0.020907552912831306, 0.01334812305867672, -0.07566549628973007, 0.06489156931638718, 0.038675833493471146, 0.02036522887647152, 0.006904224865138531, -0.01105292048305273, -0.015782233327627182, -0.01553884893655777, -0.029004743322730064, -0.034025367349386215, -0.06130896508693695, 0.02826797030866146, 0.05943604186177254, 0.047941118478775024, -0.0357196107506752, -0.012902891263365746, -0.013620949350297451, -0.0546891875565052, 0.02061091735959053, -0.04978104680776596, 0.027507344260811806, -0.022737380117177963, -0.01599716953933239, -0.0004915702156722546, -0.04080839455127716, 0.05953657999634743, -0.07464472204446793, 0.03250005468726158, 0.004006212577223778, 0.016810664907097816, -0.018638867884874344, 0.018611572682857513, 0.006939642131328583, 0.011343821883201599, -0.016054725274443626, -0.0011082288110628724, -0.06458138674497604, 0.029152508825063705, -0.0584324412047863, 0.03231416270136833, 0.030745185911655426, 0.017676830291748047, 0.0162805262953043, 0.002290555043146014, 0.0009967052610591054, 0.017100011929869652, -0.014025043696165085, 0.03275652974843979, 0.01704670861363411, 0.012967952527105808, 0.007867070846259594, -0.0028648371808230877, -0.03828457370400429, 0.006211466621607542, -0.005703183822333813, 0.036741916090250015, 0.0030014771036803722, 0.03760511428117752, -0.06062660366296768, -0.041351862251758575, -0.01809283159673214, -0.028137648478150368, -0.014242229051887989, -0.03342587500810623, -0.0021932513918727636, -0.05263401195406914, -0.00939233135432005, -0.012998410500586033, -0.0020334688015282154, -0.021566089242696762, -0.033542897552251816, 0.012247034348547459, 0.010151133872568607, -0.031543705612421036, 0.0782315731048584, -0.0030841194093227386, -0.02000470645725727, 0.04647260904312134, 0.022790322080254555, -0.0033415264915674925, 0.015628542751073837, 0.025492249056696892, 0.0013601890532299876, 0.011646762490272522, 0.05100118741393089, -0.00736291753128171, -0.10944045335054398, -0.07289347797632217, 0.020521624013781548, 0.023314200341701508, 0.006063173990696669, 0.03888991102576256, -0.04076744616031647, -0.044758085161447525, 0.05540773272514343, 0.029378442093729973, 0.03980665281414986, -0.004372439347207546, 0.00043331817141734064, -0.03135369345545769, -0.000694305868819356, -0.004239275585860014, 0.0038739549927413464, 0.04322609677910805, -0.0014621454756706953, -0.04821830242872238, -0.03788699582219124, -0.006369604729115963, -0.010097968392074108, -0.03221999853849411, 0.0017428526189178228, 0.0007135061314329505, -0.026043569669127464, -0.0353584960103035, 0.06618114560842514, -0.03697574511170387, -0.012559661641716957, -0.052885688841342926, -0.008100700564682484, 0.009112936444580555, 0.013918132521212101, -0.006320262793451548, -0.02640707790851593, -0.10255018621683121, -6.571217090822756e-05, -0.0007407654193229973, -0.0395953394472599, 0.004744094796478748, -0.056000981479883194, -0.040749505162239075, 0.070612832903862, 0.036100663244724274, -0.010989128611981869, -0.035823363810777664, 0.024929633364081383, 0.0420147180557251, -0.004197180271148682, -0.02401561476290226, -0.08629076927900314, 0.03427032753825188, 0.029378240928053856, 0.05856722220778465, -0.06520085036754608, 0.020541423931717873, -0.007135912775993347, 0.015646833926439285, 0.015202578157186508, 0.02724684402346611, 0.022465188056230545, 0.04009028896689415, 0.0019450464751571417, -0.006523345597088337, 0.0057299379259347916, -0.04260559380054474, -0.05083969607949257, 0.023542098701000214, -0.07990510761737823, 0.002844784175977111, 0.02544998563826084, 0.00935053825378418, 0.016812101006507874, 0.021526774391531944, 0.023285998031497, -0.07367272675037384, 0.032387085258960724, -0.02220451831817627, 0.015659170225262642, -0.039103150367736816, 0.01410509180277586, -0.013693378306925297, 0.012430651113390923, 0.022684361785650253, 0.03326037898659706, -0.01898188330233097, 0.02361743524670601, -0.0032681359443813562, 0.05173764377832413, 0.00903458334505558, -0.0029793200083076954, -0.02216036058962345, 0.015165377408266068, -0.0538979209959507, -0.05028209835290909, 0.011873926036059856, -0.0014247407671064138, 0.04785246402025223, 0.02782207913696766, 0.019583258777856827, 0.012849860824644566, -0.025595147162675858, -0.04747341200709343, -0.043911341577768326, -0.036615531891584396, 0.028242269530892372, -0.029097650200128555, -0.019632330164313316, 0.04485500976443291, 0.010542243719100952, -0.05993027985095978, 0.007901038974523544, 0.046045005321502686, -0.019491270184516907, 0.0010265817400068045, -0.058694567531347275, -0.016236670315265656, -0.016895215958356857, 0.04983865097165108, -0.02065293677151203, 0.04129677265882492, 0.04366232082247734, -0.006790259387344122, 0.047873470932245255, -0.032320793718099594, -0.06840571016073227, -0.03609301894903183, -0.018503988161683083, -0.03910548612475395, 0.03791742026805878, 0.00860112439841032, -0.026183802634477615, 0.04495624825358391, 0.12232198566198349, -0.03337124362587929, 0.009143533185124397, -0.025829587131738663, -0.05807318538427353, 0.007065493147820234, 0.01431279256939888, 0.049353986978530884, 0.040173329412937164, 0.024008912965655327, -0.028049660846590996, -0.028981545940041542, 0.01156966295093298, -0.00320157827809453, -0.0427081324160099, -0.06698089092969894, 0.0058052376843988895, 0.0008901810506358743, 0.03577697277069092, -0.025016214698553085, -0.009914464317262173, 0.020404404029250145, 0.02560274302959442, 0.033899541944265366, 0.06685316562652588, -0.05327077955007553, -0.019230565056204796, -0.06600847095251083, 0.0806402787566185, -0.007943852804601192, -0.025540592148900032, -0.02182077057659626, 0.013275033794343472, 0.002493232721462846, 0.03568647801876068, 0.014109613373875618, -0.014042933471500874, 0.007778081111609936, -0.014510959386825562, -0.03230450674891472, -0.03793643042445183, -0.024055425077676773, 0.03270446136593819, 0.03443180024623871, 0.037650927901268005, 0.05470450595021248, -0.04698279872536659, 0.04047249257564545, -0.029444964602589607, 0.002052118768915534, 0.05842797830700874, -0.039342354983091354, -0.0023192341905087233, -0.007614795118570328, 0.008860339410603046, -0.01118102390319109, 0.01474424172192812, 0.018627377226948738, -0.00918620266020298, -0.00867217592895031, -0.0041269599460065365, -0.040469199419021606, 0.017093660309910774, -0.0464416965842247, 0.05632321909070015, -0.011168165132403374, -0.01809256337583065, 0.017965132370591164, -0.014264525845646858, 0.09229455888271332, -0.045538000762462616, 0.018904900178313255, 0.03435051813721657, -0.02388501726090908, -0.11224288493394852, -0.006745202001184225, 0.014599131420254707, 0.003627409692853689, 0.013338630087673664, 0.02894917130470276, 0.02810976840555668, 0.01506271306425333, -0.003180272877216339, 0.026642058044672012, -0.04980570822954178, -0.06994617730379105, -0.04207292199134827, -0.07264146953821182, 0.030243590474128723, -0.01425261702388525, -0.008648493327200413, -0.03352867066860199, 0.019995590671896935, -0.008852140046656132, -0.0537397526204586, -0.014976178295910358, 0.005942809395492077, 0.02680100128054619, -0.05962366610765457, 0.04168302193284035, 0.01593439280986786, -0.008169325068593025, -0.051130231469869614, -0.11417074501514435, 0.07074972242116928, -0.014676718972623348, -0.023141685873270035, -0.048420485109090805, -0.017755605280399323, 0.056378111243247986, 0.0013829629169777036, -0.009665276855230331, -0.0029879705980420113, -0.02365514449775219, 0.03928793966770172, -0.05946364998817444, 0.02106621116399765, 0.0727192834019661, 0.0371723547577858, 0.021842146292328835, -0.0026721071917563677, 0.035955313593149185, 0.039211079478263855, 0.006208526901900768, -0.07731509953737259, -0.026279672980308533, 0.03956136852502823, 0.0060977512039244175, -0.004279065877199173, 0.013940742239356041, -0.01668560318648815, 0.012989833950996399, -0.030726483091711998, -0.06381358951330185, -0.008126587606966496, -0.0070971958339214325, 0.0215443205088377, -0.005218517500907183, -0.018275968730449677, 0.05413668602705002, -0.06613298505544662, 0.05431738123297691, 0.02840752899646759, -0.028267687186598778, 0.051138654351234436, -0.0001259200944332406, 0.0034174611791968346, -0.02204209379851818, 0.054236698895692825, 0.025746185332536697, -0.05861963704228401, 0.05067360773682594, 0.01668783463537693, -0.022759228944778442, -0.010830540210008621, -0.052847784012556076, -0.006444585043936968, -0.03723439201712608, -0.04520526900887489, 0.015888303518295288, -0.0042700134217739105, -0.017141180112957954, -0.009139611385762691, -0.06651989370584488, 0.05904620885848999, 0.0066947368904948235, -0.03033136948943138, 0.011732013896107674, 0.055863939225673676, -0.0029667350463569164, -0.014311965554952621, 0.061476510018110275, 0.026492804288864136, 0.07466389983892441, -0.005284265149384737, 0.0034330212511122227, 0.01699650287628174, -0.03587348014116287, -0.02008535899221897, 0.00078655278775841, 0.015537606552243233, 0.036270882934331894, -0.007761579472571611, -0.027649423107504845, 0.004580805078148842, -0.005947563331574202, 0.040626347064971924, 0.005101772490888834, 0.03391788527369499, 0.031121879816055298, -0.025875529274344444, -0.029224876314401627, -0.045948468148708344, 0.09091537445783615, -0.020884471014142036, -0.03220553323626518, 0.028651196509599686, -0.01625184156000614, -0.03849303722381592, -0.009359211660921574, 0.027037007734179497, -0.01389808114618063, -0.0004621772386599332, 0.033606987446546555, 0.031880732625722885, 0.021311582997441292, 0.04109248146414757, -0.0018856259994208813, 0.02311117947101593, -0.027562908828258514, -0.0067741647362709045, -0.03458181023597717, 0.0054613021202385426, -0.022409668192267418, 0.01737792417407036, -0.009803881868720055, -0.004695033188909292, -0.06258313357830048, -0.030164571478962898, 0.03356843441724777, -0.03873205557465553, 0.023272758349776268, -0.08901868015527725, 0.0541682094335556, 0.04776247963309288, -0.03252757713198662, 0.02520112507045269, 0.0067305113188922405, 0.012358455918729305, 0.0037115623708814383, 0.0011110322084277868, -0.05252230539917946, 0.026618434116244316, -0.004994633141905069, 0.017466498538851738, 0.035048723220825195, 0.018135203048586845, -0.007586641237139702, 0.029485074803233147, -0.00553235225379467, -0.04674578085541725, 0.01893315091729164, 0.05960419774055481, 0.08620334416627884, 0.044149138033390045, -0.005521932151168585, -0.07549635320901871, -0.02039846032857895, -0.02709447778761387, -0.004118455108255148, -0.006029403768479824, -0.04278460517525673, 0.05173642560839653, -0.019005291163921356, -5.753462610229456e-33, 0.0007649212493561208, -0.010317246429622173, -0.04355999454855919, -0.01833413727581501, -0.05943235009908676, 0.018450427800416946, 0.024808472022414207, -0.01847357116639614, -0.0367460697889328, -0.02847198396921158, -0.054920393973588943, 0.0024627610109746456, -0.016635579988360405, 0.01653553918004036, 0.02836652472615242, -0.020819056779146194, -0.013790717348456383, -0.03790254890918732, 0.02870158664882183, 0.03141827881336212, 0.03309222310781479, 0.014386313036084175, 0.009830379858613014, -0.0162524301558733, -0.0010393258417025208, 0.024580730125308037, -0.01901901140809059, 0.06156093254685402, -0.00671881390735507, 0.03490990027785301, -1.8910647270331538e-07, 0.0011856344062834978, 0.004924445413053036, -0.05170556157827377, -0.005669394973665476, 0.020720453932881355, -0.00020631587540265173, -0.06429237127304077, -0.06563249975442886, 0.006819534115493298, -0.036367256194353104, 0.01276102103292942, 0.10663829743862152, -0.04529400169849396, -0.06433334946632385, 0.02467940002679825, 0.007437600754201412, 0.04654960706830025, -0.006744632963091135, -0.02611943520605564, 0.004673887509852648, 0.010822376236319542, -0.026189463213086128, 0.033407364040613174, -0.015392564237117767, 0.04154069349169731, -0.037526097148656845, -0.045855842530727386, -0.03819083049893379, -0.018756691366434097, -0.018866388127207756, 0.035151828080415726, -0.002949630841612816, 0.029516464099287987, 0.04104619473218918, 0.04270516335964203, 0.04108356311917305, -0.004015685059130192, -0.05749860778450966, -0.0342223234474659, 0.039302583783864975, -0.0029291787650436163, 0.07409845292568207, 0.008402871899306774, 0.042522188276052475, -0.09699111431837082, -0.00999547354876995, 0.010264872573316097, 0.034619443118572235, 0.05046635493636131, 0.012309961952269077, -0.024759182706475258, -0.029871784150600433, 0.030875684693455696, -0.005012119188904762, -0.06819327175617218, -0.01734609343111515, 0.01600484549999237, 0.0012032126542180777, 0.013758101500570774, 0.005718382075428963, 0.0006865921313874424, 0.013690738938748837, -0.051867593079805374, 0.06625576317310333, 0.027652941644191742, 0.041721999645233154, 0.0803186222910881, 0.028888629749417305, 0.002681892132386565, -0.05764437094330788, -0.003758043749257922, -0.06110849604010582, 0.03925999626517296, -0.006009622011333704, 0.03585425019264221, 0.05158726125955582, 0.0060227131471037865, 0.06333010643720627, -0.020966267213225365, -0.01857898384332657, 0.012675385922193527, 0.03207032382488251, 0.06575722992420197, 0.07880502939224243, -0.04109806939959526, -0.0029405176173895597, 0.046298056840896606, 0.012337488122284412, -0.001172283780761063, -0.04736587777733803, 0.012123926542699337, 0.0336158461868763, 0.03194132074713707, -0.050913628190755844, -0.030992135405540466, -0.050585199147462845, 0.06910432130098343, 0.006843953859061003, -0.04929374158382416, 0.0251579899340868, -0.019411727786064148, 2.7984717121398717e-07, -0.04695407673716545, -0.019977783784270287, 0.009388278238475323, 0.01682550087571144, 0.027084439992904663, 0.01957724802196026, -0.04688549041748047, 0.04242200031876564, -0.042512983083724976, -0.00017614707758184522, 0.021944018080830574, -0.02244936302304268, -0.007534237112849951, -0.01930203288793564, -0.017274904996156693, -0.06773736327886581, -0.049066461622714996, 0.06906242668628693, 0.008321725763380527, -0.002363293431699276, 0.0449540801346302, 0.019903026521205902, 0.015842881053686142, -0.020623264834284782, 0.03917815163731575, -0.001293631037697196, 0.0013376723509281874, -0.00984862819314003, 0.033449914306402206, -0.006841632071882486, 0.06939243525266647, 0.011124496348202229, -0.015921926125884056, 0.0010776858543977141, -0.012159748934209347, 0.103941909968853, -0.04578797146677971, 0.03922169655561447, 0.02767963521182537, -0.06285159289836884, 0.009815335273742676, 0.05589767172932625, 0.012837725691497326, -0.02762228436768055, 0.06639952212572098, -0.020084813237190247, 0.016219086945056915, -0.0012954451376572251, 0.04851679876446724, 0.006437124218791723, 0.0696503147482872, -0.005052671302109957, -0.005440837703645229, -0.008534157648682594, 0.0044137779623270035, -0.0018007298931479454, 0.0005106549942865968, -0.053254224359989166, 0.04870111122727394, 0.03425971418619156, -0.023564863950014114, 0.005684553645551205, -0.04644937440752983, 0.03247526288032532, 0.03874986991286278, 0.013451023027300835, -0.04015416279435158, 2.5051557041098796e-34, 0.0017223319737240672, -0.05808774009346962, 0.024581527337431908, -0.016372885555028915, -0.040676381438970566, 0.006660314276814461, -0.013210508041083813, 0.03821093216538429, 0.010295418091118336, -0.025880755856633186, -0.012159011326730251]

['Konrad Zolna']

1612.01589v1

The method presented extends a given regression neural network to make its performance improve. The modification affects the learning procedure only, hence the extension may be easily omitted during evaluation without any change in prediction. It means that the modified model may be evaluated as quickly as the original one but tends to perform better. This improvement is possible because the modification gives better expressive power, provides better behaved gradients and works as a regularization. The knowledge gained by the temporarily extended neural network is contained in the parameters shared with the original neural network. The only cost is an increase in learning time.

Improving the Performance of Neural Networks in Regression Tasks Using Drawering

http://arxiv.org/pdf/1612.01589v1

Title Improving Performance Neural Networks Regression Tasks Using Drawering Summary method presented extends given regression neural network make performance improve modification affect learning procedure hence extension may easily omitted evaluation without change prediction mean modified model may evaluated quickly original one tends perform better improvement possible modification give better expressive power provides better behaved gradient work regularization knowledge gained temporarily extended neural network contained parameter shared original neural network cost increase learning time Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.00877348706126213, 0.0447792187333107, -0.028045685961842537, 0.007741921115666628, 0.001329071819782257, -0.01616915501654148, 0.04684789851307869, 0.024029122665524483, -0.03844287246465683, 0.011336134746670723, -0.013169636949896812, 0.04185344651341438, 0.03981006518006325, 0.0020347849931567907, 0.04718023166060448, -0.06182952970266342, -0.005614733323454857, 0.02048993483185768, 0.026462292298674583, -0.0018907008925452828, -0.00986556988209486, -0.0550878569483757, 0.020186567679047585, 0.04940728098154068, -0.06856541335582733, -0.002562417183071375, -0.0013842331245541573, -0.009325322695076466, -0.00598220294341445, 0.00934181734919548, 0.07420040667057037, 0.01966555044054985, -0.021104969084262848, 0.03552498295903206, 2.261913550682948e-06, -0.04371173307299614, 0.018499918282032013, 0.0026994163636118174, 0.012445461004972458, 0.017228491604328156, 0.03089987486600876, -0.01876380667090416, 0.022163866087794304, 0.010666435584425926, -0.018368732184171677, -0.03699226304888725, -0.010238463059067726, 0.06773233413696289, 0.003427020041272044, 0.048762425780296326, -0.0003077610454056412, -0.0043092588894069195, 0.03145064041018486, -0.008751400746405125, -0.007880293764173985, -0.06026126816868782, -0.011663367971777916, 0.019369836896657944, -0.03560673072934151, -0.03556995093822479, 0.00674373609945178, 0.06981770694255829, 0.06815459579229355, -0.0036807938013225794, 0.05508696287870407, 0.020412864163517952, -0.0373697467148304, 0.00875217467546463, -0.005650578066706657, 0.002368168206885457, -0.08975321054458618, 0.020471252501010895, -0.016762344166636467, -0.014972615987062454, 0.020614126697182655, -0.030761869624257088, -0.04042688012123108, -0.03903641924262047, -0.010990941897034645, -0.026959100738167763, -0.04147610813379288, 0.04979763925075531, 0.03597624972462654, 0.027350883930921555, 0.011281202547252178, 0.0026588509790599346, -0.021357491612434387, -0.005943636409938335, 0.013856668956577778, -0.008212476968765259, -0.0034947888925671577, 0.015344090759754181, 0.00926447194069624, -0.000995964976027608, -0.03584526479244232, -0.013330689631402493, 0.04919074475765228, -0.06551216542720795, 0.008862670511007309, -0.06672097742557526, 0.1002316102385521, 0.03781832009553909, -0.010130222886800766, -0.02114024944603443, -0.0802752897143364, 0.11138951033353806, -0.029856763780117035, 0.0455922894179821, -0.03221040219068527, 0.04255160316824913, -0.06208366900682449, -0.01890704035758972, -0.009918930940330029, 0.021246857941150665, 0.010452290065586567, -0.03567696735262871, -0.056861747056245804, -0.020963432267308235, 0.01064417976886034, -0.037278711795806885, 0.027057332918047905, 0.08556202054023743, 0.0055959755554795265, 0.0121730025857687, -0.00474603520706296, 0.05439657345414162, -0.026293417438864708, 0.032026663422584534, -0.010800654999911785, 0.03304591029882431, 0.01133405975997448, -0.0015989317325875163, -0.022274287417531013, 0.029049640521407127, 0.018983997404575348, 0.010361932218074799, 0.033527348190546036, 0.050909437239170074, -0.07211065292358398, -0.018837418407201767, -0.0079158004373312, -0.03763280063867569, 0.004116413649171591, -0.05679494887590408, 0.024376634508371353, -0.03629656881093979, -0.025778671726584435, 0.0009036221308633685, -0.029766494408249855, -0.05192585289478302, -0.03947186842560768, 0.021357854828238487, -0.038780584931373596, -0.017748890444636345, 0.05961037799715996, 0.009952191263437271, -0.03140171617269516, 0.022545291110873222, 0.03626668080687523, 0.060882918536663055, 0.008189195767045021, -0.009698521345853806, -0.014692559838294983, 0.012632984668016434, 1.1906996405741666e-05, -0.08701035380363464, -0.053941696882247925, -0.03211678937077522, 0.011430077254772186, 0.03676898404955864, 0.018368855118751526, 0.010879648849368095, 0.003616988193243742, -0.032646965235471725, 0.050298746675252914, 0.00025812993408180773, 0.11051587015390396, 0.04168781638145447, -0.010813727043569088, 0.0003356572997290641, 0.006070341449230909, -0.01809479109942913, -0.013334662653505802, 0.026005685329437256, -0.04012630134820938, -0.014158212579786777, -0.05273056402802467, -0.031680263578891754, -0.049845725297927856, -0.07760363072156906, 0.023675566539168358, -0.00826037023216486, 0.020347556099295616, 0.0001790164824342355, 0.04866476356983185, 0.008887585252523422, -0.0382874496281147, -0.039068374782800674, 0.028349000960588455, 0.026093345135450363, -0.048834070563316345, -0.061338696628808975, 0.00033479847479611635, 0.0004286429029889405, -0.013616208918392658, -0.025100629776716232, -0.06400811672210693, -0.019730163738131523, -0.042205676436424255, -0.04346427321434021, -0.0068950289860367775, 0.005200674291700125, 0.049976591020822525, -0.03597297891974449, -0.013154389336705208, 0.023141363635659218, 0.019503053277730942, 0.06182336062192917, 0.00610007531940937, 0.0026543207932263613, 0.04104581102728844, 0.009578578174114227, -0.021015338599681854, 0.014865010976791382, -0.024838397279381752, 0.005665186792612076, 0.06382916122674942, 0.027284983545541763, -0.01464210543781519, 0.0011359956115484238, 0.037465017288923264, -0.03650455176830292, 0.01836998574435711, -0.040238797664642334, -0.04622845724225044, -0.021864809095859528, -0.019892318174242973, -0.0450860969722271, 0.021061252802610397, 0.07523277401924133, 0.025312134996056557, 0.05342399701476097, -0.029228774830698967, -0.053638383746147156, -0.0037441435270011425, -0.013280173763632774, 0.04204469919204712, 0.024141106754541397, 0.0015276799676939845, -0.016982747241854668, -0.019208276644349098, -0.010915917344391346, 0.04083891212940216, 0.0012967681977897882, 0.02886902168393135, -0.03688223659992218, -0.021642295643687248, 0.05844708904623985, -0.007343693170696497, 0.013737312518060207, -0.005211129318922758, -0.033885762095451355, 0.03887450695037842, 0.01201793272048235, 0.03248312696814537, -0.001342320116236806, -0.005251775961369276, -0.01472777035087347, 0.016932904720306396, -0.01441142801195383, -0.025913601741194725, -0.01716596819460392, -0.010164417326450348, 0.02078230492770672, -0.03358841314911842, -0.005054493900388479, 0.06073089316487312, -0.009984958916902542, -0.05981241166591644, 0.0058888825587928295, 0.06976065039634705, 0.01667499728500843, -0.016988936811685562, -0.034772563725709915, -0.006785811856389046, 0.03266333416104317, 0.03718072548508644, -0.011744494549930096, -0.021105464547872543, 0.026115722954273224, -0.01844877563416958, -0.027478693053126335, -0.00027420345577411354, -0.04391246661543846, -0.05478214845061302, -0.008110332302749157, -0.04100511223077774, 0.05237230286002159, -0.010952282696962357, -0.018605995923280716, -0.0012194000883027911, 0.05348582565784454, -0.06317510455846786, 0.0010693133808672428, -0.0017937762895599008, 0.021791137754917145, 0.025780459865927696, 0.005343262571841478, -0.022363979369401932, -0.038069672882556915, 0.05304630473256111, -0.006617535371333361, -0.017721299082040787, 0.04377562552690506, 0.007323467172682285, -0.021701328456401825, -0.10723352432250977, -0.01052168570458889, 0.016067340970039368, -0.007863192819058895, 0.004901019390672445, -0.04006357118487358, 0.007717004977166653, 0.036588285118341446, 0.024544183164834976, -0.002303175861015916, -0.03388872370123863, -0.00045277774916030467, 0.010228989645838737, 0.0025207281578332186, -0.014553516171872616, -0.006499119568616152, -0.01473233476281166, -0.008450026623904705, 0.007858209311962128, -0.032124005258083344, -0.015187934972345829, -0.005982350558042526, 0.026423467323184013, -0.03129773959517479, 0.00939452089369297, -0.017745019868016243, -0.07033264636993408, -0.027767200022935867, 0.05919104442000389, 0.011831755749881268, -0.009067007340490818, 0.004964150954037905, -0.004231961444020271, 0.04150576889514923, -0.02555987611413002, 0.05045795068144798, -0.07020960003137589, -0.020075973123311996, 0.013270575553178787, 0.02339559607207775, -0.025233959779143333, -0.012812192551791668, -0.001693461206741631, 0.02957536093890667, 0.06276638805866241, -0.019767992198467255, -0.005221656057983637, 0.023789728060364723, -0.13613376021385193, 0.022113166749477386, -0.03304610773921013, 0.03156394883990288, -0.021022027358412743, -0.02006918005645275, -0.03426872193813324, -0.09190165996551514, 0.04221880063414574, 0.07238622009754181, 0.01900102011859417, -0.029060184955596924, -0.03332876041531563, -0.020138943567872047, -0.00011549317423487082, -0.014066590927541256, 0.05705716833472252, 0.04905767738819122, 0.041770029813051224, -0.0057037509977817535, 0.0695873498916626, -0.007580056320875883, -0.01903056912124157, 0.010683889500796795, -0.040904056280851364, 0.03382359817624092, 0.005131599027663469, -0.06688105314970016, -0.003953666891902685, -0.0381501205265522, -0.01201607845723629, -0.04199684038758278, 0.009736341424286366, 0.027115626260638237, 0.03550388664007187, -0.015584765933454037, 0.06358598917722702, -0.08881346881389618, -0.02133087068796158, -0.017158493399620056, -0.06751366704702377, -0.031739965081214905, 0.03128785640001297, 0.04601958394050598, -0.02023734711110592, 0.004276270978152752, 0.024930158630013466, 0.03299160674214363, 0.05376637354493141, -0.03841634467244148, 0.07717741280794144, 0.041068121790885925, -0.02099509723484516, -0.024176182225346565, 0.02665434591472149, -0.009654059074819088, 0.05462992563843727, 0.0019343263702467084, 0.02930830605328083, -0.01093533355742693, -0.010501709766685963, -0.034537866711616516, -0.006809713784605265, -0.0023421652149409056, -0.027134520933032036, -0.00835286732763052, -0.031793829053640366, 0.025162655860185623, 0.0025939482729882, -0.016808172687888145, 0.023433784022927284, 0.03414885699748993, -0.003393973223865032, 0.022668957710266113, -0.04645795747637749, -0.08897987008094788, -0.005039616953581572, 0.0023866770789027214, 0.05773356556892395, 0.007035116199404001, 0.025160551071166992, 0.00023782379867043346, 0.028697539120912552, -0.018957221880555153, -0.012253782711923122, 0.09800758212804794, 0.010974879376590252, 0.0039053475484251976, 0.050921082496643066, 0.053602028638124466, -0.00820567924529314, -0.021608293056488037, -0.07063689082860947, -0.013581839390099049, -0.002202069852501154, -0.018179209902882576, 0.0968688353896141, 0.010507951490581036, 0.022804249078035355, -0.06155695393681526, -0.03543108329176903, -0.005503125488758087, 0.051457446068525314, -0.0012319531524553895, -0.01556171290576458, 0.037221476435661316, -0.02908952161669731, 0.005112825892865658, -0.014352206140756607, 0.006045251153409481, 0.06157040596008301, 0.01802736334502697, -0.03740836679935455, -0.007864966057240963, -0.03452819213271141, -0.007041321136057377, 0.00649596331641078, 0.060388822108507156, 0.0293563399463892, -0.06408972293138504, -0.00044046423863619566, 0.010513986460864544, 0.009434501640498638, -0.013642335310578346, -0.018204668536782265, 0.011373873800039291, 0.038241662085056305, 0.04066422954201698, -0.03038085252046585, -0.02478545531630516, 0.06058269739151001, -0.04670470580458641, -0.06456893682479858, 0.026561686769127846, -0.03990573063492775, 0.04014728218317032, -0.05437636747956276, 0.061709679663181305, -0.03422318771481514, -0.02568795718252659, 0.03350910171866417, 0.002902464708313346, -0.03166333585977554, 0.010213399305939674, -0.004358080215752125, 0.013300297781825066, -0.06011318787932396, 0.01924147643148899, -0.005666162818670273, -0.0578790009021759, -0.05535077676177025, 0.0038264705799520016, 0.018894929438829422, -0.05999905616044998, -0.03321082890033722, -0.006056163460016251, 0.012888815253973007, -0.05009596794843674, 0.017112113535404205, 0.00669120205566287, 0.030323779210448265, 0.03483043238520622, -0.017497878521680832, -0.002431302098557353, -0.02673690766096115, 0.0019188413862138987, 0.018757222220301628, -0.019058959558606148, -0.00744712445884943, 0.0037361897993832827, -0.04194287955760956, 0.03481728956103325, 0.07569415122270584, 0.04001333564519882, -0.038183026015758514, 0.01987598091363907, 0.030163777992129326, -0.028779316693544388, 0.03539614751935005, 0.030708223581314087, 0.10126067698001862, -0.022121714428067207, 0.017380939796566963, -0.025810053572058678, -0.019029667600989342, 0.010532761923968792, -0.024200214073061943, -0.06368142366409302, -0.019151322543621063, 0.02239060401916504, -0.016124529764056206, -5.3148015466231795e-33, 0.006543085444718599, -0.024786191061139107, -0.025851398706436157, -0.016308575868606567, -0.04510045796632767, 0.01610179990530014, -0.021945171058177948, -0.004873814061284065, 0.001094699720852077, -0.005191749427467585, -0.029822073876857758, 0.02846577763557434, 0.0020640017464756966, 0.0011795028112828732, 0.019607894122600555, -0.012241397053003311, 0.014826411381363869, -0.01209369208663702, 0.041004277765750885, -0.042956527322530746, 0.020829351618885994, 0.0864943191409111, 0.0032710935920476913, -0.0611596517264843, -0.05907800793647766, 0.021201077848672867, -0.011358335614204407, -0.0163152776658535, -0.015179000794887543, -0.007859214209020138, 0.013554004952311516, 0.03606965392827988, 0.02943313494324684, -0.024327479302883148, -0.013965396210551262, -0.0020482854451984167, -0.020478488877415657, -0.012714388780295849, -0.046817369759082794, 0.032178569585084915, -0.010892067104578018, 0.008475886657834053, 0.12699607014656067, -0.005025892052799463, -0.05463084578514099, 0.015784738585352898, 0.035803429782390594, -0.03462153673171997, -0.01908961869776249, -0.025081712752580643, -0.053651031106710434, -0.003510597161948681, 0.014179362915456295, -0.0501081645488739, -0.006246409844607115, 0.08082748204469681, -0.03640497475862503, -0.04433919116854668, -0.07868755608797073, -0.041554324328899384, -0.020081980153918266, 0.004717747215181589, -0.010747336782515049, 0.04495255649089813, 0.02074565924704075, 0.01646922342479229, 0.0005023005069233477, -0.002655673772096634, 0.000999193754978478, -0.05518164113163948, 0.039405640214681625, 0.04769332706928253, 0.13297095894813538, -0.05034155398607254, 0.11026003956794739, -0.11106923222541809, -0.04940386489033699, 0.06572932004928589, 0.008901041001081467, 0.03558146208524704, -0.0025451802648603916, -0.005701334215700626, -0.030354754999279976, -0.003592493711039424, 0.0047493744641542435, -0.008798046037554741, -0.020883111283183098, -0.04364001750946045, 0.05468634143471718, -0.011448868550360203, -0.011218242347240448, -0.020188311114907265, 0.00174251152202487, -0.08054208755493164, 0.09214849025011063, 0.015864325687289238, -0.00283522205427289, 0.050883740186691284, 0.02413851022720337, -0.023297511041164398, -0.03023316152393818, -0.008144366554915905, -0.0117915328592062, 0.06077369302511215, 0.03961136192083359, -0.015489415265619755, 0.05070480704307556, -0.0067528546787798405, -0.005806272849440575, -0.011852019466459751, 0.007386340294033289, -0.005739080253988504, 0.01739412359893322, 0.02803533710539341, 0.029251504689455032, -0.02093590795993805, 0.003210263093933463, 0.0320737324655056, -0.0015697155613452196, -0.010163956321775913, -0.02084922231733799, 0.015676284208893776, 0.04732988029718399, -0.015658125281333923, -0.03736879304051399, -0.02916235290467739, -0.020407479256391525, 0.011247720569372177, -0.07303851842880249, -0.02864491380751133, -0.02775735966861248, -0.007711966522037983, 2.688144888907118e-07, 0.003639236791059375, 0.03279730677604675, -0.01496178563684225, -0.013813504949212074, 0.0037836425472050905, -0.03378571569919586, -0.030903588980436325, -0.014802717603743076, -0.002957091433927417, 0.013517085462808609, 0.053371500223875046, -0.052072830498218536, 0.04678609222173691, 0.00847071036696434, -0.06203308701515198, -0.0377543680369854, 0.0029465509578585625, 0.003208901733160019, -0.026375779882073402, 0.05059409514069557, 0.06889723986387253, 0.07312434911727905, 0.05311783403158188, -0.03824476897716522, 0.030145008116960526, 0.00776368984952569, -0.006897853687405586, 0.009024242870509624, 0.037779323756694794, -0.04862194135785103, 0.06224316731095314, 0.07353357970714569, -0.02775811217725277, 0.004860753193497658, 0.005206711124628782, 0.056666050106287, -0.0014221423771232367, -0.012440274469554424, -0.026477273553609848, 0.019404133781790733, 0.05152033269405365, 0.043441418558359146, 0.058059606701135635, -0.06429310888051987, 0.015355276875197887, -0.009752859361469746, -0.023556450381875038, -0.002945215906947851, 0.041589297354221344, 0.028429271653294563, 0.09231267869472504, -0.023694606497883797, 0.013010179623961449, -0.01792457327246666, 0.022902898490428925, -0.07508213073015213, -0.006032115314155817, -0.0369267463684082, -0.021638521924614906, 0.07517978549003601, -0.023170173168182373, -0.011489033699035645, 0.0035805392544716597, 0.03063805028796196, 0.07560157030820847, 0.0003491102543193847, -0.0134976115077734, 2.5437791883177864e-34, 0.0024146358482539654, 0.010344525799155235, 0.02008644863963127, 0.019025815650820732, -0.003979518078267574, 0.015475582331418991, 0.0016155325574800372, -0.007161201909184456, 0.026404527947306633, -0.037897348403930664, -0.011342835612595081]

['Yujia Li', 'Kevin Swersky', 'Richard Zemel']

1412.5244v1

A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient factors. We propose that an important aim for these representations are to be unbiased. Different forms of representation learning can be derived from alternative definitions of unwanted bias, e.g., bias to particular tasks, domains, or irrelevant underlying data dimensions. One very useful approach to estimating the amount of bias in a representation comes from maximum mean discrepancy (MMD) [5], a measure of distance between probability distributions. We are not the first to suggest that MMD can be a useful criterion in developing representations that apply across multiple domains or tasks [1]. However, in this paper we describe a number of novel applications of this criterion that we have devised, all based on the idea of developing unbiased representations. These formulations include: a standard domain adaptation framework; a method of learning invariant representations; an approach based on noise-insensitive autoencoders; and a novel form of generative model.

Learning unbiased features

http://arxiv.org/pdf/1412.5244v1

Title Learning unbiased feature Summary key element transfer learning representation learning representation developed expose relevant factor underlying data new task domain learned readily based mapping salient factor propose important aim representation unbiased Different form representation learning derived alternative definition unwanted bias eg bias particular task domain irrelevant underlying data dimension One useful approach estimating amount bias representation come maximum mean discrepancy MMD 5 measure distance probability distribution first suggest MMD useful criterion developing representation apply across multiple domain task 1 However paper describe number novel application criterion devised based idea developing unbiased representation formulation include standard domain adaptation framework method learning invariant representation approach based noiseinsensitive autoencoders novel form generative model Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.021625731140375137, -0.013297004625201225, -0.03595166280865669, 0.02415221743285656, -0.0011171476216986775, -0.00457181828096509, 0.07256867736577988, -0.016797970980405807, -0.022556159645318985, -0.04133708029985428, -0.030532395467162132, 0.027638962492346764, -0.00877831969410181, 0.08131878077983856, 0.013822102919220924, -0.09685692936182022, -0.0005646120989695191, 0.02368205226957798, -0.006757278926670551, -0.016644978895783424, -0.00864957645535469, -0.01835872419178486, 0.0033082205336540937, 0.033392440527677536, -0.05393806844949722, 0.024422716349363327, -2.9793762223562226e-05, -0.012819570489227772, -0.005292906891554594, -0.02214210294187069, 0.02168876864016056, 0.033179111778736115, 0.023077325895428658, -0.013526813127100468, 2.614201775941183e-06, -0.042501650750637054, -0.034188054502010345, -0.03543419390916824, 0.04390012472867966, -0.049413349479436874, 0.048422690480947495, -0.06056481972336769, -0.013574427925050259, -0.009173082187771797, -0.024859359487891197, -0.03304195776581764, 0.05709192901849747, 0.05309130623936653, 0.016215091571211815, 0.016842376440763474, -0.02207624539732933, -0.010279325768351555, -0.011774841696023941, -0.019753945991396904, 0.03669783100485802, -0.03660675883293152, 0.012322165071964264, 0.004994960967451334, -0.06377876549959183, -0.001840010634623468, -0.06855904310941696, 0.03276204317808151, 0.02267422154545784, -0.00886177085340023, 0.09356988966464996, 0.0043211812153458595, -0.0078169796615839, -0.01178298145532608, -0.024300221353769302, 0.06106763333082199, -0.041846271604299545, 0.026109879836440086, -0.015833983197808266, -0.01738871820271015, -0.021852580830454826, 0.00624730484560132, -0.04426306486129761, -0.021158993244171143, 0.01539634633809328, -0.00482976995408535, -0.08759777247905731, 0.06441326439380646, -0.017853137105703354, -0.03505302220582962, -0.00896431878209114, 0.0012351887999102473, -0.007430692669004202, 0.02100880816578865, -0.02165471948683262, -0.021412162110209465, -0.0026171067729592323, 0.0033865480218082666, 0.06684610247612, 0.007541525177657604, 0.010419984348118305, -0.0410144217312336, -0.015058008022606373, -0.08269073814153671, 0.02943972311913967, -0.052886057645082474, 0.06415466219186783, -0.032577481120824814, -0.05092393606901169, -0.0031354776583611965, -0.05270860344171524, 0.026989564299583435, -0.030168447643518448, 0.010998409241437912, -0.0468532033264637, -0.022190295159816742, -0.0388789102435112, 0.017258016392588615, 0.005333281122148037, 0.010615997016429901, -0.009785172529518604, -0.011712654493749142, -0.038540951907634735, -0.022561373189091682, -0.049710001796483994, -0.03089716285467148, 0.029728548601269722, 0.0672529935836792, -0.04187034070491791, -0.03389079123735428, -0.026775771751999855, 0.04610786214470863, -0.05709616467356682, 0.09026336669921875, -0.0017449992010369897, 0.02551198936998844, 0.028403501957654953, 0.024874247610569, 0.05418173223733902, -0.01466439850628376, 0.006048278417438269, 0.10604199022054672, 0.023431800305843353, 0.06152691692113876, -0.05034058913588524, -0.018732603639364243, 0.012289248406887054, 0.027025707066059113, 0.01668686233460903, -0.06502678990364075, 0.020656108856201172, -0.02682686783373356, -0.03272880241274834, -0.052230630069971085, -0.025245068594813347, -0.0644841343164444, -0.0013152345782145858, 0.09400259703397751, -0.038105227053165436, 0.004353682976216078, 0.09093070775270462, -0.028719676658511162, 0.012792261317372322, 0.00904472079128027, 0.023510457947850227, 0.00794186256825924, 0.013817517086863518, -0.020358148962259293, 0.006427882704883814, -0.015274913050234318, -0.00932872574776411, -0.03465159609913826, -0.0025673210620880127, -0.03361503779888153, -0.003226127475500107, 0.010789892636239529, 0.04392864182591438, -0.031284525990486145, 0.039922405034303665, -0.027653567492961884, 0.02740330435335636, 0.0005390546866692603, 0.04019022732973099, 0.022568831220269203, 0.007446637377142906, 0.011291841976344585, -0.06273180991411209, -0.03827711194753647, 0.034681983292102814, 0.0711539089679718, -0.006788067519664764, -0.019766176119446754, 0.006246098317205906, 0.024271339178085327, -0.041060492396354675, -0.042753614485263824, 0.047252003103494644, -0.029623547568917274, 0.0034725419245660305, -0.03440365567803383, 0.046031396836042404, 0.03961855545639992, 0.01677696406841278, 0.02605462074279785, 0.02573985420167446, -0.00877922773361206, -0.01659911498427391, -0.02303926832973957, 0.00901112612336874, -0.01293047796934843, -0.012639934197068214, -0.01943606697022915, -0.016095371916890144, -0.04884125664830208, -0.0018133586272597313, 0.00800497829914093, 0.025930510833859444, -0.011017104610800743, 0.023730183020234108, -0.05455537140369415, -0.08113981783390045, 0.025319695472717285, 0.016252154484391212, 0.018086930736899376, -0.06505587697029114, 0.02776881866157055, 0.06454967707395554, -0.030024908483028412, 0.037112463265657425, 0.015333534218370914, 0.001253822585567832, -0.035994142293930054, 0.04831014573574066, 0.04583162069320679, -0.004475332330912352, 0.019509410485625267, 0.01678280532360077, -0.005105993244796991, 0.019530506804585457, -0.044739980250597, -0.020370248705148697, 0.018810996785759926, -0.021354299038648605, 0.008945735171437263, -0.0023628550115972757, -0.042664576321840286, 0.014660046435892582, 0.007884806953370571, -0.03719199076294899, -0.03774469345808029, 0.03565070405602455, 0.011938631534576416, -0.05219408497214317, 0.008958433754742146, 0.024287035688757896, -0.0025170089211314917, 0.020220186561346054, -0.02101219817996025, 0.03097211942076683, 0.04026801139116287, -0.027653362601995468, -0.0392582006752491, 0.0005781597574241459, 0.018670693039894104, -0.020169157534837723, 0.055900976061820984, -0.007910267449915409, -0.02198626473546028, -0.0030356990173459053, 0.022331207990646362, 0.0307417381554842, -0.010995926335453987, 0.03787264600396156, -0.012034420855343342, -0.010077045299112797, 0.029528506100177765, -0.0028602834790945053, 0.023589011281728745, 0.01802520826458931, 0.0008015302591957152, -0.042217157781124115, -0.056034110486507416, 0.03730277717113495, -0.037644464522600174, -0.04255013167858124, 0.04847235977649689, -0.02022150531411171, 0.026487506926059723, -0.027096549049019814, -0.018706783652305603, -0.008779531344771385, 0.03769287094473839, 0.06034300848841667, -0.05191739276051521, -0.007885174825787544, 0.020754555240273476, -0.011614454910159111, 0.031347572803497314, 0.0499754399061203, -0.03344830870628357, -0.018679162487387657, -0.03716602921485901, 0.024842090904712677, 0.05012809857726097, 0.021663393825292587, -0.022181693464517593, -0.0006582061760127544, 0.003503332147374749, -0.016901841387152672, 0.007019958458840847, -0.0669960007071495, 0.06197083368897438, 0.019400211051106453, 0.010732848197221756, 0.0012984939385205507, -0.018648115918040276, 0.04328422248363495, -0.006368828937411308, 0.005821944214403629, 0.027869027107954025, 0.02872193045914173, -0.008056771010160446, -0.032520852982997894, 0.0032520657405257225, 0.02451374940574169, 0.03646722063422203, -0.03517436608672142, -0.01025904156267643, 0.01409284956753254, 0.04586400091648102, 0.05724365636706352, -0.0387822687625885, 0.0007668356993235648, -0.011577978730201721, 0.0233534537255764, 0.005000338423997164, 0.034408003091812134, 0.006355812307447195, -0.02249114401638508, -0.02889143116772175, 0.018181106075644493, 0.027845388278365135, -0.018233370035886765, 0.0015118017327040434, -0.02278805337846279, -0.04773471876978874, 0.009813794866204262, -0.023600643500685692, -0.037560731172561646, 0.02034122683107853, 0.04055814817547798, 0.00452223839238286, -0.03639516979455948, 0.0035081496462225914, -0.02949029579758644, -0.030090615153312683, -0.013759014196693897, 0.08343572914600372, -0.0035619023256003857, -0.010782993398606777, -0.0076708379201591015, 0.05438779294490814, 0.03517831489443779, 0.048059992492198944, -0.024312349036335945, 0.019255252555012703, -0.003233209950849414, 0.01927119679749012, -0.020431481301784515, 0.004887066315859556, -0.07854538410902023, 0.04278678819537163, -0.021656783297657967, -0.002337165642529726, 0.024537328630685806, -0.008028276264667511, 0.0504450723528862, -0.04797552525997162, 0.00486130453646183, 0.05903654173016548, 0.00956716574728489, -0.04799090698361397, 0.012905299663543701, -0.026799771934747696, -0.035559576004743576, 0.002909313654527068, 0.016808949410915375, -0.0035223059821873903, -0.023025639355182648, -0.027338039129972458, -0.00039008763269521296, -0.010598897933959961, -0.019405091181397438, 0.024050865322351456, -0.10098972171545029, 0.028835833072662354, 0.020909201353788376, -0.027523456141352654, -0.11933212727308273, -0.0056654103100299835, 0.008788477629423141, -0.037267785519361496, -0.02324158325791359, 0.004024193622171879, 0.025856880471110344, -0.014440145343542099, 0.04999900981783867, -0.04585184529423714, -0.05418497696518898, -0.027644025161862373, -0.0758800134062767, 0.05200422555208206, 0.08796297758817673, 0.05117488652467728, -0.02882908470928669, -0.027253340929746628, -0.006796340923756361, 0.018631471320986748, -0.005076844245195389, -0.029902858659625053, 0.10786721855401993, 0.039346225559711456, 0.004079122096300125, 0.019615573808550835, 0.063544362783432, -0.039420902729034424, 0.024403123185038567, 0.05559714883565903, 0.03997964411973953, -0.009883299469947815, 0.0022422438487410545, -0.06550254672765732, -0.03582165390253067, 0.055315226316452026, -0.01431960053741932, 0.02564498595893383, 0.01025144848972559, -0.003639435162767768, -0.039822597056627274, 0.026115337386727333, -0.015399587340652943, -0.01673150435090065, -0.016405373811721802, -0.016231877729296684, -0.020675059407949448, -0.08806668967008591, -0.011919127777218819, 0.0042989980429410934, 0.0430050753057003, 0.04423539340496063, -0.0427117720246315, 0.004606336355209351, -0.02647150121629238, -0.04883934557437897, -0.035179831087589264, 0.05063965171575546, 0.009322413243353367, 0.006597710773348808, 0.02433944121003151, 0.025636151432991028, -0.03246031329035759, -0.010851453058421612, -0.026682281866669655, -0.03325280547142029, -0.018666308373212814, -0.009361358359456062, 0.05858200415968895, 0.016909494996070862, 0.0018562524346634746, -0.04832790046930313, -0.017236685380339622, 0.05990034341812134, 0.014311827719211578, -0.04913695529103279, -0.019055483862757683, 0.0356910414993763, -0.01981305703520775, -0.01778595522046089, -0.017047708854079247, -0.02411818318068981, 0.11731235682964325, -0.02083938755095005, -0.048948779702186584, 0.01965392753481865, -0.03747701272368431, -0.03136686235666275, -0.030302833765745163, 0.07562186568975449, 0.05419174209237099, 0.0030563706532120705, -0.07548486441373825, 0.020257584750652313, -0.01107980776578188, 0.009285859763622284, -0.04301830381155014, 0.0012679051142185926, 0.024555768817663193, 0.04663974791765213, -0.009195431135594845, -0.003329355036839843, 0.02579347975552082, -0.017154641449451447, -0.06340225785970688, 0.012165290303528309, -0.01132266502827406, 0.0527220144867897, -0.08719611912965775, 0.0379428006708622, 0.01701439917087555, -0.0005775083554908633, 0.04607652500271797, 0.04207231476902962, -0.008580880239605904, 0.004605547990649939, 0.0004012401623185724, 0.019184917211532593, -0.027348503470420837, 0.01517985388636589, -0.005505855660885572, 0.011566047556698322, -0.09713384509086609, 0.004296966828405857, -0.008582772687077522, -0.07131759077310562, 0.03929543495178223, 0.02913559228181839, 0.021799687296152115, -0.04691815748810768, 0.068475641310215, -0.01792267896234989, 0.03442634269595146, 0.03250982612371445, -0.03288746997714043, 0.006486996542662382, -0.043370604515075684, 0.048348113894462585, 0.0029180170968174934, -0.019568540155887604, -0.0827745571732521, -0.014594408683478832, -0.014716580510139465, 0.039404045790433884, 0.031958065927028656, -0.03790922462940216, 0.0031938666943460703, 0.014598692767322063, 0.006778330076485872, -0.03553728386759758, 0.01064466591924429, -0.038900814950466156, 0.04684114456176758, 0.022641697898507118, 0.030532868579030037, 0.027067525312304497, -0.031093310564756393, -0.022285375744104385, -0.002419908531010151, -0.03765278309583664, -0.020026782527565956, 0.01452050730586052, -0.05039013549685478, -6.686770227293812e-33, -0.007313502952456474, -0.030986018478870392, -0.058476753532886505, -0.03135494142770767, -0.03295718505978584, -0.015511655248701572, -0.04292522743344307, -0.02189445123076439, -0.011285768821835518, -0.00027725539985112846, 0.03749699145555496, 0.00275795697234571, 0.007925021462142467, 0.031233161687850952, 0.07237745821475983, 0.016890760511159897, 0.059377409517765045, -0.013455426320433617, 0.055226199328899384, 0.010089951567351818, 0.018314050510525703, 0.05878182873129845, 0.047974083572626114, -0.11420443654060364, -0.022808397188782692, 0.04779037833213806, -0.010184051468968391, -0.04368704929947853, 0.04288908466696739, 0.014794789254665375, 0.02382432110607624, 0.05935099720954895, -0.002602245192974806, -0.020167766138911247, -0.06433672457933426, 0.0017619954887777567, -0.0612945556640625, -0.0684676319360733, -0.08597376942634583, 0.018822509795427322, -0.002442877274006605, -0.03011428564786911, 0.08235201984643936, -0.01183844730257988, -0.014263794757425785, -0.06338011473417282, 0.08890242874622345, -0.04084117338061333, -0.0008092488278634846, -0.03532755374908447, -0.06888112425804138, 0.027521435171365738, -0.03049369901418686, -0.01246589981019497, 0.04872278869152069, 0.02720966935157776, 0.011889160610735416, -0.005180433392524719, -0.08253777027130127, 0.01616012677550316, 0.031133582815527916, 0.05370636284351349, 0.03925374895334244, 0.008886376395821571, 0.030932577326893806, 0.04469633102416992, 0.026985161006450653, -0.012029111385345459, 0.00019730502390302718, 0.01782296970486641, -0.0014356074389070272, 0.06153564155101776, 0.037487562745809555, 0.03739602863788605, 0.07289712876081467, -0.052517857402563095, -0.06375320255756378, 0.055955670773983, -0.06187410280108452, 0.03203503414988518, -0.04675668105483055, -0.0004920598003081977, -0.02435297891497612, -0.013888114131987095, 0.01527248416095972, -0.0199775081127882, -0.013163667172193527, -0.050778914242982864, 0.024121535941958427, -0.045957744121551514, -0.0034679658710956573, 0.03771911934018135, -0.00723815755918622, -0.026533225551247597, 0.04684597626328468, -0.021172411739826202, -0.011136963963508606, 0.03512442857027054, 0.02356199361383915, -0.04207842797040939, -0.013793325051665306, -0.039742037653923035, 0.027349183335900307, 0.03459661826491356, 0.013189232908189297, 0.008118056692183018, 0.015779169276356697, 0.050251465290784836, -0.032483797520399094, -0.023585457354784012, 0.012361101806163788, -0.03785509243607521, 0.06097519397735596, 0.05890457704663277, -0.021084578707814217, -0.005977350287139416, -0.02619609795510769, 0.05532629415392876, 0.012672925367951393, -0.046104636043310165, -0.017577536404132843, -0.009211243130266666, -0.0003107526572421193, 0.043195996433496475, -0.07164141535758972, -0.03906920924782753, -0.060644663870334625, -0.03658641502261162, 0.04866718500852585, -0.05099545419216156, -0.022366385906934738, -0.008027007803320885, 3.161454458222579e-07, -0.0008580462308600545, 0.004812608938664198, 0.0263846293091774, -0.05247754603624344, 0.01790270023047924, 0.03885260224342346, 0.006336072459816933, 0.07247643917798996, 0.010435604490339756, -0.02847871743142605, 0.03496463969349861, -0.004659427795559168, 0.022855741903185844, 0.024208422750234604, -0.04032416269183159, 0.013444659300148487, 0.033122844994068146, 0.02771320752799511, -0.025595441460609436, 0.03354201465845108, 0.06581764668226242, 0.08815920352935791, 0.007591780740767717, -0.02339075319468975, 0.08302002400159836, 0.04717768356204033, 0.013311382383108139, -0.02558753453195095, 0.04297291487455368, 0.008642273023724556, -0.024815909564495087, -0.007010775152593851, -0.02038341946899891, 0.048355553299188614, -0.04267829656600952, 0.029108664020895958, 0.0537540465593338, 0.007411778438836336, -0.031854450702667236, -0.01700940914452076, 0.03733350336551666, 0.023084547370672226, 0.05495290458202362, 0.003103957511484623, 0.03306426480412483, -0.023622864857316017, -0.01413745991885662, -0.04309431090950966, -0.01715964823961258, 0.06770405918359756, 0.045581553131341934, -0.01886104792356491, 0.0020061712712049484, -0.051316384226083755, 0.03620190545916557, -0.0016325499163940549, -0.007050798740237951, -0.011095697991549969, 0.00970112718641758, 0.005845141131430864, -0.01379560399800539, 0.007461496163159609, 0.004863083362579346, -0.017394687980413437, 0.06144833564758301, 0.004232540726661682, 0.027095764875411987, 2.96022607192291e-34, -0.027123549953103065, 0.024433379992842674, -0.0023736676666885614, -0.014816424809396267, -0.03535054251551628, -0.010212481953203678, -0.010404184460639954, 0.004059859551489353, 0.020446013659238815, 0.000729117717128247, -0.05060466378927231]

['David Balduzzi', 'Muhammad Ghifary']

1509.03005v1

This paper proposes GProp, a deep reinforcement learning algorithm for continuous policies with compatible function approximation. The algorithm is based on two innovations. Firstly, we present a temporal-difference based method for learning the gradient of the value-function. Secondly, we present the deviator-actor-critic (DAC) model, which comprises three neural networks that estimate the value function, its gradient, and determine the actor's policy respectively. We evaluate GProp on two challenging tasks: a contextual bandit problem constructed from nonparametric regression datasets that is designed to probe the ability of reinforcement learning algorithms to accurately estimate gradients; and the octopus arm, a challenging reinforcement learning benchmark. GProp is competitive with fully supervised methods on the bandit task and achieves the best performance to date on the octopus arm.

Compatible Value Gradients for Reinforcement Learning of Continuous Deep Policies

http://arxiv.org/pdf/1509.03005v1

Title Compatible Value Gradients Reinforcement Learning Continuous Deep Policies Summary paper proposes GProp deep reinforcement learning algorithm continuous policy compatible function approximation algorithm based two innovation Firstly present temporaldifference based method learning gradient valuefunction Secondly present deviatoractorcritic DAC model comprises three neural network estimate value function gradient determine actor policy respectively evaluate GProp two challenging task contextual bandit problem constructed nonparametric regression datasets designed probe ability reinforcement learning algorithm accurately estimate gradient octopus arm challenging reinforcement learning benchmark GProp competitive fully supervised method bandit task achieves best performance date octopus arm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0199118759483099, 0.019877638667821884, -0.012061123736202717, -0.004727119579911232, 0.021368667483329773, -0.03343823552131653, 0.021761588752269745, -0.025325322523713112, -0.034446652978658676, 0.048284150660037994, -0.047001712024211884, 0.019318830221891403, 0.004566787742078304, 0.07806970924139023, -0.010444642044603825, -0.04805256798863411, 0.019594715908169746, -0.010065277107059956, 0.03153077885508537, 0.0018111871322616935, 0.04246162623167038, -0.05587008595466614, -0.0018620823975652456, 0.03442004695534706, -0.007756800856441259, -0.0010655905352905393, -0.016134364530444145, 0.015133153647184372, 0.06384756416082382, -0.06289845705032349, 0.10543879866600037, -0.04479944705963135, 0.05873396247625351, 0.07848100364208221, 2.7158464490639744e-06, -0.022315453737974167, -0.014485026709735394, -0.027118567377328873, 0.01738194189965725, -0.06200256198644638, 0.018563007935881615, 0.039252474904060364, -0.0197924617677927, 0.035128433257341385, -0.07039446383714676, -0.04053273797035217, 0.03678807243704796, 0.09257610142230988, 0.01582912541925907, 0.0860988199710846, 0.010407080873847008, -0.03537273779511452, 0.039912983775138855, -0.05465799570083618, 0.01925543323159218, -0.047980230301618576, 0.016333503648638725, 0.04671268165111542, -0.0059565594419837, -0.046119410544633865, -0.027454471215605736, -0.019126299768686295, 0.028342265635728836, 0.003963963594287634, -0.006255213636904955, 0.01198570430278778, 0.04378056526184082, -0.008702827617526054, -0.004526527598500252, 0.024736469611525536, -0.07449260354042053, 0.020507080480456352, 0.027672678232192993, -0.014188520610332489, -0.01564796268939972, -0.03267643228173256, 0.002145797712728381, -0.03571894392371178, -0.005149716045707464, 0.0461680144071579, -0.0024499527644366026, 0.0690867155790329, -0.0021817157976329327, 0.02864943817257881, 0.01332674827426672, 0.04602371156215668, -0.053765300661325455, -0.004514471162110567, 0.004274647682905197, -0.01641904190182686, 0.008368010632693768, -0.02824465185403824, -0.008676432073116302, -0.004731823690235615, -0.06554260849952698, -0.038131486624479294, -0.06201053038239479, 0.0068769133649766445, -0.010273216292262077, -0.01357262022793293, 0.05380413681268692, 0.022241627797484398, -0.009008846245706081, 0.03262742981314659, -0.05220628157258034, 0.10056028515100479, -0.07840966433286667, 0.010301041416823864, 0.01776532642543316, 0.039644502103328705, -0.031591929495334625, 0.015398628078401089, 0.011323188431560993, 0.05447431281208992, 0.0017208136850968003, -0.045601747930049896, -0.0613832026720047, -0.02468021959066391, -0.06871654838323593, 0.01321796327829361, 0.016096897423267365, 0.05956629291176796, -0.049229346215724945, 0.026691948994994164, -0.09528744220733643, -0.014475375413894653, -0.023163462057709694, 0.08152878284454346, 0.0153901856392622, 0.04508758336305618, 0.02815636806190014, 0.0022367367055267096, 0.003680950263515115, -0.020059194415807724, 0.049557071179151535, 0.07282226532697678, 0.012203632853925228, 0.062189385294914246, -0.041827328503131866, -0.02651059441268444, 0.043816063553094864, -0.04034508019685745, -0.011302719824016094, -0.0569867305457592, -0.01887747086584568, -0.10024873912334442, -0.042376644909381866, 0.02568638324737549, 0.01324491947889328, -0.021977493539452553, 0.011065487749874592, 0.08414685726165771, 0.03917480632662773, -0.03700981289148331, 0.04008663073182106, -0.007194253616034985, -0.027796750888228416, 0.050746168941259384, 0.009802152402698994, 0.017921410501003265, -0.014729877933859825, 0.016616521403193474, -0.0414917878806591, -0.039713501930236816, 0.00605175131931901, -0.03560440614819527, -0.018848933279514313, -0.03660331666469574, 0.03384701535105705, 0.05813652649521828, 0.028903350234031677, -0.023645078763365746, -0.03377643972635269, -0.03074147179722786, 0.05235017091035843, -0.01862247847020626, 0.054090000689029694, -0.02375941351056099, 0.022159580141305923, -0.014428948052227497, -0.03784014284610748, -0.030664319172501564, -0.004579736851155758, 0.03546023368835449, 0.01763787306845188, 0.008203845471143723, -0.05111059546470642, 0.0241094958037138, -0.05137604847550392, -0.03405197709798813, 0.03878100588917732, -0.02657172456383705, 0.01097372267395258, 0.03495970740914345, 0.04470037296414375, -0.026312585920095444, -0.05167488381266594, -0.10923841595649719, 0.014288409613072872, 0.06739123910665512, -0.03535468876361847, -0.060988519340753555, 0.048760950565338135, -0.013034045696258545, -0.011709059588611126, -0.04202227294445038, -0.03825708478689194, -0.0553622767329216, -0.04615342244505882, -0.026044577360153198, 0.02951287291944027, 0.0062967948615550995, 0.017998607829213142, -0.036881204694509506, -0.04636317864060402, -0.010547593235969543, -0.031703632324934006, 0.0443035364151001, 0.031435709446668625, 0.06648426502943039, -0.004534504376351833, 0.05715227127075195, 0.017601417377591133, 0.012950936332345009, -0.03230414539575577, -0.032707590609788895, 0.04621974751353264, -0.013244551606476307, 0.025769824162125587, -0.032811082899570465, 0.01040066871792078, -0.026190079748630524, -0.035763416439294815, -0.014949305914342403, -0.005354522727429867, -0.013728107325732708, -0.05692867562174797, -0.046363428235054016, 0.03673594817519188, -0.01634328067302704, 0.04773706570267677, 0.04954313859343529, -0.017946964129805565, -0.056927189230918884, -0.02915605902671814, 0.0431022047996521, 0.014299913309514523, -0.019708318635821342, 0.00825600977987051, 0.025776108726859093, 0.04670695215463638, -0.01626385562121868, 0.018052304163575172, 0.015390130691230297, 0.009829362854361534, -0.027984248474240303, 0.062002334743738174, 0.009096772409975529, -0.07436466962099075, 0.006376283243298531, -0.013437554240226746, -0.020428089424967766, 0.004108940716832876, 0.044276513159275055, 0.04950689896941185, 0.0336855947971344, -0.009912217035889626, -0.02960425429046154, 0.030185993760824203, 0.0006179441115818918, -0.02764730155467987, -0.009461075998842716, -0.017457140609622, 0.01277809776365757, -0.03161545470356941, -0.04040311276912689, 0.055936675518751144, -0.022738035768270493, -0.037747934460639954, 0.017982205376029015, 0.04701149836182594, 0.01728140190243721, -0.030041003599762917, -0.022970672696828842, 0.010484900325536728, -0.006916470360010862, 0.007132186088711023, -0.006794252898544073, -0.00888155773282051, -0.04396231099963188, 0.011425322853028774, 0.046862147748470306, -0.01728126034140587, -0.009607464075088501, -0.008777647279202938, 0.016572263091802597, 0.00898316316306591, 0.05475621670484543, 0.01684476062655449, 0.04052276536822319, -0.03756488487124443, 0.048558034002780914, -0.079485222697258, 0.050534628331661224, -0.02754710428416729, -0.020163999870419502, -0.017874475568532944, 0.03705556318163872, 0.0010648173047229648, 0.05610143393278122, -0.002417126903310418, 0.047353725880384445, -0.052278731018304825, 0.010220416821539402, 0.008532566949725151, -0.03747154772281647, -0.010666021145880222, 0.057742681354284286, -0.0251641646027565, -0.05478327348828316, -0.008652237243950367, -0.007188793271780014, 0.037619564682245255, 0.028166528791189194, -0.006759047042578459, -0.005637358874082565, -0.08085446804761887, -0.00646190345287323, -0.019901975989341736, 0.022929251194000244, 0.007172871381044388, -0.03335979953408241, -0.04327942058444023, -0.03986169397830963, -0.012040508911013603, 0.04191778600215912, -0.016668420284986496, -0.01573246717453003, 0.024037064984440804, 0.007947622798383236, -0.019068680703639984, -0.028321782127022743, -0.03194696828722954, 0.0141068110242486, 0.0010116561315953732, 0.022621726617217064, -0.03674717992544174, -0.04438214749097824, -0.004466621670871973, -0.014809521846473217, 0.00026676899869926274, 0.05141868442296982, -0.065180204808712, -0.015773288905620575, -0.01234456617385149, 0.011463870294392109, 0.07699373364448547, -0.013878030702471733, -0.02028988115489483, 0.0030643013305962086, 0.06140603497624397, 0.004545914474874735, 0.028240427374839783, 0.008221540600061417, -0.09851190447807312, 0.03490495681762695, 0.0073753781616687775, -0.004418315831571817, -0.006968484725803137, 0.03059910237789154, -0.014268292114138603, -0.09696833044290543, 0.013825688511133194, 0.006504158955067396, -0.036930978298187256, -0.048143818974494934, -0.04101722687482834, -0.02758469618856907, 0.02758098766207695, -0.0004351471725385636, 0.010048536583781242, -0.043741144239902496, -0.026520641520619392, -0.013231744058430195, 0.030922235921025276, -0.034810278564691544, -0.03522154688835144, -0.007267750799655914, -0.056129466742277145, 0.03400484472513199, -0.0368497297167778, -0.0346049927175045, -0.01734728179872036, -0.007804504130035639, 0.019578972831368446, -0.037535786628723145, 0.00031290235347114503, 0.03711407631635666, 0.0285788606852293, -0.03308563679456711, 0.019796188920736313, -0.011139665730297565, 0.0009797867387533188, 0.013745979405939579, -0.05574393272399902, -0.004254977218806744, 0.1264086365699768, 0.010041153989732265, -0.042608972638845444, 0.0005039144889451563, 0.02442835085093975, 0.024692589417099953, 0.0057870447635650635, 0.025778334587812424, 0.021386077627539635, -0.01568153128027916, -0.024874137714505196, 0.03271155804395676, 0.09282657504081726, 0.022919759154319763, 0.04083818942308426, 0.0016918070614337921, 0.0414845235645771, 0.005715773906558752, -0.017989715561270714, -0.04882526397705078, -0.03763439878821373, 0.05439765006303787, -0.009695842862129211, -0.051194481551647186, -0.02234400436282158, -0.10098128020763397, -0.006717605981975794, -0.022831076756119728, -0.04363805055618286, -0.018045013770461082, -0.0017122345743700862, 0.012259317561984062, -0.009639939293265343, -0.01968969590961933, -0.022948453202843666, -0.04113178327679634, 0.037022802978754044, -0.027116870507597923, 0.014535189606249332, -0.008530734106898308, 0.02366119623184204, -0.0443459190428257, -0.04017147049307823, 0.037988219410181046, 0.025576965883374214, -0.060646869242191315, 0.04339224845170975, 0.0002958657860290259, -0.018251031637191772, -0.026966413483023643, -0.03669918328523636, -0.03465152904391289, -0.02454199455678463, -0.027268506586551666, 0.05327218025922775, -0.00013379041047301143, -0.0009470630320720375, -0.019159696996212006, 0.0069092875346541405, 0.06326315551996231, 0.011374441906809807, 0.04121323674917221, -0.012551731429994106, 0.05866483971476555, 0.04649162292480469, -0.011694331653416157, 0.020318616181612015, -0.020986313000321388, 0.01304631307721138, -0.02446061559021473, 0.022599687799811363, 0.002732283901423216, 0.04944789782166481, 0.015208740718662739, -0.07663270086050034, 0.028992239385843277, 0.05272034555673599, -0.02061387710273266, -0.02100028470158577, 0.01816137321293354, 0.04084499180316925, -0.007451364304870367, -0.03730819374322891, 0.02516711689531803, 0.02550388313829899, -0.00628520455211401, 0.028775164857506752, -0.043379638344049454, 0.07759260386228561, -0.040341973304748535, -0.02637655846774578, 0.03761841729283333, 0.023374920710921288, 0.06576574593782425, -0.018626227974891663, 0.010088280774652958, 0.0101133082062006, 0.028321105986833572, 0.016387393698096275, 0.008985261432826519, -0.004362207371741533, 0.016295213252305984, 0.02232779562473297, 0.018658410757780075, 0.015095407143235207, -0.030324609950184822, -0.006797261070460081, -0.07642120122909546, -0.03781929612159729, 0.01025531254708767, 0.04392854496836662, -0.007249659858644009, -0.0327792651951313, -0.0314549058675766, 0.01800473965704441, -0.010236375033855438, 0.0012926673516631126, -0.04563736170530319, 0.027949487790465355, 0.07097878307104111, 0.005752173252403736, -0.008854163810610771, 0.016507690772414207, 0.05517324432730675, 0.062285952270030975, 0.017621511593461037, -0.036265622824430466, 0.0171294454485178, 0.007095444481819868, -0.019498055800795555, 0.05312798172235489, 0.007869217544794083, 0.00041587927262298763, -0.0045795682817697525, 0.04619395360350609, -0.008815068751573563, -0.00997219793498516, 0.027174005284905434, 0.02314794808626175, -0.0004946000990457833, 0.00823983270674944, -0.028434745967388153, -0.045961037278175354, 0.03819536045193672, -0.012385123409330845, -4.4563123083207756e-05, -0.016158511862158775, -0.003111479105427861, -0.05812565237283707, -6.867993252624207e-33, 0.01933877170085907, -0.0077907731756567955, -0.007010461296886206, -0.08506620675325394, -0.04844726249575615, 0.03592367470264435, -0.008400472812354565, -0.05566704645752907, 0.00651525380089879, 0.007933683693408966, -0.005248492117971182, 0.04076875373721123, 0.011782919056713581, 0.028909770771861076, 0.020325811579823494, -0.06291069090366364, 0.0023234295658767223, -0.00023233873071148992, 0.03281174600124359, 0.00961254257708788, 0.02214750088751316, 0.028596200048923492, 0.008817299269139767, -0.0418177992105484, -0.019195346161723137, 0.05816585198044777, -0.008949300274252892, -0.01783062145113945, 0.012293776497244835, 0.056022096425294876, 0.0027825406286865473, 0.002021270338445902, -0.01815563440322876, -0.08248047530651093, -0.017725197598338127, -0.0025810208171606064, -0.03738937899470329, -0.0371941477060318, -0.061221711337566376, 0.011918151751160622, -0.07084177434444427, 0.010573115199804306, 0.05704474076628685, 0.0010638340609148145, -0.003208525711670518, -0.0006710286252200603, 0.03533165529370308, 0.01711563766002655, -0.004381084814667702, -0.032034922391176224, -0.020513737574219704, -0.003263372229412198, 0.018310902640223503, 0.028160901740193367, 0.04624159261584282, 0.015075738541781902, -0.019750360399484634, 0.006461641285568476, -0.04591429606080055, -0.008573796600103378, -0.04508746787905693, 0.05084359273314476, -0.03165597468614578, 0.07169076800346375, 0.0695333480834961, 0.005604761186987162, -0.03527522832155228, -0.03490791097283363, 0.01305339951068163, -0.034501656889915466, -0.02030211314558983, 0.07254939526319504, -0.031929317861795425, 0.026215810328722, 0.09285794943571091, -0.052850473672151566, -0.015246901661157608, 0.04366503283381462, 0.007806912064552307, 0.03764457628130913, 0.00614688266068697, 0.0051435986533761024, -0.09133977442979813, 0.0364367738366127, 0.0024864741135388613, -0.02393457666039467, -0.02592676505446434, -0.048316776752471924, 0.031062079593539238, 0.03028438426554203, 0.056740984320640564, 0.006441902369260788, 0.02244013175368309, -0.06213153526186943, 0.02587856911122799, -0.006320998538285494, 0.0035724418703466654, 0.03160051628947258, 0.018819546326994896, 0.010947879403829575, -0.04599858075380325, -0.041658636182546616, -0.031546927988529205, -0.0011902411933988333, 0.02483941614627838, 0.02601950615644455, -0.03490857034921646, 0.025319106876850128, -0.0015620313351973891, -0.012155276723206043, -0.0008233247208409011, 0.0003666759002953768, 0.013013320043683052, 0.034522540867328644, 0.03344815596938133, -0.030311983078718185, -0.0012301828246563673, 0.07351228594779968, -0.004508973564952612, -0.021344255656003952, -0.034517742693424225, 0.012673664838075638, -0.013698353432118893, 0.033368516713380814, -0.047978293150663376, 0.03331310302019119, -0.04980894550681114, 0.04435222968459129, -0.07104431837797165, -0.0673917755484581, 0.02182546630501747, 0.009191961027681828, 3.3561917689439724e-07, -0.08930961787700653, -0.03170911967754364, 0.008040488697588444, 0.029255831614136696, -0.012753228656947613, 0.0478239469230175, 0.011684784665703773, 0.009209594689309597, -0.041154175996780396, -0.001636429806239903, 0.04425261542201042, -0.031870584934949875, 0.02824932336807251, 0.014499322511255741, -0.010904914699494839, -0.03326414152979851, -0.030705520883202553, 0.05126630514860153, -0.035348713397979736, -0.03702351823449135, -0.001956046326085925, 0.056187354028224945, 0.05569078028202057, -0.019335603341460228, 0.06965352594852448, 0.044242843985557556, 0.016023313626646996, 0.021333016455173492, 0.03271162882447243, -0.006638191640377045, 0.010909847915172577, 0.032037459313869476, -0.017936276271939278, -0.007364092394709587, -0.014129338786005974, 0.0930057018995285, -0.02989805117249489, 0.04027421772480011, -0.01355696003884077, -0.053506724536418915, 0.0025327724870294333, 0.011453252285718918, 0.025960363447666168, -0.059956129640340805, 0.031311023980379105, 0.0019743076991289854, -0.007821706123650074, -0.016289614140987396, 0.009710521437227726, 0.01577572524547577, 0.059316761791706085, -0.008471502922475338, -0.025021230801939964, -0.04466507211327553, 0.025167006999254227, -0.0037260272074490786, -0.01262905914336443, -0.03720493242144585, 0.02167574129998684, 0.04350557178258896, -0.039718128740787506, 0.01903778314590454, -0.04057425633072853, 0.0766526311635971, 0.0538497269153595, -0.03528745099902153, 0.006052305921912193, 3.4127390507566805e-34, -0.012359924614429474, -0.01639677584171295, -0.0025072917342185974, 0.008077769540250301, -0.021975133568048477, 0.028072040528059006, 0.019750069826841354, 0.018832972273230553, 0.06454121321439743, 0.005637279711663723, -0.05715468153357506]

['Takayuki Osogami', 'Makoto Otsuka']

1509.08634v1

We propose a particularly structured Boltzmann machine, which we refer to as a dynamic Boltzmann machine (DyBM), as a stochastic model of a multi-dimensional time-series. The DyBM can have infinitely many layers of units but allows exact and efficient inference and learning when its parameters have a proposed structure. This proposed structure is motivated by postulates and observations, from biological neural networks, that the synaptic weight is strengthened or weakened, depending on the timing of spikes (i.e., spike-timing dependent plasticity or STDP). We show that the learning rule of updating the parameters of the DyBM in the direction of maximizing the likelihood of given time-series can be interpreted as STDP with long term potentiation and long term depression. The learning rule has a guarantee of convergence and can be performed in a distributed matter (i.e., local in space) with limited memory (i.e., local in time).

Learning dynamic Boltzmann machines with spike-timing dependent plasticity

http://arxiv.org/pdf/1509.08634v1

Title Learning dynamic Boltzmann machine spiketiming dependent plasticity Summary propose particularly structured Boltzmann machine refer dynamic Boltzmann machine DyBM stochastic model multidimensional timeseries DyBM infinitely many layer unit allows exact efficient inference learning parameter proposed structure proposed structure motivated postulate observation biological neural network synaptic weight strengthened weakened depending timing spike ie spiketiming dependent plasticity STDP show learning rule updating parameter DyBM direction maximizing likelihood given timeseries interpreted STDP long term potentiation long term depression learning rule guarantee convergence performed distributed matter ie local space limited memory ie local time Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.023196227848529816, -0.07988418638706207, -0.03992109000682831, 0.012567665427923203, 0.015530785545706749, 0.014076362363994122, 0.028746625408530235, -0.01719609461724758, -0.006394918542355299, 0.04103895276784897, 0.008705190382897854, 0.029434477910399437, 0.0034950783010572195, 0.06274043768644333, 0.03900062292814255, -0.03250966593623161, 0.06540630012750626, 0.01042582280933857, 0.0009419082780368626, -0.05037889629602432, 0.0731574073433876, -0.04354081675410271, -0.0171426460146904, 0.010257535614073277, -0.026693962514400482, -0.013370118103921413, -0.011652004905045033, -0.028975553810596466, 0.05579884722828865, -0.030700966715812683, -0.002811918267980218, -0.03796182572841644, 0.0020289199892431498, 0.01995670422911644, 2.096443495247513e-06, 0.013728436082601547, 0.037283577024936676, -0.010024890303611755, 0.005816708318889141, -0.03749804571270943, -0.0010032361606135964, -0.04922035336494446, -0.006614626385271549, -0.007913569919764996, -0.0054320357739925385, -0.04934345930814743, 0.044743359088897705, 0.025356873869895935, 0.0003614072338677943, 0.040406081825494766, -0.004974625073373318, -0.03043547086417675, 0.04993734508752823, 0.0006179889314807951, 0.03470822051167488, 0.011572368443012238, 0.0028129953425377607, 0.024674922227859497, 0.0064418623223900795, 0.00032568309688940644, -0.050192177295684814, 0.038102611899375916, 0.033958323299884796, 0.02584516443312168, 0.0830894336104393, 0.02322624810039997, -0.049205973744392395, -0.0063838898204267025, -0.012190678156912327, 0.02630559913814068, -0.04370184242725372, 0.011446366086602211, 0.002403523540124297, -0.01938512921333313, -0.03806013613939285, -0.036708712577819824, -0.025996234267950058, -0.016618309542536736, -0.011188097298145294, 0.02169872634112835, -0.014678068459033966, 0.037141427397727966, 0.04963609576225281, -0.0317809171974659, 0.02601110190153122, 0.030510447919368744, -0.001755186589434743, 0.028823314234614372, -0.0389864519238472, -0.026887530460953712, 0.03968081250786781, 0.024638717994093895, -0.04086839407682419, 0.01568560302257538, 0.012855962850153446, 0.0018294657347723842, -0.02807559072971344, -0.024006042629480362, 0.01671864651143551, -0.01667729765176773, 0.01078183576464653, -0.007819795981049538, 0.018264129757881165, -0.015512307174503803, -0.03876722976565361, -0.02892870083451271, -0.05691874772310257, 0.04381118342280388, 0.003253769362345338, 0.016702549532055855, -0.0810747966170311, 0.009000699035823345, 0.04858934506773949, 0.04066188633441925, 0.04673846811056137, 0.007065888028591871, -0.10574118793010712, 0.05601891502737999, -0.01421862468123436, -0.04527205973863602, -0.06329523026943207, 0.006813131272792816, -0.0016870254185050726, 0.01211460679769516, -0.04020766541361809, -0.017151573672890663, -0.010575535707175732, 0.024204595014452934, 0.008981455117464066, 0.006714981514960527, -0.012888568453490734, -0.01897510513663292, -0.02022487297654152, 0.03303568437695503, -0.034254446625709534, 0.08254963904619217, 0.0238413754850626, 0.021552033722400665, -0.0804288387298584, 0.030432770028710365, -0.0340762734413147, 0.03669147565960884, -0.010875677689909935, -0.019795536994934082, 0.016823653131723404, 0.0009346693404950202, -0.015401133336126804, 0.0463179387152195, 0.0009671805310063064, -0.023677274584770203, 0.026784969493746758, 0.03423380106687546, 0.004900278057903051, -0.029196081683039665, 0.08098847419023514, -0.033336445689201355, -0.02324107103049755, 0.020653190091252327, 0.028721265494823456, -0.0007849248358979821, 0.01020901184529066, 0.0031648094300180674, 0.012698451057076454, 0.0024910212960094213, -0.0011435268679633737, -0.01961711421608925, -0.07855566591024399, -0.08860855549573898, 0.05982934683561325, 0.022065965458750725, 0.0032858431804925203, 0.00901363231241703, -0.022102510556578636, -0.013679813593626022, 0.03686720132827759, 0.017834551632404327, 0.010619626380503178, 0.05163147300481796, -0.0005636580754071474, -0.04000256955623627, 0.007506050635129213, -0.020264336839318275, 0.017937444150447845, 0.07123654335737228, -0.03104529343545437, 0.02121211402118206, -0.06620968878269196, -0.007462302688509226, -0.014774090610444546, -0.029919084161520004, 0.022577092051506042, -0.03540879115462303, -0.008818884380161762, -0.033120181411504745, 0.025866501033306122, -0.02544652856886387, -0.013373298570513725, -0.016517478972673416, -0.01925167441368103, 0.04765214025974274, -0.037227123975753784, -0.00619689654558897, -0.0200317595154047, 0.002583645051345229, 0.0027430779300630093, -0.0403752401471138, -0.0035380187910050154, -0.0020847588311880827, -0.02911921963095665, -0.014269169420003891, -0.04602276161313057, 0.0010032241698354483, 0.02442498691380024, -0.04652455076575279, 0.023989684879779816, -0.02289678156375885, -0.014503144659101963, 0.02235681749880314, -0.03365248441696167, -0.008213633671402931, 0.0031779909040778875, 0.04100186377763748, -0.038312822580337524, -0.010827356018126011, -0.011234893463551998, 0.01479192916303873, 0.0606570765376091, 0.001595262554474175, 0.006079273764044046, -0.05154991149902344, 0.008238988928496838, -0.03009639121592045, 0.010933870449662209, -0.07181432843208313, 0.0036521495785564184, 0.0340893417596817, -0.03702405467629433, -0.020268727093935013, -0.007354918401688337, 0.046340201050043106, 0.036984290927648544, -0.035141799598932266, -0.02210879512131214, -0.06820745766162872, 0.013932991772890091, 0.0315714105963707, 0.0014435434713959694, -0.008155758492648602, 0.01417379267513752, 0.012555278837680817, 0.03815026581287384, -0.009379287250339985, 0.02103542350232601, 0.03233496472239494, -0.022983718663454056, -0.014402789063751698, 0.05869610980153084, 0.024960393086075783, -0.047340769320726395, -0.019924979656934738, 0.0036017191596329212, 0.011454521678388119, -0.018028350546956062, -0.033508460968732834, -0.04847591742873192, -0.01444315630942583, 0.01048049982637167, 0.05551047995686531, -0.010321974754333496, 0.02761474810540676, -0.03217686340212822, -0.054964903742074966, 0.01550999004393816, 0.015515079721808434, 0.007677690591663122, -0.02270900458097458, 0.13411423563957214, -0.026943925768136978, -0.06921440362930298, 0.08169208467006683, 0.010332788340747356, 0.01651308499276638, -0.02572416514158249, -0.04211127385497093, -0.016692008823156357, 0.06017396226525307, 0.021986687555909157, -0.03821057453751564, 0.018918771296739578, 0.015642989426851273, 0.01254662498831749, 0.015329858288168907, 0.006045022048056126, -0.04261713847517967, 0.008186549879610538, -0.012575874105095863, 0.05714947730302811, 0.038670413196086884, 0.06166043132543564, -0.05284198001027107, 0.005479289684444666, 0.023814747110009193, 0.0012869049096480012, 0.009833254851400852, -0.0537593737244606, 0.05418764427304268, 0.007507191505283117, 0.029184462502598763, -0.030194738879799843, 0.04880734160542488, 0.04847997426986694, -0.0012710231821984053, -0.034772202372550964, 0.026545142754912376, 0.01800493709743023, 0.028389066457748413, -0.023256437852978706, 0.005810962524265051, -0.03556087240576744, 0.004660650622099638, 0.005595755763351917, -0.042190875858068466, 0.07346426695585251, 0.06070229038596153, 0.06949859112501144, 0.01423526182770729, -0.029879381880164146, -0.0019849941600114107, 0.0006451455992646515, 0.033076342195272446, 0.033173590898513794, 0.017381807789206505, 0.0017323960782960057, -0.009650776162743568, 0.01724761165678501, -0.024843282997608185, 0.02035043016076088, 0.0023352797143161297, 0.010225534439086914, -0.031137406826019287, 0.005842039827257395, -0.011475837789475918, -0.04428813233971596, 0.051130469888448715, -0.010625920258462429, 0.01660594902932644, 0.01044338010251522, -0.015682697296142578, 0.018444521352648735, -0.0341888926923275, 0.013588395901024342, 0.01923762634396553, -0.04930538311600685, -0.026127584278583527, -0.046210289001464844, -0.006606288254261017, -0.02356642670929432, -0.020484812557697296, 0.002182441297918558, 0.033204007893800735, 0.07053086161613464, -0.03730419650673866, -0.014173927716910839, 0.023891353979706764, -0.11667735874652863, -0.002919981023296714, -0.04578423127532005, 0.024220436811447144, -0.005053576081991196, -0.0016886134399101138, -0.008561517111957073, -0.05056781694293022, 0.008342990651726723, 0.0026262719184160233, -0.023109307512640953, -0.0676010251045227, -0.024310315027832985, -0.03317752480506897, -0.03279896453022957, -0.014006712473928928, 0.016651149839162827, -0.03754492104053497, -0.01732231117784977, -0.05713905021548271, 8.435388735961169e-05, -0.00851510465145111, 0.018531350418925285, 0.009490147233009338, -0.009183892980217934, 0.009672724641859531, 0.013720781542360783, -0.01764610782265663, 0.057357948273420334, -0.010391028597950935, -0.0522049255669117, -0.020100196823477745, -0.0016531947767361999, 0.039161231368780136, 0.022914351895451546, 0.03527442738413811, 0.021332383155822754, 0.004759571980684996, -0.037436142563819885, 0.039000287652015686, -0.08586132526397705, 0.049718864262104034, 0.07647344470024109, -0.03284798189997673, -0.06662667542695999, -0.020310476422309875, 0.00021050895156804472, -0.011882362887263298, 0.02471698261797428, -0.01990431360900402, 0.00423792190849781, 0.048559002578258514, -0.04489421099424362, -0.03377649188041687, 0.0754840224981308, 0.005779601167887449, -0.0025672370102256536, -0.03604404628276825, 0.018662143498659134, -0.009527282789349556, 0.03421363979578018, -0.04567592963576317, -0.0112643763422966, -0.037404537200927734, 0.0026478797663003206, 0.005689505022019148, -0.030983783304691315, -0.07333642244338989, -0.03696473315358162, 0.020294316112995148, -0.06620598584413528, -0.03646480664610863, 0.011302023194730282, 0.021418221294879913, -0.05544552579522133, -0.06887854635715485, 0.04513736441731453, -0.05854111909866333, 0.061832256615161896, 0.03773865848779678, 0.0036712950095534325, 0.05454220622777939, -0.018733184784650803, -0.005973024759441614, -0.043558232486248016, 0.08013900369405746, 0.006214464083313942, -0.06114177033305168, 0.003259718418121338, 0.0780882015824318, -0.03840461000800133, 0.02300160937011242, -0.03507066145539284, -0.040360935032367706, -0.027512889355421066, 0.03827010840177536, 0.06169923394918442, -0.007678372319787741, 0.013232406228780746, -0.021474607288837433, -0.018223010003566742, 0.042046383023262024, 0.046369072049856186, 0.028046568855643272, 0.03148205950856209, 0.038330450654029846, 0.018613357096910477, -0.033693231642246246, 0.0026496832724660635, 0.007000709883868694, 0.07637637853622437, 0.007764454465359449, 0.018829500302672386, -0.048751816153526306, 0.04800371080636978, -0.00676859263330698, -0.022959213703870773, 0.05456458777189255, 0.05000925064086914, -0.027766555547714233, -0.00749788386747241, 0.018904076889157295, 0.07169163227081299, 0.061138782650232315, -0.02102230302989483, -0.009753523394465446, 0.054751280695199966, -0.019625365734100342, -0.015968184918165207, -0.08489476144313812, 0.06948976218700409, -0.06416235864162445, 0.027842139825224876, 0.002409344306215644, -0.01180463470518589, 0.03237762674689293, -0.05883866548538208, 0.03771049156785011, -0.01664367876946926, 0.04626155644655228, -0.03232964128255844, -0.006964861415326595, -0.002195719163864851, 0.03540058434009552, -0.0031389635987579823, 0.03841855376958847, -0.07873177528381348, -0.01147280354052782, -0.01497119665145874, 0.03211550414562225, 0.015217732638120651, -0.03705914691090584, -0.008174876682460308, 0.008562305010855198, -0.004417578689754009, 0.00537215918302536, 0.015303175896406174, -0.03030708245933056, 0.01998766139149666, -0.028393156826496124, 0.04075554758310318, 0.04430639371275902, 0.03615432232618332, -0.007890094071626663, -0.0295504629611969, 0.05603167414665222, 0.0049778977409005165, -0.033511850982904434, 0.00277884304523468, -0.009696321561932564, 0.03590593859553337, 0.035279788076877594, -0.04092613235116005, -0.02188938856124878, 0.003896209178492427, -0.03689362853765488, 0.006462952587753534, 0.0031308552715927362, 0.042648736387491226, 0.03291276842355728, 0.0744854137301445, -0.03035632334649563, 0.00018221345089841634, 0.028479482978582382, 0.022803187370300293, -0.038032349199056625, -0.009703126735985279, -0.014898298308253288, 0.09418883919715881, -0.010450608097016811, -0.010484417900443077, -5.593773906722156e-33, 0.03584323823451996, 0.010483695194125175, -0.0047873095609247684, 0.047310955822467804, -0.004867199808359146, 0.036898866295814514, -0.030580749735236168, 0.014036212116479874, 0.006789871957153082, -0.03525524213910103, -0.025356965139508247, 0.029094522818922997, 0.0035770537797361612, -0.0020412851590663195, 0.09131655842065811, -0.034988902509212494, -0.03654257580637932, -0.039812617003917694, 0.06253096461296082, 0.02086770534515381, 0.06823058426380157, 0.0374150313436985, 0.0009770687902346253, 0.032859139144420624, -0.01860516145825386, 0.0352153517305851, -0.01299259066581726, -0.06275874376296997, -0.014833939261734486, 0.001899361377581954, -0.05879511684179306, 0.011470816098153591, -0.026115044951438904, -0.04070283845067024, -0.030395567417144775, -0.06025420501828194, -0.025252213701605797, 0.03170676529407501, -0.06330784410238266, -0.04548223689198494, -0.04047757759690285, -0.011447065509855747, 0.09367204457521439, -0.01365363597869873, -0.056613072752952576, 0.02869938500225544, 0.01266392506659031, -0.06278550624847412, -0.004503754433244467, -0.08788403868675232, 0.006000937428325415, 0.0075715165585279465, -0.000716543581802398, 0.032606542110443115, 0.009842791594564915, -0.043368253856897354, -0.028596263378858566, 0.058358293026685715, -0.09791425615549088, 0.017826547846198082, 0.047891758382320404, 0.044232290238142014, -0.02519175037741661, 0.061739228665828705, 0.09457259625196457, 0.04165508225560188, 0.07411157339811325, 0.03594356030225754, 0.01436631754040718, 0.048576682806015015, 0.031139399856328964, 0.033491093665361404, 0.07077806442975998, 0.03588305041193962, 0.08904460072517395, -0.043885182589292526, -0.05941964313387871, 0.05643573775887489, 0.05014324188232422, 0.011930015869438648, 0.007900910452008247, 0.02395995520055294, 0.00718869362026453, -0.0323442704975605, 0.060841236263513565, 0.03588559105992317, -0.015721075236797333, -0.04623599350452423, -0.026411624625325203, -0.04320777580142021, 0.027560904622077942, 0.0026213431265205145, -0.028732405975461006, -0.01848471909761429, 0.08674099296331406, 0.0027082152664661407, 0.003626435762271285, 0.01525293942540884, 0.025639411062002182, -0.02218911238014698, -0.01475647371262312, -0.0120085459202528, -0.04557988792657852, 0.0055214776657521725, 0.007699060253798962, 0.0022991413716226816, -0.02631826512515545, 0.044254787266254425, 0.048412345349788666, -0.02511628158390522, 0.02340817265212536, -0.056289512664079666, 0.047427818179130554, 0.014136734418570995, -0.0037601995281875134, -0.06783035397529602, 0.0006050041411072016, 0.0441160649061203, -0.028263816609978676, 0.02050074003636837, -0.019675785675644875, 0.013831800781190395, 0.017354920506477356, 0.07861705124378204, -0.04377627372741699, -0.048244550824165344, -0.035660769790410995, 0.015539000742137432, -0.05177824944257736, -0.0813041552901268, -0.017143430188298225, 0.03216654807329178, 2.8056160772393923e-07, -0.04586922749876976, -0.0002473277854733169, 0.0010292829247191548, -0.02743375115096569, 0.049833934754133224, 0.019331980496644974, -0.02026597037911415, -0.03113127127289772, -0.016906317323446274, -0.04281668737530708, 0.03280056267976761, 0.0065030804835259914, 0.02246139757335186, 0.007774096913635731, -0.05672977864742279, -0.03552357852458954, 0.018967004492878914, 0.05177188292145729, -0.006102941930294037, -0.02694735676050186, -0.04184229299426079, 0.041322145611047745, 0.00910750962793827, -0.016799230128526688, 0.07504765689373016, 0.026989439502358437, 0.02441231533885002, 0.018965966999530792, 0.007677449844777584, -0.009165214374661446, -0.000745505909435451, -0.012485356070101261, -0.01678536646068096, -0.006633051671087742, -0.017823603004217148, -0.00435073534026742, -0.05570552870631218, -0.036881692707538605, -0.008876408450305462, -0.04104076325893402, 0.05000120401382446, 0.020231012254953384, 0.02082146517932415, -0.0030576977878808975, 0.02979627624154091, -0.04937365651130676, -0.03818662092089653, 0.02386101894080639, 0.030830159783363342, -0.014605768024921417, 0.08215460181236267, -0.03153596073389053, -0.011383241042494774, -0.042870305478572845, -0.032823123037815094, -0.03647880256175995, -0.008422446437180042, -0.037775956094264984, 0.03300243616104126, 0.07459469139575958, -0.014266951009631157, 0.026973692700266838, -0.06520775705575943, 0.0033132662065327168, 0.040688641369342804, 0.019753437489271164, -0.013596635311841965, 2.294721781914795e-34, 0.028635669499635696, -0.035450536757707596, -0.04095317795872688, 0.033635713160037994, -0.029789283871650696, -0.0007555161137133837, -0.054721228778362274, -0.003819108474999666, -0.02914045751094818, -0.06447046250104904, -0.06729180365800858]

['Yujia Li', 'Daniel Tarlow', 'Marc Brockschmidt', 'Richard Zemel']

1511.05493v4

Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is previous work on Graph Neural Networks (Scarselli et al., 2009), which we modify to use gated recurrent units and modern optimization techniques and then extend to output sequences. The result is a flexible and broadly useful class of neural network models that has favorable inductive biases relative to purely sequence-based models (e.g., LSTMs) when the problem is graph-structured. We demonstrate the capabilities on some simple AI (bAbI) and graph algorithm learning tasks. We then show it achieves state-of-the-art performance on a problem from program verification, in which subgraphs need to be matched to abstract data structures.

Gated Graph Sequence Neural Networks

http://arxiv.org/pdf/1511.05493v4

Title Gated Graph Sequence Neural Networks Summary Graphstructured data appears frequently domain including chemistry natural language semantics social network knowledge base work study feature learning technique graphstructured input starting point previous work Graph Neural Networks Scarselli et al 2009 modify use gated recurrent unit modern optimization technique extend output sequence result flexible broadly useful class neural network model favorable inductive bias relative purely sequencebased model eg LSTMs problem graphstructured demonstrate capability simple AI bAbI graph algorithm learning task show achieves stateoftheart performance problem program verification subgraphs need matched abstract data structure Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.004501670598983765, 0.04923496022820473, 0.006892047822475433, 0.03186250478029251, -0.04291075840592384, -0.03801732137799263, 0.0056146360002458096, 0.047856032848358154, 0.07702115923166275, -0.02041093073785305, 0.029697367921471596, -0.00595736363902688, -0.0017703132471069694, 0.09651996940374374, 0.01963501051068306, -0.019595561549067497, 0.027039317414164543, 0.01223447173833847, 0.017459845170378685, -0.005635842215269804, 0.020410217344760895, 0.007075871340930462, 0.01139416079968214, 0.05240536481142044, -0.035339951515197754, 0.008322940208017826, -0.012395843863487244, -0.007119625806808472, 0.0032018297351896763, -0.09022475779056549, 0.032301608473062515, 0.0411633625626564, 0.02911345288157463, 0.02341090887784958, 2.1457801722135628e-06, -0.043259941041469574, -0.03418359160423279, -0.013861383311450481, 0.012099739164113998, -0.028092065826058388, 0.023922262713313103, -0.034772586077451706, 0.03651163727045059, -0.0025070144329220057, -0.07460558414459229, -0.04079319164156914, 0.0588204562664032, -0.0031815040856599808, 0.026314809918403625, 0.051728256046772, -0.012197325937449932, -0.023391271010041237, -0.002723843324929476, -0.027862820774316788, 0.018257996067404747, -0.04088843986392021, 0.050819020718336105, 0.011476218700408936, 0.03877171128988266, -0.02055359072983265, -0.02768821455538273, 0.04755126312375069, -0.013562826439738274, -0.014114167541265488, 0.05924002453684807, 0.02281138300895691, 0.017079081386327744, -0.02684919163584709, -0.0012874770909547806, 0.10508473962545395, -0.03595677763223648, -0.02469361573457718, 0.010645399801433086, -0.014671830460429192, -0.03685303032398224, -0.017288006842136383, -0.014178158715367317, -0.029757194221019745, -0.016151050105690956, 0.010340261273086071, -0.030109407380223274, 0.01663113385438919, 0.0477168969810009, -0.02480880543589592, -0.005867308937013149, 0.0587967149913311, -0.03283582627773285, 0.007626196835190058, 0.012022064067423344, -0.019599081948399544, -0.004799252841621637, -0.03460369259119034, 0.026765624061226845, 0.04319051653146744, -0.017694110050797462, -0.005321761127561331, 0.02709423378109932, -0.009930451400578022, 0.036074090749025345, -0.007474843878298998, 0.0356566421687603, -0.0553109385073185, 0.02824035845696926, 0.016741324216127396, 0.015073646791279316, -0.0011365590617060661, -0.017047880217432976, 0.04127570614218712, -0.023355834186077118, 0.04858793690800667, -0.07548020780086517, 0.004274141043424606, -0.009977811016142368, 0.05659136548638344, 0.039428986608982086, -0.029256943613290787, -0.08313695341348648, -0.015362000092864037, -0.00967000424861908, 0.013183578848838806, 0.053543977439403534, 0.08374657481908798, 0.052258387207984924, 0.010450921021401882, 0.019124170765280724, 0.029550444334745407, 0.02033526450395584, 0.01104904618114233, -0.01828203909099102, -0.00957044493407011, -0.004383245948702097, 0.0034709384199231863, 0.05336727574467659, 0.037895072251558304, -0.025734804570674896, 0.11220216751098633, 0.06872646510601044, -0.0550641193985939, -0.035537660121917725, -0.04113701730966568, 0.027794124558568, -0.025641867890954018, 0.025773197412490845, -0.03539091721177101, 0.03390439599752426, -0.015463401563465595, -0.020717792212963104, -0.0303808581084013, 0.02818555384874344, -0.045114319771528244, -0.012585306540131569, 0.09789454936981201, -0.022206656634807587, -0.040777403861284256, -0.0015311416937038302, -0.008571240119636059, 0.0069993105717003345, -0.014774776063859463, 0.04623883590102196, 0.029174473136663437, 0.015194248408079147, -0.03972778469324112, -0.012438942678272724, -0.017189335078001022, 0.030670443549752235, -0.06801516562700272, 1.1888246262969915e-05, -0.058748308569192886, -0.02680140733718872, 0.029681392014026642, -0.028547678142786026, 0.012225938029587269, 0.002279999665915966, -0.03353133797645569, 0.02646019123494625, 0.04948034882545471, 0.022030731663107872, 0.01662428118288517, 0.028285915032029152, 0.013440718874335289, -0.03136967867612839, -0.0017794438172131777, -0.04663189500570297, 0.04860679805278778, -0.008416248485445976, 0.002969845198094845, -0.019613303244113922, -0.010514440014958382, -0.000560135580599308, -0.03248036280274391, 0.008818153291940689, -0.02619379386305809, 0.07337646186351776, -0.03770682215690613, 0.03533504158258438, -0.0009420012356713414, -0.08091217279434204, -5.847093780175783e-05, 0.0011634154943749309, -0.01662791147828102, -0.041585829108953476, 0.008015064522624016, -0.0002242719492642209, 0.04646601155400276, 0.023624487221240997, -0.056490372866392136, -0.08554267883300781, 0.006691255606710911, -0.04545215517282486, -0.04889916628599167, 0.0009624859667383134, -0.023956777527928352, -0.0027074299287050962, -0.05454147607088089, -0.02664310857653618, 0.005075452849268913, -0.008953526616096497, 0.017235828563570976, -0.046426091343164444, 0.009170642122626305, 0.02728603407740593, 0.003602970391511917, -0.027300940826535225, -0.00366824958473444, 0.010002017952501774, -0.002368407789617777, 0.010934101417660713, 0.029067780822515488, 0.03494057059288025, 0.02345549687743187, 0.03917017951607704, 0.029463108628988266, 0.07237592339515686, -0.056244462728500366, -0.03010609559714794, -0.03832340985536575, -0.021319689229130745, -0.040866997092962265, 0.03142281249165535, -0.007247609551995993, 0.0025862629991024733, 0.005171433091163635, -0.08706124126911163, -0.040996257215738297, 0.0668114647269249, -0.048262517899274826, 0.0034836516715586185, 0.018358908593654633, -0.0010459880577400327, 0.01881985552608967, 0.0398244671523571, -0.01460165623575449, 0.020633773878216743, -0.01970413140952587, 0.03364642336964607, -0.02885035052895546, -0.04156649112701416, 0.016440529376268387, -0.03908033296465874, 0.04367564246058464, 0.004786183591932058, -0.010727006942033768, -0.010372609831392765, 0.03840915858745575, 0.019999098032712936, -0.025843091309070587, 0.04638450965285301, -0.015589900314807892, 0.0027459198608994484, 0.022414252161979675, 0.011124844662845135, -0.020771751180291176, -0.0035624918527901173, 0.030087685212492943, -0.06561675667762756, -0.040350086987018585, 0.062038604170084, 0.00020964523719158024, -0.03736906498670578, 0.057626981288194656, -0.004166060127317905, -0.04713212326169014, -0.046049587428569794, -0.06540632992982864, -0.04054512456059456, 0.08718354254961014, 0.03267597407102585, -0.08633884787559509, 0.00046783220022916794, 0.009589633904397488, -0.014525525271892548, 0.04372024908661842, -0.002371649956330657, -0.021384526044130325, -0.01955171674489975, -0.006470367778092623, -0.011587399058043957, 0.04330237954854965, 0.02578938566148281, 0.0024520866572856903, 0.023552080616354942, 0.011517847888171673, -0.0015509953955188394, -0.020587634295225143, -0.0720556303858757, 0.054115813225507736, 0.03591662272810936, -0.031764592975378036, -0.02561471052467823, 0.01106390729546547, 0.0012347194133326411, 0.0028268771711736917, -0.01740235649049282, 0.030457258224487305, 0.024508437141776085, 0.01100799348205328, -0.028471166267991066, -0.03144988790154457, 0.029331812635064125, -0.033460017293691635, 0.005171505734324455, -0.021092107519507408, 0.06716988980770111, 0.02482578158378601, 0.007532777730375528, -0.009211253374814987, -0.03791021928191185, -0.03576800972223282, 0.034224558621644974, 0.0671519935131073, 0.019591402262449265, 0.05087883025407791, -0.03090834803879261, -0.024619489908218384, -0.005239581223577261, 0.01104711089283228, -0.04705006629228592, -0.0064536090940237045, 0.006429641041904688, 0.02184002287685871, -0.0048596677370369434, -0.007946062833070755, -0.018585089594125748, 0.03978870436549187, -0.004416101146489382, 0.02008880488574505, 0.005618174560368061, -0.028612708672881126, 0.0270809605717659, 0.033595193177461624, -0.017257044091820717, 0.00466372724622488, -0.03301446884870529, 0.021130384877324104, -0.014093758538365364, 0.08036230504512787, 0.048353347927331924, -0.0590866319835186, -0.00026871031150221825, 0.013191982172429562, 0.005338548682630062, 0.04824763163924217, -0.03353987634181976, -0.012331592850387096, -0.08387525379657745, 0.011136455461382866, -0.03023351915180683, -0.018559932708740234, -0.02119702473282814, -0.0161831546574831, -0.04241856560111046, -0.07337222248315811, 0.010122970677912235, 0.03449530154466629, 0.0061281416565179825, -0.05449921637773514, -0.0023410466965287924, 0.0683080404996872, -0.03217322379350662, 0.003956815227866173, 0.0026460648514330387, -0.08221907913684845, 0.006631570868194103, -0.05309685692191124, 0.023218614980578423, -0.0005004876875318587, -0.053020548075437546, -0.04984330013394356, -0.060061633586883545, 0.02896251156926155, 0.022739708423614502, -0.062332477420568466, -0.04923248291015625, -0.08050617575645447, -0.05744079127907753, -0.01377648301422596, -0.04596126452088356, 0.008817998692393303, -0.001022751210257411, -0.036652352660894394, 0.03395725414156914, -0.046635691076517105, -0.027439499273896217, 0.03110085055232048, -0.0052101402543485165, -0.013672295026481152, 0.013431607745587826, 0.027103599160909653, 0.02340807020664215, -0.006102694198489189, 0.07731273770332336, 0.02182198502123356, -0.0036763919051736593, -0.04589514806866646, 0.06346328556537628, 0.04015205800533295, -0.014328479766845703, -0.0032337792217731476, 0.03390930965542793, -0.052129000425338745, 0.012485943734645844, -0.04543255642056465, 0.1047288030385971, -0.0008660044986754656, -0.07376689463853836, -0.054963596165180206, 0.028036905452609062, 0.02267465740442276, -0.030829809606075287, 0.03366902470588684, 0.018136031925678253, -0.09126889705657959, -0.011071895249187946, 0.041566912084817886, -0.06361151486635208, -0.022888528183102608, 0.008782155811786652, -0.026338035240769386, -0.03568677976727486, -0.0760798305273056, 0.00687379390001297, -0.036839164793491364, 0.02309335023164749, -0.0036670342087745667, -0.004113819915801287, 0.10345147550106049, -0.06670693308115005, -0.07660800963640213, 0.0017139469273388386, 0.04607043415307999, 0.02119133621454239, -0.04299420863389969, -0.012948460876941681, 0.03742599114775658, 0.010348692536354065, -0.02085810713469982, 0.010327639058232307, -0.0634789988398552, -0.08833776414394379, -0.03785480558872223, 0.04852071776986122, 0.008793842978775501, 0.024669425562024117, -0.00872642733156681, -0.03244975209236145, 0.04301777854561806, 0.009005401283502579, 0.041139911860227585, -0.0484546422958374, 0.02034047245979309, -0.00913962908089161, -0.046018775552511215, -0.008327868767082691, -0.029989084228873253, 0.06263240426778793, 0.01376501563936472, 0.001954818144440651, -0.023645030334591866, -0.03584263473749161, 0.03359082713723183, 0.06224757805466652, 0.032261043787002563, 0.06994883716106415, 0.018041176721453667, -0.036905866116285324, 0.006329094059765339, 0.02193833515048027, 0.0016850584652274847, -0.01304700132459402, -0.008981416001915932, 0.026475517079234123, -0.005759224761277437, -0.00892697460949421, -0.08576652407646179, 0.021717289462685585, -0.001954674953594804, -0.0040161279030144215, 0.013448866084218025, -0.01428629644215107, 0.0051419660449028015, 0.03369663655757904, 0.0039648315869271755, -0.02795063704252243, 0.019455553963780403, -0.0029762894846498966, 0.04661395400762558, -0.016699854284524918, -0.009224445559084415, 0.013668868690729141, 0.04362402483820915, -0.0756048932671547, 0.055734433233737946, -0.024583904072642326, 0.01717086136341095, -0.038311462849378586, 0.03580734133720398, 0.05510089918971062, 0.02091618999838829, 0.000334452954120934, 0.008817057125270367, 0.0321844182908535, -0.03588099032640457, 0.097123883664608, -0.03847617655992508, -0.020893728360533714, 0.06281595677137375, 0.015402626246213913, -0.01671542227268219, 0.026891818270087242, 0.061252038925886154, 0.05846623331308365, -0.012115422636270523, 0.029024763032794, -0.06034422665834427, -0.03467458486557007, -0.01333160325884819, -0.012339727021753788, 0.010124211199581623, -0.010805482044816017, 0.01055272575467825, -0.015209993347525597, -0.05233392491936684, 0.05587610602378845, 0.0387502945959568, 0.0553615503013134, 0.03417310118675232, 0.040519606322050095, -0.013119797222316265, 0.025754163041710854, -0.05226374417543411, -0.009657256305217743, 0.0327238030731678, -0.013916315510869026, -0.03786274045705795, -0.00249369814991951, -6.382994569050501e-33, 0.006136136129498482, -0.091111920773983, -0.007671855390071869, 0.04491191357374191, -0.047930169850587845, 0.005766699090600014, -0.08814126253128052, -0.03117230162024498, -0.006708321627229452, 0.038023389875888824, -0.00018226768588647246, -0.0022928558755666018, 0.004174752160906792, 0.0011318918550387025, 0.030485974624753, -0.019379258155822754, -0.00845409743487835, 0.04145685210824013, 0.039598606526851654, 0.026830172166228294, 0.06380096822977066, 0.07139399647712708, 0.04792386293411255, -0.0530591681599617, -0.010839701630175114, 0.025048252195119858, 0.04726564511656761, -0.0051783351227641106, -0.015062520280480385, 0.02540411613881588, -0.01652311161160469, 0.05193762108683586, 0.01933969371020794, 0.014201952144503593, -0.012666543945670128, -0.0020137112587690353, -0.055742282420396805, -0.06753259897232056, -0.06019275635480881, 0.0068619586527347565, -0.04111073911190033, 0.012025440111756325, 0.07382423430681229, 0.005495971534401178, -0.023794135078787804, -0.0018465177854523063, 0.05799861624836922, 0.023190641775727272, -0.03971629962325096, -0.02185903862118721, -0.05781349539756775, 0.014218270778656006, -0.004378246609121561, 0.021675582975149155, -0.010308663360774517, 0.02859552763402462, 0.002864025766029954, 0.001379939028993249, -0.03490136191248894, 0.04672398790717125, -0.054455943405628204, 0.03112322837114334, 0.022188153117895126, 0.02862662263214588, 0.032696910202503204, -0.0017938404344022274, -0.002701431280001998, 0.02183312550187111, 0.016549190506339073, 0.021925384178757668, -0.021915974095463753, 0.04976378008723259, 0.047332797199487686, -0.05193634703755379, 0.019734011963009834, -0.030693011358380318, -0.10110798478126526, -0.009834028780460358, -0.01595979556441307, 0.033224690705537796, -0.053342144936323166, 0.023085014894604683, 0.03286398947238922, -0.022986041381955147, 0.055180471390485764, 0.009836194105446339, -0.011539778672158718, -0.0384862907230854, -0.01868390291929245, -0.021230917423963547, -0.027986476197838783, 0.011872361414134502, -0.03254721686244011, -0.05898620933294296, -0.010343438945710659, 0.05230352655053139, 0.030667180195450783, 0.018275009468197823, 0.004338144790381193, 0.01689007692039013, -0.06735557317733765, -0.011420963332057, -0.006113981828093529, -0.025711797177791595, 0.01918020285665989, 0.01998395100235939, 0.03812557831406593, 0.010294501669704914, 0.01267332211136818, -0.02144780196249485, -0.03166608884930611, -0.011813799850642681, -0.004840684123337269, -0.016808301210403442, 0.037557847797870636, 0.013289393857121468, -0.019158607348799706, 0.10016860067844391, 0.04494873806834221, 0.02074524015188217, 0.007709300611168146, 0.03252275288105011, 0.017410485073924065, 0.04915072023868561, -0.049270860850811005, -0.018514705821871758, -0.05061596259474754, 0.053162142634391785, -0.01364982221275568, -0.04578205198049545, -0.028286628425121307, -0.01983199454843998, 2.9330547590689093e-07, 0.03858474642038345, 0.0024092651437968016, 0.07000693678855896, 0.04178042709827423, -0.014214826747775078, -0.0075538139790296555, -0.010020509362220764, 0.037953536957502365, -0.07580932229757309, -0.019337119534611702, 0.057024724781513214, -0.029898466542363167, -0.022684065625071526, -0.0019194782944396138, -0.05121421813964844, 0.022732581943273544, -0.04073326662182808, -0.022734304890036583, -0.028026586398482323, -0.011796531267464161, 0.02743278257548809, 0.03656812757253647, 0.04121866822242737, -0.009311633184552193, 0.021717365831136703, -0.019685575738549232, 0.011156260035932064, 0.03773112967610359, -0.0014947181334719062, 0.003169568721204996, 0.012358885258436203, -0.04664762318134308, -0.039945319294929504, 0.05123397707939148, -0.04259496182203293, 0.028968263417482376, -0.004710000474005938, -0.024696046486496925, -0.03728658705949783, -0.022055013105273247, 0.03078504279255867, -0.00783421192318201, 0.045883435755968094, 0.0028611510060727596, 0.028896475210785866, -0.010905762203037739, -0.06025553122162819, -0.012250518426299095, -0.014886213466525078, -0.018456127494573593, 0.04593117535114288, 0.008667530491948128, 0.018927831202745438, 0.010757740586996078, 0.005500551778823137, -0.028820009902119637, 0.04001402109861374, -0.05974788963794708, 0.029506968334317207, 0.019216764718294144, 0.008276012726128101, -0.0075962054543197155, 0.015171067789196968, 0.05334154888987541, 0.020599817857146263, 0.03009941056370735, -0.023142999038100243, 2.9387742183753647e-34, 0.04180322214961052, -0.02431352250277996, 0.011039595119655132, 0.017693253234028816, 0.0011726705124601722, -0.02925879880785942, -0.05854421108961105, 0.02784908376634121, 0.013246515765786171, -0.06115544214844704, -0.05189961940050125]

['Gabriel Dulac-Arnold', 'Richard Evans', 'Hado van Hasselt', 'Peter Sunehag', 'Timothy Lillicrap', 'Jonathan Hunt', 'Timothy Mann', 'Theophane Weber', 'Thomas Degris', 'Ben Coppin']

1512.07679v2

Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods are difficult or even often impossible to apply. An ability to generalize over the set of actions as well as sub-linear complexity relative to the size of the set are both necessary to handle such tasks. Current approaches are not able to provide both of these, which motivates the work in this paper. Our proposed approach leverages prior information about the actions to embed them in a continuous space upon which it can generalize. Additionally, approximate nearest-neighbor methods allow for logarithmic-time lookup complexity relative to the number of actions, which is necessary for time-wise tractable training. This combined approach allows reinforcement learning methods to be applied to large-scale learning problems previously intractable with current methods. We demonstrate our algorithm's abilities on a series of tasks having up to one million actions.

Deep Reinforcement Learning in Large Discrete Action Spaces

http://arxiv.org/pdf/1512.07679v2

Title Deep Reinforcement Learning Large Discrete Action Spaces Summary able reason environment large number discrete action essential bringing reinforcement learning larger class problem Recommender system industrial plant language model many realworld task involving large number discrete action current method difficult even often impossible apply ability generalize set action well sublinear complexity relative size set necessary handle task Current approach able provide motivates work paper proposed approach leverage prior information action embed continuous space upon generalize Additionally approximate nearestneighbor method allow logarithmictime lookup complexity relative number action necessary timewise tractable training combined approach allows reinforcement learning method applied largescale learning problem previously intractable current method demonstrate algorithm ability series task one million action Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0021167639642953873, 0.0476946122944355, -0.014139327220618725, -0.011740886606276035, 0.005617568269371986, -0.009041255339980125, 0.04904504492878914, -0.0007096983026713133, 0.0023235927801579237, -0.004593364428728819, -0.019344856962561607, 0.009114304557442665, -0.09643930196762085, 0.08340571820735931, 0.010020531713962555, -0.01678519695997238, 0.026494786143302917, -0.03764833137392998, 0.007063119672238827, -0.009943615645170212, 0.01905670575797558, -0.025465045124292374, -0.01103869080543518, 0.0515567921102047, -0.017182758077979088, -0.010560472495853901, -0.0444195419549942, -0.0549464225769043, 0.0391329862177372, -0.07635815441608429, 0.03971389681100845, -0.015209706500172615, 0.08177204430103302, 0.09552750736474991, 2.2615299712924752e-06, -0.02477191761136055, -0.03228446841239929, -0.0469592809677124, 0.0005214794655330479, -0.03143008425831795, -0.01741534098982811, -0.04268549755215645, -0.0003456116246525198, 0.007657462731003761, -0.019765634089708328, -0.04993060231208801, 0.06164855137467384, 0.08016839623451233, 0.013171771541237831, 0.046192463487386703, -0.014920187182724476, -0.010275143198668957, 0.014332716353237629, -0.0408470593392849, 0.03583814948797226, -0.031036140397191048, 0.023609083145856857, 0.03415891155600548, 0.05618979036808014, 0.011519042775034904, -0.04101452976465225, -0.001380185130983591, 0.036456894129514694, -0.046484190970659256, 0.056819505989551544, 0.061779871582984924, 0.038580212742090225, 0.024197043851017952, -0.03318822756409645, 0.05611749738454819, -0.06516873836517334, 0.03859592229127884, 0.02064201608300209, -0.03254997730255127, -0.04813636839389801, -0.0427793525159359, -0.020034220069646835, 0.004906518384814262, -0.002695988165214658, 0.0007145025883801281, -0.019662855193018913, 0.031836558133363724, -0.0016277567483484745, 0.03679700940847397, -0.029589859768748283, 0.018055874854326248, -0.04295123741030693, -0.011543712578713894, 0.01290028914809227, -0.010374967008829117, 0.004125138279050589, -0.03071322850883007, 0.017919927835464478, 0.024332627654075623, -0.10413148999214172, -0.03518937900662422, 0.024054517969489098, 0.0032056819181889296, 0.03870629891753197, -0.02829623967409134, 0.07680336385965347, -0.028938809409737587, 0.039913907647132874, 0.06595154106616974, 0.013019155710935593, 0.06081593781709671, -0.08103334903717041, 0.006808693055063486, -0.005333845037966967, 0.028897156938910484, -0.0705832690000534, 0.009735309518873692, -0.035447657108306885, 0.05477000027894974, -0.020591149106621742, -0.04711790382862091, -0.04796886071562767, 0.01860138401389122, -0.06621182709932327, 0.020031074061989784, 0.012781118042767048, 0.05795609951019287, -0.02345665544271469, -0.006946134846657515, -0.05693699046969414, 0.01544116623699665, -0.07261963188648224, 0.036014702171087265, -0.021214788779616356, 0.029958780854940414, 0.03676551207900047, -0.00579094048589468, 0.010217325761914253, -0.011537539772689342, 0.019109634682536125, 0.08614424616098404, 0.004690536763519049, 0.022006386891007423, -0.0164079200476408, -0.017093857750296593, 0.018190260976552963, -0.04249690845608711, -0.05292513966560364, -0.09916050732135773, -0.00899814534932375, -0.07739497721195221, -0.02238396555185318, 0.0046041314490139484, 0.006685182917863131, -0.02241225726902485, -0.003781075356528163, 0.09103832393884659, 0.05934726819396019, 0.015551384538412094, 0.043839290738105774, -0.015336927957832813, 0.019677262753248215, 0.03823550045490265, 0.022739658132195473, 0.03363018110394478, -0.0004143220721744001, 0.03078397735953331, 0.028801778331398964, 0.001545229577459395, -0.02655155584216118, 0.000262874411419034, 0.037407368421554565, 0.012859637849032879, 0.022576091811060905, 0.0933183878660202, 0.032496996223926544, -0.009876635856926441, -0.0335119366645813, -0.030880022794008255, 0.030077824369072914, 0.0468478724360466, 0.018335485830903053, 0.021350540220737457, 0.030490634962916374, 0.03202357143163681, -0.05464800074696541, -0.08478633314371109, -0.01091877743601799, 0.06520742923021317, 0.03557639941573143, -0.05750164017081261, -0.014545148238539696, 0.012588981539011002, -0.050585947930812836, -0.025336841121315956, 0.06826625019311905, 0.003931679762899876, 0.0004857707826886326, 0.01703803241252899, 0.03767221421003342, -0.032490987330675125, -0.032547030597925186, -0.032421473413705826, 0.007563506718724966, 0.045975591987371445, -0.01565602608025074, -0.03433588519692421, 0.04246074706315994, 0.026656758040189743, -0.020798807963728905, -0.07716140151023865, -0.020015303045511246, -0.03653527423739433, -0.02306731790304184, -0.026380065828561783, 0.01946103945374489, -0.03806525096297264, 0.020604221150279045, -0.012161310762166977, -0.044386643916368484, 0.00624596793204546, -0.004271874204277992, 0.04120311141014099, 0.0064910282380878925, 0.01253257505595684, -0.04365167021751404, 0.05264560133218765, -0.01629883050918579, 0.00858524814248085, -0.01202249713242054, -0.08918924629688263, 0.0581662617623806, 0.025689974427223206, 0.044235680252313614, -0.01771026849746704, 0.012990190647542477, -0.016257628798484802, 0.035380538552999496, -0.018989484757184982, -0.038131359964609146, -0.05529307201504707, 0.006656700279563665, 0.0048529887571930885, 0.016406377777457237, -0.016539594158530235, -0.02944709174335003, 0.04513156786561012, -0.04429405555129051, -0.017019908875226974, -0.027220480144023895, -0.01794041320681572, -0.014580629765987396, 0.015941819176077843, -0.02373279072344303, 0.017329419031739235, 0.008767648600041866, -0.04326470568776131, 0.04620480164885521, 0.017976203933358192, -0.006697385106235743, -0.00023776358284521848, -0.007093497551977634, 0.03769531473517418, -0.08734188228845596, 0.011850429698824883, 0.01644890196621418, -0.021369460970163345, 0.018884295597672462, 0.050172898918390274, 0.032317642122507095, 0.0007494963356293738, 0.011395290493965149, -0.043954938650131226, 0.02459557168185711, -0.010226728394627571, -0.002422444289550185, -0.01621350646018982, 0.013650096021592617, 0.018174879252910614, -0.040946077555418015, -0.04100847616791725, 0.01880420558154583, 0.0077058011665940285, 0.025767190381884575, 0.03172461315989494, 0.046104706823825836, -0.02804948017001152, -0.011731297709047794, -0.013485479168593884, 0.011774775572121143, 0.005016286391764879, 0.049464695155620575, -0.0027507413178682327, -0.015783637762069702, -0.019891057163476944, -0.02205107919871807, 0.05040299519896507, -0.015706490725278854, -0.034203749150037766, 0.012694714590907097, -0.05279017239809036, 0.004585383925586939, 0.04252083972096443, 0.001612875727005303, 0.053702134639024734, 0.03433367609977722, 0.05272626504302025, -0.06942637264728546, 0.037617459893226624, -0.04746374115347862, -0.05015464872121811, -0.01861177571117878, 0.04167524352669716, 0.03216063231229782, 0.04050195589661598, -0.021806791424751282, 0.02267952263355255, -0.024530988186597824, -0.0102023771032691, 0.01109352894127369, -0.035673052072525024, -0.0409192219376564, 0.023712463676929474, -0.012026268988847733, 0.0411662720143795, -0.009890517219901085, -0.024728523567318916, 0.06787265837192535, 0.09808776527643204, 0.0017324481159448624, -0.013891056180000305, -0.064556784927845, -0.008479174226522446, 0.07821309566497803, 0.03025285340845585, 0.039670564234256744, -0.046751800924539566, -0.04293064773082733, -0.04353801906108856, -0.01964695192873478, -0.0002312446740688756, -0.006143852602690458, 0.027320804074406624, -0.012841980904340744, 0.029916314408183098, 0.0020353354047983885, -0.07904190570116043, -0.03675547242164612, -0.001959677552804351, -0.025419097393751144, 0.003782129380851984, -0.03146084398031235, -0.023787762969732285, -0.04480726271867752, -0.005061622243374586, 0.041528452187776566, 0.035301726311445236, -0.014950964599847794, -0.04267829284071922, 0.004603059496730566, 0.025212692096829414, 0.05212603509426117, -0.005778278224170208, -0.027768028900027275, -0.006428757216781378, 0.023539623245596886, 0.064229317009449, 0.02965589612722397, 0.008645142428576946, -0.08503283560276031, 0.04898165911436081, 0.008783907629549503, -0.0339183434844017, -0.008301597088575363, 0.017545467242598534, 0.015245302580296993, -0.05885663256049156, 0.002238569315522909, 0.02140338532626629, 0.0032003805972635746, -0.06897477060556412, 0.016165422275662422, 0.00718632061034441, 0.019374703988432884, -0.011232690885663033, 0.060620035976171494, -0.03755732625722885, -0.01106700487434864, -0.04379136487841606, -0.03230452537536621, -0.02522176317870617, -0.044724345207214355, 0.025535941123962402, -0.1158003881573677, 0.060559630393981934, -0.014534389600157738, -0.022241467610001564, -0.053150422871112823, -0.022258803248405457, 0.0020753832068294287, -0.06847244501113892, -0.014452150091528893, 0.03009183146059513, 0.011217545717954636, -0.051065921783447266, 0.020342020317912102, 0.011650297790765762, 0.01126974169164896, 0.05483592674136162, -0.07402518391609192, 0.0057805124670267105, 0.041369736194610596, 0.048152804374694824, -0.005919067654758692, 0.0042196824215352535, -0.03686940670013428, 0.02156772091984749, -0.025683298707008362, -0.0031448379158973694, 0.055160846561193466, 0.011832213029265404, -0.0071875848807394505, 0.007007003296166658, 0.049487024545669556, 0.017970064654946327, -0.008984391577541828, 0.0413653589785099, 0.08817686140537262, -0.019202668219804764, 0.021097363904118538, -0.01417746301740408, -0.003979462664574385, 0.03537306934595108, -0.003519444027915597, -0.06369107216596603, -0.021952521055936813, -0.06575462222099304, -0.0020728486124426126, -0.02158134989440441, -0.03323626145720482, -0.0035503674298524857, -0.02884342521429062, -0.017593279480934143, 0.005474308505654335, -0.04223046824336052, 0.005374380853027105, 0.028899775817990303, 0.03918829932808876, -0.01884308084845543, -0.00388459418900311, 0.028556177392601967, 0.029197584837675095, -0.013579116202890873, -0.011230065487325191, 0.005232192575931549, 0.04451785981655121, -0.04073192924261093, 0.011426708661019802, 0.025927789509296417, -0.0008921338012441993, -0.010681088082492352, -0.02976427599787712, -0.04136732220649719, -0.037618622183799744, -0.022663993760943413, 0.041787371039390564, 0.020408354699611664, 0.04617669805884361, -0.011487088166177273, -0.026445353403687477, 0.06214887648820877, -0.00637875497341156, -0.03152008354663849, -0.031054796651005745, 0.06031147018074989, 0.03756656125187874, -0.007608145475387573, 0.043259426951408386, -0.058895766735076904, 0.048504140228033066, -0.022069593891501427, -0.006969743873924017, -0.08111924678087234, 0.014507660642266273, 0.0019461330957710743, -0.04761968553066254, 0.02700692228972912, 0.04020983353257179, -0.0034870265517383814, -0.04873426631093025, 0.015950776636600494, 0.01034446433186531, -0.005246051587164402, -0.056809380650520325, 0.008702895604074001, 0.04745302349328995, 0.011812247335910797, 0.008410105481743813, -0.01394549012184143, 0.05655762925744057, -0.019785139709711075, -0.021446330472826958, 0.020837198942899704, 0.033820025622844696, 0.0321023091673851, 0.02095579169690609, 0.04503511264920235, 0.007982127368450165, -0.01841387152671814, 0.04619058966636658, 0.029485857114195824, 0.023303117603063583, 0.011094718240201473, 0.045237086713314056, 0.020246580243110657, -0.056870706379413605, -0.0256574135273695, -0.0457705557346344, -0.06849934160709381, 0.025038694962859154, 0.02952105924487114, 0.035539425909519196, -0.029038172215223312, -0.028179045766592026, -0.058970630168914795, 0.003034682013094425, -0.00791307631880045, 0.006259656045585871, -0.03841431438922882, 0.002960307989269495, 0.01988907717168331, 0.0554514043033123, 0.0219857320189476, 0.05523410439491272, 0.05754489451646805, 0.024599529802799225, 0.0015129860257729888, -0.002194436965510249, -0.01473035104572773, -0.02163708209991455, 0.008243221789598465, 0.007228678558021784, 0.040827587246894836, 0.015005647204816341, -0.0012619250919669867, -0.00833362340927124, -0.008652754127979279, -0.0031602662056684494, 0.013202386908233166, -0.008382253348827362, -0.03664782643318176, 0.023766841739416122, -0.02140052244067192, 0.01077920664101839, 0.037822578102350235, -0.029795194044709206, -0.02832970581948757, -0.022426018491387367, -0.04109511896967888, -0.06694747507572174, -5.791364956203782e-33, 0.051233068108558655, -0.06653377413749695, 0.00497985677793622, -0.04871617630124092, -0.06792937219142914, 0.0034140378702431917, -0.01910441927611828, -0.05613517761230469, 0.028950456529855728, 0.04510483890771866, -0.004230427090078592, -0.02407880313694477, -0.00041607351158745587, 0.023320309817790985, 0.06602101027965546, -0.018548939377069473, 0.036864809691905975, -0.008595640771090984, 0.002771412255242467, 0.0534764789044857, 0.010074233636260033, 0.001517074415460229, -0.020731355994939804, -0.007893496192991734, -0.03325243666768074, 0.049023717641830444, -0.019474957138299942, 0.03420921042561531, -0.02194819040596485, 0.06535982340574265, -0.004327244125306606, 0.027939798310399055, -0.010777460411190987, -0.08844326436519623, -0.002604409586638212, 0.00992362666875124, -0.092911496758461, -0.03498705476522446, -0.09482835233211517, -0.009779387153685093, -0.0060014883056283, 0.0018058273708447814, 0.00418325187638402, 0.010963698849081993, -0.016691340133547783, -0.012921435758471489, 0.050121109932661057, -0.02519065886735916, -0.02542727254331112, -0.033030200749635696, -0.036179069429636, -0.0015609709080308676, -0.01014874316751957, 0.013574304059147835, 0.028004417195916176, 0.008898945525288582, -0.0069075399078428745, 0.0017571860225871205, -0.014463260769844055, 0.009862453676760197, 0.0025267088785767555, 0.03424159809947014, -0.014576654881238937, 0.0453343391418457, 0.06676013767719269, 0.03709215670824051, -0.002412149216979742, -0.02324836142361164, 0.008573146536946297, 0.011207424104213715, -0.032457735389471054, 0.0462227389216423, 0.003778234589844942, 0.03293943405151367, 0.08412438631057739, 0.03289557620882988, -0.0809347927570343, -0.008793991059064865, 0.013519467785954475, 0.04584014043211937, 0.004830862861126661, 0.047586262226104736, -0.013662196695804596, -0.0026203501038253307, 0.023708689957857132, 0.02862308733165264, -0.012408430688083172, -0.027060944586992264, 0.018706757575273514, 0.03752613812685013, 0.007002517115324736, 0.026955075562000275, 0.01670708879828453, -0.0385817289352417, -0.015019509941339493, 0.0018552844412624836, 0.023085027933120728, 0.031097857281565666, 0.03212188929319382, -0.01693277806043625, -0.0490678995847702, -0.049255792051553726, -0.03401888906955719, -0.018192386254668236, -0.011268828995525837, 0.017151203006505966, -0.015084536746144295, 0.03797502815723419, -0.03700705245137215, 0.004704168997704983, 0.0033265009988099337, -0.017410509288311005, -0.002487088553607464, 0.03258273005485535, 0.009319907985627651, -0.04776812344789505, 0.014765864238142967, 0.07340577989816666, -0.011677159927785397, -0.0390811562538147, 0.029802517965435982, -0.02129337750375271, -0.02751728519797325, 0.021366775035858154, -0.05608949437737465, 0.001014566165395081, -0.09943372011184692, -0.001114408252760768, 0.01788376085460186, -0.07550270110368729, 0.007798820734024048, -0.014127359725534916, 2.779985379675054e-07, -0.08363360911607742, 0.0028905454091727734, 0.013185619376599789, -0.04310046136379242, 0.01477764267474413, 0.030671458691358566, 0.02749568037688732, 0.03288286551833153, -0.0030211929697543383, 0.029094038531184196, 0.0731024369597435, 0.006656867451965809, 0.0030487189069390297, -0.011166899465024471, -0.08344016224145889, 0.012116080150008202, -0.030293263494968414, 0.03213810548186302, -0.08971033245325089, -0.015164542943239212, -0.008549033664166927, 0.11618369072675705, 0.05671188607811928, -0.0174417681992054, 0.07231973856687546, -0.02938126027584076, 0.01829826459288597, -0.01851477660238743, 0.042475953698158264, -0.02678924985229969, -0.000526229094248265, 0.004893491510301828, -0.03404979035258293, -0.028183067217469215, -0.04309431463479996, 0.009725438430905342, -0.010609343647956848, 0.07421578466892242, 0.0013378318399190903, 0.004711857531219721, -0.015170353464782238, -0.02743726782500744, 0.026346709579229355, -0.0052559031173586845, 0.03361764922738075, -0.06376244872808456, 0.001112226047553122, 0.01714356057345867, 0.0032782433554530144, -0.03121449612081051, 0.019250646233558655, -0.008656002581119537, -0.02210606075823307, -0.01439232099801302, 0.012925215996801853, -0.034917254000902176, 0.03303946927189827, -0.04658036306500435, 0.04375462606549263, 0.01448552031069994, -0.0004883567453362048, 0.003864531870931387, -0.001694036298431456, 0.012753095477819443, 0.04048269987106323, -0.020333915948867798, -0.02391819655895233, 2.728138487677473e-34, 0.008419227786362171, -0.004403723869472742, -0.013419627211987972, -0.03540045768022537, -0.012219179421663284, 0.022692644968628883, -0.01548865344375372, 0.026578258723020554, 0.10723989456892014, -0.035915542393922806, -0.03575073927640915]

['Aviv Tamar', 'Yi Wu', 'Garrett Thomas', 'Sergey Levine', 'Pieter Abbeel']

1602.02867v4

We introduce the value iteration network (VIN): a fully differentiable neural network with a `planning module' embedded within. VINs can learn to plan, and are suitable for predicting outcomes that involve planning-based reasoning, such as policies for reinforcement learning. Key to our approach is a novel differentiable approximation of the value-iteration algorithm, which can be represented as a convolutional neural network, and trained end-to-end using standard backpropagation. We evaluate VIN based policies on discrete and continuous path-planning domains, and on a natural-language based search task. We show that by learning an explicit planning computation, VIN policies generalize better to new, unseen domains.

Value Iteration Networks

http://arxiv.org/pdf/1602.02867v4

Title Value Iteration Networks Summary introduce value iteration network VIN fully differentiable neural network planning module embedded within VINs learn plan suitable predicting outcome involve planningbased reasoning policy reinforcement learning Key approach novel differentiable approximation valueiteration algorithm represented convolutional neural network trained endtoend using standard backpropagation evaluate VIN based policy discrete continuous pathplanning domain naturallanguage based search task show learning explicit planning computation VIN policy generalize better new unseen domain Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.004493028856813908, 0.019453197717666626, -0.03255758062005043, -0.01281800027936697, -0.006495372857898474, -0.06049295514822006, 0.009518175385892391, -0.04015645384788513, -0.07157497107982635, 0.05011313036084175, 0.04419944807887077, 0.05142959579825401, -0.02482539974153042, 0.11494502425193787, -0.009485242888331413, -0.0525505356490612, 0.04132620617747307, -0.015510792843997478, -0.010399413295090199, -0.017776159569621086, 0.029644453898072243, -0.044815827161073685, -0.00017901287355925888, 0.032813914120197296, -0.048017267137765884, 0.010214295238256454, -0.04981197416782379, -0.004059964790940285, 0.03615182638168335, -0.06894510239362717, 0.0586128793656826, 0.00886234175413847, 0.03387487679719925, 0.04365575686097145, 2.5116241886280477e-06, -0.02840893343091011, -0.022666193544864655, -0.03292236104607582, -0.00769457034766674, -0.04118281230330467, 0.011558164842426777, 0.017469527199864388, -0.003235436277464032, 0.039936065673828125, -0.03648465499281883, 0.018379952758550644, 0.00878581777215004, -0.000313539378112182, 0.0373300276696682, 0.027492627501487732, -0.0015416829846799374, -0.04309999197721481, -0.0035585290752351284, -0.00858399923890829, -0.010249587707221508, -0.07783512026071548, 0.005087548401206732, 0.0488356314599514, 0.031231803819537163, -0.03457770496606827, -0.013701309449970722, 0.028734305873513222, 0.04267410188913345, -0.0011631943052634597, -0.009791892021894455, 0.042194172739982605, 0.035641223192214966, -0.055351439863443375, -0.014822803437709808, 0.0168001651763916, -0.020012004300951958, -0.020444998517632484, 0.021444914862513542, -0.014108249917626381, -0.03266553208231926, -0.04383264109492302, 0.0006664483807981014, 0.005515370052307844, -0.009124689735472202, -0.01866731233894825, -0.019595233723521233, 0.0405033603310585, -0.024556495249271393, 0.04774704575538635, -0.005628569051623344, 0.02787429466843605, -0.05303727462887764, 0.006753947120159864, 0.02351626381278038, -0.00504196947440505, -0.006159751210361719, -0.03444349765777588, 0.032042670994997025, 0.05930209532380104, -0.06140907481312752, -0.024177003651857376, -0.0017551573691889644, -0.03482479974627495, -0.005099625792354345, -0.05541139841079712, 0.04430251941084862, -0.0017376235919073224, -0.01880582794547081, 0.018295839428901672, 0.002484320430085063, 0.018355440348386765, -0.05077555403113365, 0.007189102005213499, -0.01844949834048748, 0.06069390848278999, -0.033611685037612915, 0.02455410361289978, -0.015989122912287712, 0.038002606481313705, -0.01524143572896719, -0.005383742973208427, -0.0191221721470356, -0.011719574220478535, -0.029214151203632355, 0.04151393473148346, 0.006233375519514084, 0.0736914649605751, 0.0019694215152412653, -0.004145358689129353, -0.06508514285087585, 0.0068565960973501205, -0.08730150014162064, 0.025935640558600426, -0.006982866674661636, 0.017739422619342804, 0.025411332026124, -0.010583445429801941, -0.019834468141198158, 0.012289985083043575, 0.010592791251838207, 0.06533098965883255, 0.025028632953763008, 0.06262751668691635, -0.020354030653834343, -0.028531622141599655, 0.03595852479338646, -0.031208842992782593, 0.034748997539281845, -0.06015404686331749, -0.035315100103616714, -0.04945044964551926, -0.0404583141207695, 0.0282769612967968, 0.009143057279288769, -0.005724024958908558, 0.022109899669885635, 0.05184841528534889, 0.03231380507349968, -0.0009696246706880629, 0.051910851150751114, -0.012794730253517628, 0.008182217366993427, 0.040454789996147156, 0.03689708188176155, 0.053649935871362686, -0.04553796350955963, 0.027734197676181793, 0.0003863069578073919, 0.007643566932529211, 0.00468252832069993, -0.051476411521434784, -0.07181036472320557, -0.039410512894392014, -0.015214063227176666, 0.06670261174440384, -0.035156216472387314, -0.011873829178512096, -0.039873551577329636, 0.0007635120418854058, 0.027324333786964417, -0.01753983087837696, 0.017772147431969643, -0.0009035684051923454, 0.024878036230802536, 5.575552859227173e-05, -0.030866658315062523, -0.10921274125576019, -0.024983296170830727, 0.0642286166548729, -0.016361432150006294, -0.04493581876158714, -0.07749534398317337, -0.02152279019355774, -0.03283677622675896, -0.07021475583314896, 0.026768378913402557, -0.007996145635843277, 0.02625996246933937, -0.004819515161216259, 0.0420493558049202, -0.007212618365883827, -0.02568129263818264, -0.06731487065553665, -0.009919806383550167, 0.06608732789754868, -0.03412390872836113, -0.03463021665811539, 0.05598316714167595, 0.01458950899541378, 0.033666204661130905, -0.03355410695075989, -0.04984702542424202, -0.010461856611073017, -0.055181071162223816, -0.0035934175830334425, 0.03701411187648773, -0.017398256808519363, 0.0006013240199536085, -0.011925037950277328, -0.011582876555621624, 0.029038207605481148, -0.007880911231040955, 0.01710786297917366, -0.016281675547361374, 0.005235535092651844, -0.03884584829211235, 0.01101386547088623, 0.0047594839707016945, 0.030361410230398178, -0.009439042769372463, 0.005395109765231609, 0.03264123201370239, 0.02701241336762905, 0.00821464229375124, -0.03072616644203663, 0.028886079788208008, 0.0027460658457130194, -0.003290771506726742, -0.017590049654245377, -0.010570595972239971, -0.01733681559562683, -0.017724020406603813, -0.04590730741620064, 0.05414768308401108, 0.0077631608583033085, 0.025691013783216476, 0.013695972040295601, -0.03467961400747299, -0.036446623504161835, -0.012078830040991306, -0.022209716960787773, -0.04389889910817146, 0.018621664494276047, 0.016364125534892082, 0.02591898664832115, 0.006723756901919842, -0.031120378524065018, 0.02326580323278904, -0.004536692518740892, -0.012124419212341309, -0.03431906923651695, 0.042426567524671555, 0.04231966286897659, -0.04069822281599045, -0.005404653958976269, -0.02282504364848137, -0.036550432443618774, 0.006681940983980894, 0.0069524808786809444, 0.06682351976633072, 0.01532310713082552, 0.009352854453027248, -0.04848245531320572, -0.002278957050293684, -0.012247801758348942, -0.05531476438045502, -0.011927428655326366, -0.005297439638525248, 0.02703946828842163, -0.04587422311306, -0.0003524647618178278, 0.09275185316801071, -0.010309237986803055, -0.043657831847667694, 0.019198747351765633, 0.04574906453490257, -0.010025438852608204, -0.03993068262934685, -0.03609626740217209, 0.0029017070773988962, 0.008076932281255722, 0.009935881942510605, -0.0069551109336316586, -0.015588052570819855, -0.009721650741994381, -0.029495585709810257, 0.04386789724230766, -0.004682411905378103, -0.04234094172716141, -0.015425250865519047, -0.005536672659218311, -0.04499649628996849, 0.022602368146181107, 0.033341020345687866, -0.0073940930888056755, 0.003683812217786908, 0.03355523943901062, -0.1160476878285408, 0.04765911027789116, -0.09122267365455627, -0.005304188001900911, 0.01137651689350605, 0.04263446480035782, -0.002434954047203064, 0.011626512743532658, -0.041899655014276505, 0.05042044073343277, -0.03912045434117317, 0.028516588732600212, 0.03384783864021301, -0.05510800704360008, -0.007311545312404633, 0.038417864590883255, -0.01069953478872776, 0.04697980359196663, -4.038010229123756e-05, -0.036112092435359955, 0.03679293766617775, 0.04853959381580353, -0.009412352927029133, 0.0007387817604467273, -0.002310756128281355, -0.015307500958442688, 0.028425054624676704, 0.05375925078988075, 0.011421585455536842, -0.037384867668151855, 0.0044595422223210335, -0.016538089141249657, 0.0034914184361696243, -0.0049225809052586555, -0.030523361638188362, 0.0194670632481575, -0.023727115243673325, 0.010822019539773464, 0.011038749478757381, -0.047335993498563766, -0.06154974550008774, 0.017526991665363312, -0.0075578936375677586, 0.03534944728016853, -0.05550004169344902, -0.0007883207290433347, 0.024372084066271782, -0.025475693866610527, 0.032722294330596924, 0.06584029644727707, -0.043799981474876404, -0.006510403472930193, 0.0020110206678509712, -0.03287206590175629, 0.023476803675293922, 0.016110703349113464, 0.000299102277494967, 0.03465381637215614, 0.06556127220392227, 0.0059563773684203625, -0.014478346332907677, 0.017696859315037727, -0.10550722479820251, 0.04856853559613228, -0.009000246413052082, -0.010298886336386204, -0.019036944955587387, 0.038802046328783035, -0.0025112037546932697, -0.05170665681362152, -0.049809422343969345, 0.02209402807056904, 0.02255103550851345, -0.06512406468391418, 0.0063804201781749725, -0.062246356159448624, 0.040886856615543365, 0.005084598902612925, 0.07165408134460449, -0.035558875650167465, 0.029637210071086884, 0.017679164186120033, 0.05979367345571518, -0.035604432225227356, -0.016814609989523888, -0.01921597309410572, -0.07548743486404419, 0.0725909098982811, -0.021047858521342278, -0.02776365354657173, -0.0023414643947035074, -0.011647024191915989, -0.02393515035510063, -0.05130352824926376, -0.02157895267009735, 0.041142020374536514, 0.04054928570985794, -0.018498798832297325, 0.02413259632885456, -0.030178911983966827, -0.013843940570950508, 0.013591867871582508, -0.03225924074649811, 0.01202045101672411, 0.1485065221786499, 0.02813122048974037, -0.026692567393183708, -0.007203962188214064, 0.014507785439491272, 0.04142618551850319, 0.02498393878340721, -0.049960944801568985, 0.03912007063627243, 0.040253832936286926, 0.004437947180122137, 0.03325766697525978, 0.047647297382354736, -0.001992048928514123, -0.02829272300004959, 0.04595049098134041, 0.06320954114198685, -0.044281505048274994, -0.003910866100341082, -0.06697390973567963, 0.015265132300555706, 0.031218156218528748, -0.05582425743341446, -0.022009894251823425, -0.01657181978225708, -0.06984537839889526, -0.005763413850218058, 0.005447189323604107, -0.07676391303539276, -0.05918244644999504, -0.03236423060297966, 0.010219333693385124, -0.008171223104000092, -0.04393124580383301, -0.030399221926927567, -0.0042934296652674675, 0.07314129173755646, -0.0030027141328901052, -0.054908785969018936, 0.023045727983117104, 0.030584977939724922, -0.011876431293785572, -0.032286785542964935, 0.03520248457789421, 0.04513014853000641, -0.035913582891225815, 0.04924409091472626, 0.015468615107238293, -0.0632534995675087, -0.049412451684474945, -0.06099320948123932, -0.02292426861822605, -0.03385201096534729, 0.034667376428842545, 0.09189716726541519, 0.01058411318808794, 0.03457055613398552, -0.04264219477772713, -0.039958368986845016, 0.07781824469566345, -0.01526670902967453, 0.014684965834021568, -0.022614166140556335, 0.027076389640569687, 0.05373671278357506, -0.008722180500626564, 0.025221502408385277, -0.01243748888373375, 0.08203469216823578, 0.012135572731494904, 0.01149067748337984, -0.002636938588693738, 0.017405055463314056, 0.023936590179800987, -0.01328817754983902, 0.027482207864522934, 0.059404198080301285, -0.004414756316691637, -0.02514488436281681, 0.0036679136101156473, 0.03967339172959328, -0.02216411754488945, -0.047736331820487976, 0.05939330905675888, -0.008838842622935772, -0.0022075059823691845, 0.016969671472907066, -0.043233275413513184, 0.08730027824640274, -0.041779402643442154, 0.030395520851016045, 0.02120848372578621, 0.004160293843597174, 0.06899586319923401, -0.004336701240390539, 0.04025905206799507, 0.015065559186041355, 0.0002189742517657578, 0.017555080354213715, 0.06421227008104324, -0.013586048036813736, 0.03533410653471947, 0.017939120531082153, 0.02195253223180771, -0.031171808019280434, -0.039864521473646164, 0.01188763976097107, -0.11340457946062088, -0.02389848791062832, 0.021904712542891502, -2.422169200144708e-05, 0.005276280455291271, -0.03428279235959053, -0.07558485865592957, 0.047067686915397644, -0.002005065558478236, -0.03276157006621361, -0.05561085045337677, 0.04025832563638687, 0.03519974648952484, 0.008405779488384724, -0.0004933136515319347, -0.050790946930646896, 0.018588829785585403, 0.021691320464015007, 0.02652561105787754, -0.03942078724503517, 0.009275116957724094, -0.04405577480792999, 0.002395917661488056, -0.019029833376407623, 0.028163393959403038, 0.012481466867029667, -0.01322084479033947, -0.018193496391177177, 0.006929164752364159, -0.0061096567660570145, 0.05864445120096207, 0.031175745651125908, -0.01648288033902645, 0.011629488319158554, -0.02453821711242199, -0.030800802633166313, 0.015297790989279747, -0.01942797191441059, -0.002858187770470977, -0.02604137919843197, -0.018395956605672836, -0.059837691485881805, -6.323007622960101e-33, 0.005478032864630222, -0.01606132462620735, 0.04542156308889389, -0.05043936148285866, -0.06767588108778, -0.014615713618695736, -0.017212463542819023, -0.021786021068692207, -0.01721690408885479, 0.022234363481402397, -0.035919275134801865, -0.02047266811132431, 0.026911936700344086, -0.0014994572848081589, 0.05940034240484238, -0.032502394169569016, 0.0036918804980814457, -0.02467424049973488, 0.001182291191071272, -0.01939406618475914, 0.006130502093583345, 0.04449651390314102, 0.024973705410957336, -0.04426262900233269, -0.03498537838459015, 0.0718390941619873, -0.027011193335056305, 0.03791625425219536, -0.0380232073366642, 0.014538092538714409, 0.011678663082420826, -0.024758877232670784, -0.0009616428869776428, -0.020093968138098717, -0.035360414534807205, 0.004930100403726101, -0.05496416613459587, -0.06244092062115669, -0.06633570790290833, 0.0343603640794754, -0.06804359704256058, 0.023800717666745186, 0.10118074715137482, -0.013323957100510597, -0.030986525118350983, 0.040797892957925797, 0.030519520863890648, 0.021390311419963837, -0.00999037828296423, -0.0017493517370894551, -0.022781385108828545, 0.011234254576265812, -0.0030359127558767796, -0.02207247167825699, 0.05849756672978401, 0.03766576200723648, -0.01546385046094656, -0.015046399086713791, -0.05241594463586807, 0.01983872801065445, -0.06959746032953262, 0.033741019666194916, 0.0035168963950127363, 0.03191279247403145, 0.043231233954429626, 0.04534902796149254, 0.018244443461298943, -0.035934507846832275, -0.048204950988292694, -0.018330004066228867, 0.0039023447316139936, 0.06197965517640114, 0.035017937421798706, -0.03840995952486992, 0.046578746289014816, -0.023766569793224335, -0.0058885542675852776, -0.004851143807172775, -0.03880600258708, 0.08373852074146271, 0.022889604791998863, -0.025827720761299133, -0.03334454447031021, 0.010979033075273037, -0.019591396674513817, -0.047880869358778, -0.007270253729075193, -0.026497596874833107, 0.01581684872508049, 0.025460341945290565, -0.003401864320039749, 0.03394636884331703, 0.007637154310941696, -0.013756549917161465, 0.04383978992700577, 0.03794151172041893, 0.03892611712217331, 0.046317245811223984, 0.02657010219991207, 0.021766260266304016, -0.059828534722328186, -0.012073113583028316, -0.06568455696105957, -0.027802851051092148, 0.0007866086671128869, 0.047738783061504364, -0.040611352771520615, 0.03722603619098663, 0.0019369382644072175, 0.002939334837719798, -0.032795507460832596, -0.014907297678291798, -0.0020269048400223255, 0.05641542747616768, 0.047059398144483566, -0.029726987704634666, -0.023056721314787865, 0.0635673776268959, 0.01758543774485588, -0.050786614418029785, -0.03582574427127838, -0.01117604412138462, 0.012430544942617416, 0.051122602075338364, -0.065053291618824, -0.005075723864138126, -0.05529339984059334, 0.02126721665263176, -0.04684055596590042, -0.041485946625471115, 0.045043740421533585, 0.04848146066069603, 3.1096183761292195e-07, -0.029503369703888893, 0.014045339077711105, 0.0200493261218071, 0.03260423243045807, 0.006393000017851591, 0.03660197928547859, 0.03368644788861275, -0.01396268792450428, -0.0678706169128418, -0.008660785853862762, 0.049026116728782654, -0.015954677015542984, 0.04226914420723915, 0.014064122922718525, -0.020572291687130928, -0.02217813953757286, 0.010368497110903263, 0.0471433587372303, -0.01829797402024269, -0.05094729736447334, 0.03863758593797684, 0.06437867879867554, 0.06331402063369751, 0.009118222631514072, 0.07504383474588394, 0.06655662506818771, -0.0012480159057304263, 0.017443479970097542, 0.027658848091959953, 0.00039322912925854325, 7.704817835474387e-05, -0.009209459647536278, 0.0033953282982110977, -0.027126651257276535, -0.014145472086966038, 0.07744761556386948, -0.032366156578063965, 0.043562766164541245, -0.007870943285524845, -0.06707513332366943, 0.024210667237639427, -0.012138702906668186, 0.021634558215737343, -0.02815243974328041, 0.001501239836215973, -0.015088657848536968, 0.01725691556930542, 0.013810956850647926, 0.012726268731057644, 0.03150278702378273, 0.06539326161146164, 0.007707621436566114, -0.008575927466154099, -0.015117429196834564, 0.01138263288885355, -0.006259737070649862, -0.016782300546765327, -0.0342840813100338, 0.020166754722595215, -0.012153219431638718, -0.04919860139489174, 0.018518542870879173, -0.0250955019146204, 0.08405320346355438, -0.00448220781981945, 0.018838955089449883, -0.03635573759675026, 2.9295261543235146e-34, -0.0025202303659170866, -0.0332152284681797, -0.03391727805137634, 0.03190780431032181, -0.027883142232894897, 0.04535230994224548, 0.05811364948749542, 0.04523950070142746, 0.05156281962990761, 0.0003737077349796891, -0.06781081110239029]

['Mikael Henaff', 'Arthur Szlam', 'Yann LeCun']

1602.06662v2

Although RNNs have been shown to be powerful tools for processing sequential data, finding architectures or optimization strategies that allow them to model very long term dependencies is still an active area of research. In this work, we carefully analyze two synthetic datasets originally outlined in (Hochreiter and Schmidhuber, 1997) which are used to evaluate the ability of RNNs to store information over many time steps. We explicitly construct RNN solutions to these problems, and using these constructions, illuminate both the problems themselves and the way in which RNNs store different types of information in their hidden states. These constructions furthermore explain the success of recent methods that specify unitary initializations or constraints on the transition matrices.

Recurrent Orthogonal Networks and Long-Memory Tasks

http://arxiv.org/pdf/1602.06662v2

Title Recurrent Orthogonal Networks LongMemory Tasks Summary Although RNNs shown powerful tool processing sequential data finding architecture optimization strategy allow model long term dependency still active area research work carefully analyze two synthetic datasets originally outlined Hochreiter Schmidhuber 1997 used evaluate ability RNNs store information many time step explicitly construct RNN solution problem using construction illuminate problem way RNNs store different type information hidden state construction furthermore explain success recent method specify unitary initialization constraint transition matrix Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01747208833694458, 0.08482013642787933, -0.0024121911264955997, 0.022803330793976784, -0.014167627319693565, -0.023958789184689522, -0.001385111128911376, -0.005846528336405754, -0.018839579075574875, -0.0077763148583471775, -0.0014658243162557483, -0.020521823316812515, 0.025712769478559494, -0.02004188299179077, -0.007842961698770523, -0.031002148985862732, 0.016371162608265877, 0.02404065988957882, -0.06354144960641861, 0.0016848434461280704, -0.01740211620926857, -0.047121863812208176, -0.015023880638182163, 0.013214056380093098, -0.010788469575345516, 0.008534141816198826, 0.0030950652435421944, -0.040060024708509445, -0.01207969430834055, -0.0931088924407959, 0.014080367051064968, 0.02574194222688675, 0.06755631417036057, 0.058238331228494644, 2.419815473331255e-06, -0.0254615917801857, 0.008790337480604649, -0.02452099695801735, 0.012511293403804302, -0.028091076761484146, 0.018398629501461983, 0.019856266677379608, 0.002022822853177786, 0.02935025282204151, -0.04570803791284561, -0.05116409808397293, -0.0005712983547709882, 0.052959345281124115, 0.023582350462675095, 0.05034137889742851, -0.00784138310700655, -0.047010865062475204, 0.015209581702947617, -0.04772261530160904, 0.018769128248095512, -0.021987678483128548, 0.04331660643219948, -0.05290381982922554, -0.027851277962327003, -0.02788586914539337, -0.027786480262875557, 0.05029281601309776, 0.032608386129140854, 0.03931977599859238, -0.0029013161547482014, 0.029727686196565628, 0.04167310893535614, 0.025114672258496284, 0.003421430243179202, 0.055775970220565796, -0.05948281288146973, 0.0013001078041270375, 0.04913749173283577, 0.006053217686712742, -0.005248295143246651, -0.05898546054959297, -0.010119144804775715, 0.004655197262763977, -0.03153209388256073, 0.01962852105498314, -0.010941523127257824, 0.05099862441420555, 0.02824629656970501, -0.00813677441328764, -0.05247705057263374, 0.021878499537706375, -0.02332284487783909, -0.011240577325224876, -0.0037005760241299868, -0.08640634268522263, 0.011753370985388756, -0.0381544791162014, -0.001551470602862537, 0.05701703205704689, -0.004871413577347994, -0.0005243301275186241, -0.005409023258835077, -0.05398695170879364, 0.021968338638544083, -0.04654017463326454, 0.055810343474149704, -0.00854320079088211, -0.028100043535232544, -0.020779700949788094, -0.041172467172145844, 0.03488332778215408, -0.07412812858819962, -0.03809303045272827, 0.005134080536663532, 0.05338600277900696, -0.0717344582080841, -0.009236347861588001, 0.009080491028726101, 0.06489341706037521, 0.004233284387737513, 0.005997487809509039, -0.03937157243490219, -0.040099162608385086, 0.0013272418873384595, -0.019972918555140495, 0.02340085431933403, 0.06666248291730881, -0.006649774499237537, 0.020544573664665222, -0.06261608749628067, 0.018201053142547607, 0.0217282772064209, 0.042849235236644745, -0.030995383858680725, -0.03178000450134277, 0.008127251639962196, 0.0410585030913353, 0.013817752711474895, 0.022435609251260757, -0.014269867911934853, 0.07757706195116043, 0.031214514747262, 0.016703076660633087, -0.07280614972114563, -0.00960775651037693, 0.005688234232366085, -0.06431524455547333, 0.022847801446914673, -0.07028231024742126, -0.029836518689990044, -0.04207563027739525, -0.03876468911767006, -0.016367079690098763, 0.028276169672608376, 0.017487498000264168, -0.023899856954813004, 0.031171949580311775, -0.022214077413082123, -0.0009785279398784041, 0.04105949029326439, -0.0038091856986284256, 0.092169389128685, 0.0021276052575558424, 0.04541851580142975, 0.01774793118238449, -0.01846463233232498, -0.013630656525492668, 0.017482057213783264, 0.010537014342844486, -0.01821218617260456, -0.0692126676440239, -0.010276556946337223, -0.030488882213830948, 0.003951810300350189, 0.06368476897478104, -0.004944521468132734, 0.010453443974256516, 0.031498152762651443, -0.006785113830119371, 0.023899829015135765, 0.010136820375919342, 0.08444176614284515, 0.08573726564645767, 0.005670951679348946, -0.04790729656815529, -0.03276640921831131, 0.022239528596401215, 0.041538044810295105, 0.0805610790848732, 0.028073392808437347, -0.01738549955189228, -0.040638625621795654, 0.011095548048615456, -0.026906931772828102, -0.032701753079891205, 0.021928569301962852, -0.04096059128642082, -0.04939192160964012, -0.029740460216999054, 0.05157501995563507, 0.023478925228118896, -0.054228562861680984, 0.01850985735654831, 0.003445729147642851, 0.03498957306146622, -0.03134613856673241, -0.023443153128027916, 0.013009119778871536, -0.012930000200867653, 0.006588994059711695, -0.055871378630399704, -0.014946709387004375, -0.04793305695056915, -0.026574477553367615, -0.039576206356287, -0.0002858136431314051, 0.029578179121017456, 0.01234402321279049, -0.05617808178067207, -0.007106375880539417, 0.0309099480509758, -0.011709083802998066, 0.04953419044613838, -0.03290296718478203, 0.03624632582068443, 0.024518711492419243, 0.05099276080727577, -0.03848651424050331, 0.022468483075499535, -0.05571948364377022, -0.004696601070463657, 0.04804622381925583, 0.04510343074798584, 0.02047128416597843, 0.024411708116531372, 0.033958278596401215, -0.01355703454464674, 0.047558676451444626, -0.06747685372829437, -0.030851075425744057, -0.02096422202885151, -0.0813872218132019, -0.006491346284747124, 0.006871579680591822, 0.015214658342301846, 0.03342132642865181, 0.018927088007330894, -0.0008417872013524175, -0.07355966418981552, 0.06965368241071701, -0.017312655225396156, -0.02305437996983528, -0.028496742248535156, -0.02507171407341957, 0.021996600553393364, 0.030105337500572205, -0.011058674193918705, 0.047624338418245316, -0.011841272003948689, 0.03477036952972412, 0.030694669112563133, -0.0026466415729373693, 0.05497146025300026, -0.04966837167739868, -0.02488381415605545, 0.006345533765852451, -0.05886119604110718, -0.029410390183329582, -0.021351035684347153, 0.010334674268960953, 0.01589856669306755, -0.052194397896528244, -0.026010088622570038, 0.011975106783211231, 0.0011287308298051357, -0.005602733697742224, 0.0025227873120456934, -0.011265805922448635, 0.04468950629234314, -0.013239679858088493, -0.08326465636491776, 0.06452910602092743, 0.004737866576761007, -0.075027234852314, 0.04207293316721916, 0.036570120602846146, -0.04106730967760086, -0.017591368407011032, -0.019640110433101654, -0.009630735963582993, 0.029816221445798874, 0.015320434235036373, -0.04607487469911575, -0.013695579022169113, 0.02207387238740921, -0.0034218900837004185, 0.05777282640337944, -0.017615992575883865, -0.04026816040277481, -0.027522582560777664, -0.027106987312436104, 0.08117903023958206, 0.039137113839387894, 0.01943434588611126, -0.00599218113347888, 0.02728007175028324, -0.021576937288045883, 0.001611206098459661, 0.01431842241436243, -0.04089761897921562, 0.04699211195111275, 0.016681993380188942, 0.004800803028047085, -0.02598676271736622, 0.013043224811553955, 0.029864247888326645, 0.02805798314511776, 0.04610784351825714, -0.0015266240807250142, -0.013098374009132385, -0.006690179463475943, -0.017617912963032722, 0.015092974528670311, -0.009316003881394863, 0.009873263537883759, 0.018482714891433716, 0.015400037169456482, 0.007498237304389477, 0.027674684301018715, 0.013024439103901386, -0.0327424518764019, -0.023755593225359917, -0.030960269272327423, 0.019094377756118774, -0.021344542503356934, -0.0078811040148139, -0.03065970167517662, -0.004278382286429405, -0.014002499170601368, -0.04558185115456581, -0.03752264752984047, -0.009736340492963791, -0.008784385398030281, 0.020510613918304443, -0.0008535167435184121, 0.008480798453092575, 0.008436836302280426, -0.07816114276647568, -0.010055032558739185, 0.03509203717112541, -0.008292128331959248, -0.026802465319633484, -0.03671349957585335, 0.016828805208206177, 0.020006490871310234, 0.00395607016980648, 0.05978924408555031, -0.033878717571496964, 0.02341826632618904, -0.017858881503343582, 0.052791938185691833, 0.028126617893576622, -0.010948823764920235, 0.028617722913622856, 0.05268729850649834, 0.08014979958534241, -0.01535589899867773, 0.009745757095515728, 0.0006494985427707434, -0.10702372342348099, 0.014274113811552525, -0.023881956934928894, 0.019306471571326256, -0.004149549640715122, 0.02821282297372818, -0.04539651423692703, -0.0928504541516304, -0.0013284070882946253, 0.038248393684625626, -0.009203827008605003, -0.04803188890218735, -0.006892587523907423, 0.022253410890698433, -0.05284000560641289, 0.01371797826141119, 0.00531352823600173, 0.012047086842358112, 0.01610749587416649, -0.022836031392216682, 0.017948605120182037, -0.011916402727365494, -0.028680989518761635, -0.022427231073379517, -0.03717977553606033, 0.03250247612595558, -0.019278058782219887, -0.0770602896809578, -0.06532999873161316, -0.027464084327220917, -0.031165890395641327, -0.03036464937031269, -0.01558153796941042, 0.031668636947870255, 0.01198068168014288, -0.03250233829021454, 0.041936833411455154, -0.1121969223022461, 0.003129968186840415, 0.014633950777351856, -0.06498079001903534, 0.02588856965303421, 0.0800461545586586, 0.033487945795059204, -0.03581590950489044, -0.06398526579141617, -0.004245407413691282, -0.012857816182076931, 0.033119019120931625, -0.014147643931210041, 0.03410841524600983, 0.092173732817173, -0.02818048559129238, -0.03175880014896393, 0.07607869058847427, -0.06569147855043411, 0.037127528339624405, -0.011837088502943516, 0.042803745716810226, -0.01740037463605404, -0.015847448259592056, -0.019565287977457047, -0.0074487063102424145, 0.04524117335677147, -0.01153216790407896, -0.0060013411566615105, -0.02165466919541359, -0.04033408686518669, 0.04627024009823799, 0.012758434750139713, -0.07673947513103485, 0.013872263953089714, -0.003150681033730507, 0.02325308695435524, -0.05057600513100624, -0.0651390329003334, 0.012088746763765812, -0.02028437703847885, 0.06169872358441353, 0.04655582830309868, 0.054068610072135925, 0.0554438978433609, 0.013157296925783157, -0.045925967395305634, -0.023581095039844513, 0.020038308575749397, 0.03746911883354187, -0.037591028958559036, 0.0336524061858654, 0.05577952414751053, -0.017301088199019432, 0.018588734790682793, -0.04034631699323654, -0.08348648995161057, 0.0024363240227103233, 0.052766598761081696, 0.024273507297039032, 0.004517487250268459, -0.024279547855257988, -0.01607910543680191, -0.0364193432033062, 0.018537240102887154, -0.007966507226228714, 0.016410674899816513, 0.001955160405486822, 0.05589720234274864, 0.0155793447047472, 0.007804425433278084, 0.0007634902140125632, 0.022350531071424484, 0.04285957291722298, 0.005432824604213238, -0.027166027575731277, -0.004544910974800587, -0.02234278805553913, 0.01577945426106453, -0.014755725860595703, 0.042843177914619446, 0.04531089588999748, 0.016574986279010773, -0.07791406661272049, 0.043690379709005356, 0.003524306695908308, 0.02777252160012722, -0.03766443952918053, 0.0443582683801651, 0.04377646744251251, 0.06212844327092171, 0.0024467839393764734, -0.03328724205493927, 0.07078985124826431, -0.07709310948848724, 0.005516624078154564, 0.05880795419216156, -0.04522687569260597, 0.04315138980746269, -0.04690318554639816, 0.03689667582511902, -0.02845398709177971, 0.02364531345665455, -0.007762521039694548, 0.018573878332972527, -0.015816735103726387, 0.05620824918150902, 0.018080156296491623, 0.027864567935466766, -0.02530508115887642, -0.014336763881146908, 0.003982746507972479, 0.0009644461679272354, -0.02986665442585945, -0.006934037897735834, 0.07987505197525024, -0.005416305270045996, -0.046171173453330994, -0.015038908459246159, 0.05567723140120506, -0.024476075544953346, 0.04480762407183647, -0.04490507021546364, 0.02901618555188179, 0.02217688597738743, -0.0020216761622577906, -0.047278132289648056, 0.00623543094843626, 0.08243417739868164, 0.04995539039373398, 0.026853598654270172, -0.012962847016751766, 0.03617733716964722, -0.028493093326687813, 0.027796810492873192, 0.03845944255590439, 0.02275502309203148, -0.03262432664632797, 0.005141471978276968, 0.005680045112967491, -0.04219881072640419, 0.004559174180030823, -0.00686277262866497, 0.039286624640226364, -0.023378070443868637, 0.01755785197019577, -0.027961555868387222, 0.021026240661740303, 0.04376456141471863, 0.0094667449593544, -0.012246277183294296, 0.021656334400177002, -0.049150869250297546, -0.026525849476456642, -6.23796868820177e-33, 0.03547994792461395, -0.03654315695166588, -0.015278149396181107, -0.0078027015551924706, -0.029485896229743958, 0.001364098978228867, -0.035897787660360336, -0.014603233896195889, -0.0060000354424119, -0.04306050017476082, -0.025709105655550957, 0.02213933691382408, -0.0026302130427211523, 0.03992696851491928, 0.04140070080757141, -0.006251024082303047, 0.013517647981643677, -0.0021179979667067528, 0.07754724472761154, -0.013727986253798008, 0.08027062565088272, 0.0558830127120018, 0.011927129700779915, -0.047048524022102356, -0.0480995811522007, -0.018420910462737083, -0.020000772550702095, 0.00686428090557456, -0.05430940166115761, 0.005608852952718735, -0.029781945049762726, 0.0011757451575249434, 0.02655225247144699, -0.04026201739907265, -0.01802218332886696, 0.004478557035326958, -0.048016637563705444, -0.04252495989203453, -0.04951015114784241, -0.0021049892529845238, -0.03855502977967262, 0.0006435627001337707, 0.03974977508187294, 0.005270823836326599, -0.02671171724796295, 0.05183277279138565, 0.0255748238414526, -0.016284069046378136, 0.009223307482898235, -0.002376437885686755, 0.011653296649456024, 0.008855319581925869, -0.007217725273221731, -0.01671678014099598, 0.04319874197244644, -0.01946953684091568, -0.04416649043560028, -0.06097056716680527, -0.08373426645994186, -0.004725588019937277, -0.020127128809690475, 0.08057735860347748, -0.028231212869286537, 0.04056644067168236, 0.05790451541543007, -0.008410545997321606, 0.017332984134554863, -0.004648140165954828, -0.024253034964203835, 0.01332012191414833, -0.019418425858020782, 0.02092556841671467, 0.0706496462225914, -0.03251861780881882, 0.10653803497552872, -0.06758970767259598, -0.07355880737304688, 0.01663084328174591, 0.010706482455134392, 0.01745525188744068, 0.030401326715946198, 0.0011124102165922523, 0.01257727388292551, 0.005826105363667011, 0.018735835328698158, -0.0034903043415397406, -0.04508218541741371, -0.022410137578845024, 0.03306644409894943, 0.003348210360854864, 0.01810927502810955, 0.0074008675292134285, -0.002599018160253763, -0.062488723546266556, 0.06512404978275299, -0.011405558325350285, 0.03983745723962784, -0.0055726058781147, 0.023049231618642807, -0.01653255522251129, -0.06815531104803085, -0.03216763213276863, 0.05210596323013306, 0.013078748248517513, 0.012057113461196423, 0.027748771011829376, 0.017201703041791916, 0.01569276861846447, -0.024778692051768303, -0.0406176783144474, 0.002416907576844096, 0.012920600362122059, 0.02700924314558506, 0.025034233927726746, 0.019382216036319733, -0.04147779569029808, -0.016670815646648407, 0.05247936025261879, 0.01928580552339554, -0.014641819521784782, -0.05407438427209854, -0.010570120066404343, 0.038549382239580154, 0.022998668253421783, -0.02154538407921791, -0.031435225158929825, -0.044927433133125305, 0.014680960215628147, -0.03405463322997093, -0.023347681388258934, -0.014189004898071289, 0.04432038217782974, 3.118989013728424e-07, -0.06195482611656189, -0.0062453956343233585, 0.039820581674575806, -0.010228578001260757, 0.059918247163295746, -0.038483988493680954, -0.018499452620744705, 0.010129266418516636, -0.05060398206114769, -0.018600692972540855, 0.06624888628721237, -0.01946568489074707, 0.021531842648983, -0.009990678168833256, -0.0787539929151535, -0.03654209151864052, -0.010002478025853634, 0.006988513749092817, -0.03731638193130493, -0.022719379514455795, 0.06597068905830383, 0.08236860483884811, 0.02271975390613079, -0.014088992029428482, 0.018754011020064354, 0.04497721791267395, 0.005284763406962156, 0.036486197263002396, 0.05027451738715172, -0.02977338433265686, 0.03655385598540306, 0.00042718026088550687, -0.041735369712114334, -0.002439577132463455, -0.010770580731332302, 0.06220947951078415, -0.002959972247481346, -0.00733470031991601, 0.028789592906832695, -0.09263893216848373, 0.05714171379804611, 0.054836057126522064, 0.02176172472536564, -0.006745555438101292, 0.0265986118465662, -0.029416289180517197, -0.06764543801546097, -0.00030492438236251473, 0.06497000902891159, 0.05219297111034393, 0.0245774257928133, 0.0056443666107952595, 0.02451031468808651, -0.022605126723647118, -0.010599189437925816, -0.007989942096173763, -0.004673738498240709, -0.050065502524375916, 0.02966492995619774, 0.024477051571011543, -0.027780238538980484, -0.02019740827381611, -0.02243356965482235, 0.011489564552903175, 0.0948091596364975, 0.011232757940888405, -0.03245024010539055, 3.149102759338608e-34, -0.034217122942209244, -0.029380951076745987, -0.055046726018190384, 0.018032018095254898, 0.007393193896859884, -0.02240367792546749, 0.01572175696492195, 0.049198418855667114, 0.010364186950027943, -0.07401923090219498, -0.05624933913350105]

['Hado van Hasselt', 'Arthur Guez', 'Matteo Hessel', 'Volodymyr Mnih', 'David Silver']

1602.07714v2

Most learning algorithms are not invariant to the scale of the function that is being approximated. We propose to adaptively normalize the targets used in learning. This is useful in value-based reinforcement learning, where the magnitude of appropriate value approximations can change over time when we update the policy of behavior. Our main motivation is prior work on learning to play Atari games, where the rewards were all clipped to a predetermined range. This clipping facilitates learning across many different games with a single learning algorithm, but a clipped reward function can result in qualitatively different behavior. Using the adaptive normalization we can remove this domain-specific heuristic without diminishing overall performance.

Learning values across many orders of magnitude

http://arxiv.org/pdf/1602.07714v2

Title Learning value across many order magnitude Summary learning algorithm invariant scale function approximated propose adaptively normalize target used learning useful valuebased reinforcement learning magnitude appropriate value approximation change time update policy behavior main motivation prior work learning play Atari game reward clipped predetermined range clipping facilitates learning across many different game single learning algorithm clipped reward function result qualitatively different behavior Using adaptive normalization remove domainspecific heuristic without diminishing overall performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04185480251908302, 0.030381247401237488, -0.02586919628083706, -0.039523981511592865, 0.020662624388933182, -0.030731257051229477, 0.021895112469792366, 0.008124059066176414, -0.060192834585905075, 0.04004546254873276, -0.04899836704134941, -0.0027776153292506933, -0.020518342033028603, 0.08556074649095535, -0.027214540168642998, -0.07727155834436417, 0.018571047112345695, -0.014894983731210232, 0.015786146745085716, 0.004640812985599041, -0.0027368785813450813, -0.0717981830239296, 0.01834135130047798, 0.04664100706577301, -0.021957827731966972, 0.0007607287843711674, -0.012233372777700424, -0.03489775210618973, 0.06788910925388336, -0.09479079395532608, 0.054418325424194336, -0.034723274409770966, 0.024870600551366806, 0.039167363196611404, 2.2002784589858493e-06, -0.04224187880754471, -0.03352177515625954, -0.014376956038177013, 0.07411081343889236, -0.036488715559244156, 0.03600769490003586, -0.007386588025838137, -0.023911641910672188, 0.007109418045729399, -0.03814158961176872, -0.049606792628765106, 0.04463720694184303, 0.022768257185816765, 0.037403833121061325, 0.008020145818591118, 0.010943829081952572, -0.05008361116051674, -0.005637980531901121, -0.014087259769439697, 0.004779145587235689, -0.04350944608449936, 0.010962706990540028, 0.08827739208936691, 0.00794376153498888, 0.015668941661715508, -0.018932007253170013, 0.01338728703558445, 0.03822143375873566, 0.002279327716678381, 0.05589023232460022, 0.044291283935308456, 0.07424233108758926, 0.01683294214308262, -0.03030194528400898, 0.006208179984241724, -0.09301922470331192, 0.02269100211560726, 0.004607886075973511, -0.006237783469259739, 0.024586094543337822, -0.034098315984010696, -0.043471559882164, -0.0002458026574458927, -0.021082928404211998, 0.0019724825397133827, -0.06066254898905754, 0.06054425239562988, -0.022810351103544235, 0.010142275132238865, -0.023754142224788666, 0.0027517140842974186, -0.05890125408768654, -0.011280451901257038, 0.01151930820196867, -0.030032265931367874, -0.07834754139184952, -0.0076666902750730515, -0.00611824169754982, 0.013859108090400696, -0.07914458960294724, -0.028088094666600227, -0.013162337243556976, -0.014352585189044476, 0.0187614057213068, -0.05473262071609497, 0.09503632038831711, -0.01046749111264944, 0.014848222956061363, 0.019454345107078552, -0.012948327697813511, 0.03327590972185135, -0.05472557619214058, -0.012748843990266323, -0.018468596041202545, 0.06923311948776245, -0.05683808773756027, 0.006581297609955072, -0.012118943966925144, 0.0980256125330925, -0.002158005256205797, -0.03261983022093773, -0.06327755749225616, -0.0354028195142746, -0.04017235338687897, 0.013049929402768612, 0.004087397363036871, 0.053182341158390045, -0.021708151325583458, 0.025414640083909035, -0.03992345184087753, 0.04599771648645401, -0.09044112265110016, 0.043324630707502365, 0.020006539300084114, 0.05498399958014488, 0.01023154892027378, -0.028090868145227432, -0.022648470476269722, 0.03246346488595009, 0.04790811240673065, 0.13511225581169128, 0.010281946510076523, 0.051658328622579575, -0.0008213832043111324, -0.04309910163283348, 0.020660078153014183, 0.023975322023034096, 0.013822333887219429, -0.058292947709560394, -0.05748767778277397, -0.04479905962944031, -0.010428311303257942, 0.0008261949988082051, 0.003227299079298973, 0.011363597586750984, 0.020751792937517166, 0.08654198795557022, 0.023548780009150505, -0.0064779710955917835, 0.020386971533298492, -0.007690098602324724, -0.061496321111917496, 0.04717595502734184, 0.034234657883644104, 0.01965726539492607, -0.011159154586493969, -0.006536855362355709, -0.009166257455945015, -0.005643198732286692, -0.00032400814234279096, -0.05835343152284622, -0.014740461483597755, -0.06721873581409454, -0.0036972800735384226, 0.08376371115446091, 0.0320785716176033, 0.001956891268491745, -0.05009498447179794, -0.04104185849428177, 0.06527762115001678, 0.0034255399368703365, 0.038586873561143875, 0.025655992329120636, 0.01792910136282444, -0.017808295786380768, -0.03590064495801926, -0.014622851274907589, -0.005695765838027, 0.075962133705616, 0.018490107730031013, -0.002097140997648239, -0.054166845977306366, 0.04375877603888512, -0.023576822131872177, -0.06904551386833191, 0.04460585117340088, -0.017316697165369987, -0.02456262707710266, -0.01908259466290474, 0.0156048983335495, 0.011369070038199425, -0.018625617027282715, -0.07695167511701584, 0.014127690345048904, 0.015339807607233524, -0.002177766291424632, -0.03749417886137962, 0.016815830022096634, -0.0313127376139164, -0.0054422239772975445, -0.05758223310112953, 0.00912797823548317, -0.033311836421489716, -0.05233663693070412, -0.013144977390766144, 0.017124835401773453, -0.03250301256775856, 0.01613163761794567, -0.029179977253079414, -0.02147231251001358, -0.007156100124120712, -0.0013081253273412585, 0.03272831067442894, -0.013059087097644806, -0.0025487306993454695, -0.033177588135004044, -0.0069713955745100975, 0.009347121231257915, 0.008134637027978897, -0.011221294291317463, -0.05666612088680267, 0.05018231272697449, -0.005814084783196449, -0.004942658822983503, -0.027308057993650436, 0.027509601786732674, -0.01629035547375679, 0.017441488802433014, -0.027077149599790573, -0.06609909236431122, -0.01501400675624609, -0.04500402510166168, 0.03493587672710419, 0.03938803821802139, -0.01792719028890133, 0.06835772097110748, 0.0019806833006441593, -0.0021198256872594357, 0.0021482654847204685, 0.003986118361353874, 7.469172851415351e-05, -0.011246227659285069, 0.02382003329694271, 0.021717451512813568, -0.018413284793496132, 0.02752058207988739, -0.043429385870695114, 0.03711078315973282, -0.002394429175183177, -0.018917778506875038, -0.025607392191886902, -0.03272276744246483, 0.013691429048776627, -0.01114277821034193, 0.02688964456319809, -0.009080280549824238, -0.010945511050522327, 0.007001297548413277, 0.010205092839896679, 0.027219247072935104, 0.0138392373919487, 0.007211348507553339, 0.023803437128663063, -0.01892700605094433, 0.00830215122550726, -0.0013048083055764437, 0.022959990426898003, -0.01036107074469328, 0.023789891973137856, -0.02445807121694088, 0.008595729246735573, 0.005777404177933931, -0.017109494656324387, -0.004843107890337706, 0.05428171530365944, 0.01324272621423006, -0.006186717189848423, -0.01008912269026041, -0.02102835103869438, -0.018763449043035507, 0.03688623756170273, 0.03095007687807083, 0.02032284066081047, -0.03127329424023628, 3.637523695942946e-05, -0.038848526775836945, 0.04911179840564728, -0.0038588743191212416, -0.035672806203365326, 0.0051703061908483505, -0.019280819222331047, -0.0018943174509331584, 0.09370753169059753, 0.024237986654043198, 0.017007138580083847, 0.041927121579647064, 0.05136129632592201, -0.0697387233376503, 0.014965029433369637, -0.031072542071342468, -0.03888554498553276, 0.003946182318031788, 0.03133201226592064, 0.041056077927351, 0.09373867511749268, -0.015337257646024227, 0.0018056649714708328, -0.0345696285367012, 0.0428561232984066, 0.0046616289764642715, -0.04917509853839874, -0.05391034111380577, 0.03483621031045914, 0.0007075454923324287, -0.02217358723282814, 0.006303312722593546, -0.02860429883003235, 0.07180100679397583, 0.053167615085840225, 0.02752762660384178, 0.003643204690888524, 0.006337326020002365, -0.0002165713522117585, 0.0015036503318697214, 0.003849043743684888, 0.00503028417006135, -0.015529577620327473, -0.018446244299411774, -0.02230694890022278, 0.0042500183917582035, 0.03370936959981918, -0.04333920404314995, -0.007412831299006939, 0.00269571365788579, -0.05846361070871353, 0.011652708984911442, -0.05941684916615486, -0.018783601000905037, 0.0382840558886528, 0.009215466678142548, 0.03292291983962059, 0.005795941688120365, -0.016728868708014488, -0.05271044746041298, -0.027686193585395813, 0.0683136135339737, 0.03273387625813484, -0.06184608116745949, -0.04521244019269943, 0.006852018181234598, 0.02944375015795231, 0.036471810191869736, 0.027564730495214462, 0.01194159034639597, -0.05034536495804787, 0.05972730368375778, 0.02599257044494152, 0.022368816658854485, -0.03427637368440628, -0.07547707110643387, 0.040294382721185684, -0.006709327455610037, -0.03873836249113083, -0.013540569692850113, 0.03693700209259987, 0.010763188824057579, -0.05911337211728096, -0.009845681488513947, 0.0013815201818943024, -0.0009735113708302379, -0.03977695107460022, 0.00936998799443245, -0.06674322485923767, 0.05656123161315918, -0.00996281486004591, 0.04515208676457405, -0.03351921588182449, -0.0053950827568769455, -0.028983648866415024, 0.019980482757091522, -0.047473516315221786, -0.03226182237267494, 0.036837782710790634, -0.0967433825135231, -0.012275950983166695, -0.01027202233672142, -0.05544450506567955, -0.07849960774183273, 0.020989712327718735, 0.007494919002056122, -0.01539567019790411, -0.006112429779022932, 0.041723404079675674, -0.02201269008219242, -0.021414611488580704, 0.061371929943561554, 0.02626839652657509, 0.034245289862155914, -0.010925122536718845, -0.06646116822957993, 0.010355249978601933, 0.08753573894500732, 0.024917706847190857, -0.027188429608941078, -0.03391551226377487, -0.014519435353577137, 0.05880666896700859, 0.037113260477781296, 0.004027269314974546, 0.0688994973897934, 0.03838265687227249, 0.032771360129117966, 0.006886081770062447, 0.04389796778559685, 0.07352986186742783, 0.025451723486185074, 0.03675183653831482, 0.04477692022919655, -0.006102649495005608, -0.019673731178045273, -0.02378542348742485, -0.0035346627701073885, 0.02899472787976265, -0.037522509694099426, -0.02507600374519825, -0.02764442376792431, -0.020290842279791832, -0.039606913924217224, 0.023494472727179527, -0.046465933322906494, -0.06112038716673851, -0.012609364464879036, 0.04962366819381714, -0.018872197717428207, -0.07576603442430496, 0.02114490047097206, -0.03539430350065231, 0.0425417535007, 0.041919343173503876, -0.03601975366473198, 0.006254902575165033, 0.039061881601810455, 0.013051295652985573, -0.04260344058275223, 0.010636238381266594, 0.0029014507308602333, -0.04279368370771408, 0.07681179791688919, 0.05238088592886925, -0.08552493900060654, -0.016088435426354408, -0.02892216295003891, 0.006592591293156147, -0.012304126285016537, 0.043755967170000076, 0.09048294275999069, 0.015528755262494087, 0.0008472456829622388, 0.002348747104406357, -0.028581419959664345, 0.07031562179327011, 0.0452125146985054, 0.03202131390571594, -0.007017763331532478, 0.0434771403670311, 0.01372391264885664, 0.016497742384672165, 0.006129694636911154, -0.026850132271647453, 0.0760083943605423, -0.011254877783358097, 0.02407361939549446, 0.0009671802399680018, 0.019244955852627754, 0.022312112152576447, -0.05093875154852867, 0.05525115877389908, 0.011102058924734592, -0.04138638451695442, 0.0072084106504917145, 0.02355876751244068, -0.005467608571052551, 0.0030646740924566984, -0.03352535516023636, -0.013107229955494404, 0.005124229937791824, 0.03284703567624092, -0.01223110593855381, -0.016619233414530754, 0.07931875437498093, -0.032376643270254135, -0.019718792289495468, 0.002682372694835067, 0.0032899470534175634, 0.04683079943060875, -0.04535917565226555, -0.013540511950850487, 0.04938903823494911, 0.0038782283663749695, 0.013163303956389427, 0.05586503446102142, 0.012476799078285694, 0.020777173340320587, 0.01728731021285057, 0.0033609201200306416, -0.023495448753237724, 0.011650883592665195, -0.03058406338095665, -0.0437704436480999, -0.023081867024302483, -0.028861558064818382, 0.03199740871787071, 0.02601783163845539, -0.021226273849606514, -0.007901252247393131, 0.02287236787378788, -0.001370465150102973, -0.021330952644348145, -0.019673015922307968, 0.006240204442292452, 0.021167803555727005, -0.001458971993997693, -0.018941257148981094, -0.009018993005156517, 0.008776715025305748, -0.029219750314950943, 0.022491294890642166, -0.054798878729343414, 0.02466319128870964, 0.008629372343420982, 0.017117923125624657, 0.01984238624572754, 0.016792450100183487, -0.020611541345715523, -0.046037085354328156, -0.03797534108161926, 0.012523071840405464, 0.005764389876276255, 0.049915336072444916, 0.03567170351743698, -0.03150944411754608, 0.02683807909488678, -0.016319867223501205, -0.03850886970758438, 0.007949547842144966, -0.0035882226657122374, -0.030251994729042053, -0.038335565477609634, 0.010873493738472462, -0.051192738115787506, -5.611081224328091e-33, -0.022920172661542892, -0.006784701719880104, 0.007532184012234211, -0.008927523158490658, -0.05289614945650101, -0.005792489740997553, 0.0069431038573384285, -0.007715757004916668, 0.016737064346671104, -0.009221496991813183, -0.022544806823134422, -0.05232837796211243, 0.005261936224997044, -0.004717928357422352, 0.06748945266008377, -0.04627757519483566, 0.042869385331869125, -0.05089554190635681, -0.02245231159031391, -0.008569011464715004, 0.02576552890241146, 0.026341024786233902, 0.04370894655585289, -0.04998902976512909, -0.053245268762111664, 0.10313961654901505, -0.03513157740235329, -0.0004751569067593664, -0.019538884982466698, 0.021826278418302536, 0.02298172004520893, 0.007629253901541233, -0.019309040158987045, -0.07965300977230072, -0.03932715579867363, -0.0473552942276001, -0.07070645689964294, -0.040950365364551544, -0.06473290175199509, -0.025597788393497467, 0.024692567065358162, -0.029505683109164238, 0.07623948156833649, -0.022730158641934395, -0.01992206834256649, -0.013352246023714542, 0.047908201813697815, -0.010374099016189575, 0.02435419335961342, -0.040341757237911224, -0.04106574133038521, -0.008817660622298717, 0.033926207572221756, -0.013473513536155224, 0.03787653520703316, 0.06148720160126686, -0.01060567982494831, 0.015028185211122036, -0.026796413585543633, 0.06727182120084763, -0.005644873715937138, 0.03344403952360153, -0.025183673948049545, 0.06264566630125046, 0.0645957663655281, 0.062477756291627884, 0.029451703652739525, -0.0190434530377388, -0.013399080373346806, -0.04355941712856293, 0.03859647735953331, -1.6157238860614598e-05, 0.03535785898566246, 0.011393341235816479, 0.10227522253990173, -0.03163629770278931, -0.026419486850500107, 0.06364060193300247, -0.00940539501607418, 0.04949195683002472, -0.014538253657519817, -0.015203059650957584, -0.006831718143075705, 0.03136803209781647, 0.030412692576646805, -0.03218453750014305, -0.006956668570637703, -0.06605541706085205, 0.002640432445332408, -0.010324949398636818, 0.034113138914108276, 0.03659998998045921, 0.00273203500546515, -0.024274315685033798, 0.02414271980524063, -0.014814648777246475, 0.006856159772723913, 0.06191618740558624, 0.004925440531224012, -0.05506506189703941, -0.017693916335701942, -0.031003989279270172, 0.0006281306850723922, -0.04501902684569359, 0.016044102609157562, 0.03537421673536301, -0.02543989196419716, 0.03267453610897064, -0.026686077937483788, -0.0126366401091218, 0.006609780248254538, -0.007990132085978985, 0.031772371381521225, 0.0022029296960681677, 0.029536982998251915, -0.034000348299741745, -0.016217276453971863, 0.016163723543286324, -0.002014289842918515, -0.03571433946490288, -0.06077054142951965, 0.038403160870075226, -0.008770447224378586, 0.04860594496130943, -0.039567481726408005, -0.007430625148117542, -0.08546652644872665, 0.01866377331316471, -0.09058360755443573, -0.06785441935062408, -0.02981250360608101, -0.005241401959210634, 2.8097508675273275e-07, -0.04194503650069237, 0.02783643640577793, -0.0019703865982592106, 0.02044106274843216, -0.036545027047395706, 0.0503266416490078, 0.0027271604631096125, 0.010803047567605972, 0.027063751593232155, 0.01106929313391447, 0.040531057864427567, -0.017048299312591553, 0.008043316192924976, 0.041465405374765396, -0.0341450497508049, -0.06467317789793015, 0.01253136433660984, 0.03159249573945999, 0.006020670756697655, -0.02017037570476532, -0.00912634376436472, 0.048000119626522064, 0.02539794147014618, -0.00714427325874567, 0.0918574184179306, 0.03637136146426201, 0.027105161920189857, 0.00048735763994045556, 0.04583616554737091, -0.027231940999627113, -0.060679636895656586, 0.003327693324536085, -0.028135696426033974, -0.0038639837875962257, -0.013297796249389648, 0.0448751300573349, -0.006645126733928919, 0.04533267766237259, 0.005049323663115501, 4.33885506936349e-05, 0.01344197615981102, 0.045657649636268616, 0.05216421186923981, -0.020235033705830574, 0.011331993155181408, -0.06169082224369049, -0.007805240340530872, 0.0065589649602770805, 2.3118174794944935e-05, 0.008738959208130836, 0.008525297977030277, -0.02434973418712616, -0.043838538229465485, -0.02675357647240162, -0.005984297022223473, 0.044089458882808685, 0.021283086389303207, 0.010328363627195358, 0.0011784735834226012, 0.04173750430345535, -0.005972198210656643, -0.02656807191669941, -0.023496799170970917, 0.028909113258123398, -0.019846860319375992, -0.041137609630823135, -0.02715264819562435, 2.965985994241939e-34, 0.0008377249469049275, -0.05848163738846779, 0.02529863454401493, -0.009929376654326916, -0.03214482590556145, 0.02384190261363983, 0.07266489416360855, 0.020755914971232414, 0.08482673764228821, 0.014141608960926533, -0.0455378033220768]

['Laura Deming', 'Sasha Targ', 'Nate Sauder', 'Diogo Almeida', 'Chun Jimmie Ye']

1605.07156v1

Each human genome is a 3 billion base pair set of encoding instructions. Decoding the genome using deep learning fundamentally differs from most tasks, as we do not know the full structure of the data and therefore cannot design architectures to suit it. As such, architectures that fit the structure of genomics should be learned not prescribed. Here, we develop a novel search algorithm, applicable across domains, that discovers an optimal architecture which simultaneously learns general genomic patterns and identifies the most important sequence motifs in predicting functional genomic outcomes. The architectures we find using this algorithm succeed at using only RNA expression data to predict gene regulatory structure, learn human-interpretable visualizations of key sequence motifs, and surpass state-of-the-art results on benchmark genomics challenges.

Genetic Architect: Discovering Genomic Structure with Learned Neural Architectures

http://arxiv.org/pdf/1605.07156v1

Title Genetic Architect Discovering Genomic Structure Learned Neural Architectures Summary human genome 3 billion base pair set encoding instruction Decoding genome using deep learning fundamentally differs task know full structure data therefore cannot design architecture suit architecture fit structure genomics learned prescribed develop novel search algorithm applicable across domain discovers optimal architecture simultaneously learns general genomic pattern identifies important sequence motif predicting functional genomic outcome architecture find using algorithm succeed using RNA expression data predict gene regulatory structure learn humaninterpretable visualization key sequence motif surpass stateoftheart result benchmark genomics challenge Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-7.282174192368984e-05, 0.09117594361305237, -0.03623959422111511, -0.015610825270414352, 0.018734263256192207, 0.028670238330960274, 0.0044066994450986385, 0.042840730398893356, 0.004791349172592163, 0.0667874664068222, 0.024639450013637543, -0.021972354501485825, 0.0029261228628456593, 0.10818623006343842, -0.001823633094318211, 0.030662691220641136, 0.022607902064919472, 0.03353269770741463, 0.001900402014143765, -0.03112749569118023, -0.014855414628982544, 0.011720108799636364, 0.025632888078689575, 0.019338421523571014, -0.004582622088491917, 0.006391285918653011, 0.008903658017516136, 0.004094851668924093, 0.016250066459178925, -0.028920888900756836, 0.010336771607398987, -0.0033427965827286243, 0.028571225702762604, 0.0380249097943306, 2.121764737239573e-06, 0.008709801360964775, 0.0007412420818582177, -0.016575220972299576, -0.05755407735705376, 0.0009559256723150611, -0.01154694240540266, 0.011143563315272331, 0.0030605290085077286, -0.027705155313014984, -0.008960621431469917, -0.04587266594171524, 0.08527719974517822, 0.059440355747938156, -0.00657297670841217, 0.04289359599351883, 0.01260167732834816, -0.08715632557868958, 0.04256744310259819, -0.03238052502274513, 0.044539451599121094, -0.020511800423264503, 0.025583690032362938, 0.004939083941280842, 0.020889680832624435, -0.0015912967501208186, 0.013496843166649342, 0.03878571093082428, 0.007557956967502832, 0.04053981974720955, 0.03786380961537361, 0.030998537316918373, 0.021954813972115517, -0.05051440745592117, 0.04605025425553322, 0.05920868739485741, 0.012620828114449978, -0.007770635653287172, 0.027805939316749573, 0.01740800030529499, 0.00826655700802803, -0.03198546543717384, 0.0015514931874349713, 0.0051927147433161736, -0.06143105402588844, 0.02235940657556057, -0.010372165590524673, -0.03571271896362305, 0.043870680034160614, -0.03488636761903763, 0.01121464278548956, 0.043669186532497406, -0.020626626908779144, -0.000898897647857666, -0.04110673442482948, -0.024450408294796944, -0.008016057312488556, -0.02136441320180893, 0.002641999162733555, -0.030922021716833115, -0.030828792601823807, -0.02260206826031208, 0.030415093526244164, -0.010734799318015575, 0.0490131676197052, -0.0007110321894288063, 0.06083055958151817, -0.0037945089861750603, -0.02063344232738018, -0.022512681782245636, -0.019194992259144783, 0.009405935183167458, -0.09417112171649933, 0.013037260621786118, -0.011401393450796604, 0.0168567206710577, -0.09213238209486008, 0.020005986094474792, 0.017702963203191757, 0.0626891553401947, -0.0053963735699653625, 0.02552766352891922, -0.06249569356441498, -0.040489476174116135, -0.016667667776346207, -0.009901543147861958, 0.019757568836212158, 0.08427703380584717, 0.02472064085304737, 0.06206291541457176, -0.023592250421643257, -0.01548287458717823, -0.02321535535156727, -0.01843659020960331, -0.011449368670582771, -0.03499140962958336, 0.05131945386528969, 0.011557123623788357, 0.005931115709245205, 0.03654148429632187, -0.03165892884135246, 0.09383539110422134, 0.024846652522683144, -0.007057322189211845, -0.020934654399752617, -0.022003687918186188, -0.0338011272251606, 0.011770893819630146, 0.04052407294511795, -0.02227814495563507, 0.026906119659543037, -0.03736923262476921, -0.047697652131319046, -0.0322173535823822, 0.0033832520712167025, -0.04827297478914261, -0.055194322019815445, 0.033076174557209015, -0.0247542392462492, -0.020415591076016426, 0.05162307992577553, 0.029838357120752335, 0.0034795573446899652, -0.02412789687514305, 0.0020150290802121162, 0.004426813684403896, 0.002226414857432246, -0.026401543989777565, -0.021793577820062637, 0.0005665385979227722, -0.006031292024999857, -0.07856117933988571, 0.09023423492908478, -0.027782518416643143, 0.0013451003469526768, 0.059584710747003555, -0.008035746403038502, -0.011488854885101318, -0.011896186508238316, -0.030051646754145622, -0.009733041748404503, 0.05752808600664139, 0.09461396187543869, 0.08572173863649368, 0.019838469102978706, 0.03662600368261337, -0.03080330789089203, -0.03798416629433632, 0.014244211837649345, 0.02523830719292164, -0.013948780484497547, -0.02593393251299858, -0.041040923446416855, -0.01236915122717619, -0.005079938098788261, -0.004975410643965006, 0.028556806966662407, 0.01812927983701229, -0.027880191802978516, -0.03214080631732941, 0.010084284469485283, -0.0269174724817276, -0.02886529266834259, -0.030566077679395676, 0.006390685681253672, 0.012520752847194672, 0.026798197999596596, -0.02476092427968979, 0.004040052182972431, 0.008321116678416729, -0.010350854136049747, -0.0430198572576046, -0.01460635382682085, 0.012916197068989277, -0.02642720192670822, -0.018165111541748047, -0.061498358845710754, 0.0004093012830708176, 0.013963760808110237, -0.032561276108026505, -0.02727425843477249, 0.011253739707171917, 0.003807390807196498, 0.007673903834074736, -0.059077780693769455, -0.019112130627036095, 0.028462499380111694, 0.0474892258644104, 0.0008814522298052907, 0.006869301199913025, -0.08190213888883591, 0.002385420259088278, 0.04509877413511276, 0.012514129281044006, 0.01636875607073307, 0.04525446146726608, -0.03762185946106911, 0.0034966114908456802, 0.06597187370061874, -0.06155047193169594, -0.03082406148314476, -0.04313383251428604, -0.02991856075823307, -0.002205749275162816, -0.038657188415527344, -0.05363116040825844, -0.013999449089169502, 0.023108936846256256, -0.03050224296748638, -0.06261829286813736, 0.05324390158057213, -0.07897183299064636, 0.011386539787054062, -0.005233252886682749, -0.03358125686645508, -0.0347839891910553, -0.008599362336099148, -0.031493157148361206, 0.02173101156949997, 0.024518832564353943, -0.02256913296878338, 0.01039615087211132, -0.06143223121762276, 0.02782365120947361, -0.027134688571095467, 0.029644152149558067, -0.01231339666992426, -0.0353732593357563, -0.05139710381627083, 0.030329307541251183, 0.018621720373630524, -0.0045012724585831165, 0.028832413256168365, -0.05203532055020332, 0.03834519535303116, 0.02779490500688553, 0.03366751968860626, 0.004407744854688644, -0.020521827042102814, 0.023483965545892715, -0.02881288342177868, -0.04520092159509659, 0.04931183159351349, -0.0029751728288829327, -0.048356957733631134, 0.03786748647689819, 0.03426772356033325, -0.039960186928510666, -0.03125453367829323, -0.06855212897062302, -0.07119180262088776, 0.03480932116508484, 0.043800707906484604, -0.0332489013671875, -0.015651050955057144, -0.012246157042682171, -0.0010667074238881469, 0.028542468324303627, 0.00017104088328778744, -0.047120269387960434, -0.00010554381151450798, -0.0057808090932667255, -0.01865547150373459, 0.023881886154413223, 0.005949190817773342, -0.017505161464214325, 0.016539612784981728, 0.06572143733501434, 0.03192072734236717, -0.004840459208935499, -0.03436145558953285, 0.041250813752412796, 0.0221521258354187, 0.0023443379905074835, 0.013262560591101646, 0.018386440351605415, 0.04230264574289322, -0.006203874945640564, -0.054752167314291, 0.011440630070865154, 0.027789419516921043, -0.013077588751912117, -0.033286891877651215, -0.02734849415719509, -0.016291851177811623, 0.06239113211631775, -0.000961767858825624, -0.003696144325658679, 0.05383806675672531, 0.04560836777091026, 0.02907870151102543, 0.0037400114815682173, 0.0038636988028883934, -0.019865134730935097, -0.005501001141965389, 0.0011096029775217175, 0.04691152274608612, 0.027845729142427444, -0.049384474754333496, -0.004546032752841711, 0.01810980774462223, -0.0465836338698864, -0.0460442453622818, -0.005386903882026672, -0.041823696345090866, -0.009244208224117756, 0.027647120878100395, -0.07087093591690063, -0.0457228422164917, 0.08685756474733353, 0.012464904226362705, 0.005714321509003639, 0.06533670425415039, -0.05106841400265694, -0.030484242364764214, -0.05214196816086769, -0.00257315207272768, 0.0038811492267996073, -0.012769782915711403, 0.031843628734350204, -0.014218798838555813, 0.04736671224236488, 0.0035087878350168467, -0.05327305942773819, 0.01936466060578823, -0.006568888667970896, -0.006035329774022102, 0.01838734932243824, -0.07454969733953476, 0.05390017852187157, -0.018646443262696266, 0.042600132524967194, -0.012277194298803806, 0.026219213381409645, -0.015086816623806953, 0.016926182433962822, 0.008354990743100643, -0.055253591388463974, -0.0023348741233348846, 0.055046115070581436, -0.0035587127786129713, -0.05883524939417839, 0.010317310690879822, 0.008131776005029678, -0.06146273389458656, 0.0005381753435358405, 0.07002311199903488, -0.10294073820114136, -0.01650743931531906, -0.023181471973657608, -0.02419952116906643, -0.04714202135801315, -0.06984973698854446, 0.05040210112929344, -0.0007074016029946506, 0.005601032637059689, 0.004016888327896595, -0.031687211245298386, -0.058801304548978806, -0.05273934826254845, -0.046314798295497894, -0.05338600277900696, -0.06822734326124191, 0.006994389928877354, 0.040346089750528336, -0.009257311932742596, 0.02847558632493019, -0.022738244384527206, -0.016419729217886925, 0.03841612488031387, -0.05397600308060646, 0.03208165988326073, 0.10525692254304886, 0.02109077386558056, 0.02081305906176567, -0.026641352102160454, -0.0022741120774298906, 0.033429306000471115, 0.02862977236509323, -0.03339949995279312, 0.06616558879613876, 0.06884749978780746, -0.019994065165519714, -0.08356700837612152, 0.06059970334172249, -0.09320125728845596, 0.05377766117453575, 0.012186797335743904, 0.05206434056162834, -0.007481307722628117, -0.014629950746893883, -0.046935487538576126, 0.0014388787094503641, -0.0033589331433176994, 0.019918935373425484, 0.0031060187611728907, -0.00784278567880392, -0.013613992370665073, -0.018871262669563293, 0.07278134673833847, -0.11051592230796814, -0.06965164095163345, 0.03717796131968498, 0.002286162693053484, 0.033809904009103775, -0.03160594031214714, 0.012210025452077389, -0.018047861754894257, -0.001674928585998714, 0.06436236202716827, -0.013032007031142712, 0.03940135985612869, -0.056759294122457504, -0.05175197497010231, -0.029315445572137833, 0.024571310728788376, 0.0052855233661830425, -0.07467914372682571, -0.04647655040025711, 0.059136565774679184, -0.010897060856223106, -0.006543775554746389, 0.029166098684072495, -0.028172438964247704, -0.031914323568344116, -0.053497862070798874, 0.0658542588353157, 0.003942764829844236, 0.00034725634031929076, 0.027951551601290703, -0.04019758477807045, 0.04910906404256821, -0.008445187471807003, 0.031087173148989677, -0.0373440645635128, -0.03328990563750267, -0.07211482524871826, -0.04242179915308952, 0.01310434378683567, 0.018766121938824654, 0.03355693817138672, 0.026474695652723312, -0.022788070142269135, 0.02780904993414879, 0.0564127042889595, 0.033713676035404205, 0.04667697846889496, 0.0684858039021492, 0.021739447489380836, -0.029957108199596405, -0.026668444275856018, 0.019535623490810394, 0.007085065823048353, -0.002741664182394743, -0.022830642759799957, -0.0008319393964484334, 0.04323411360383034, 0.005615852307528257, -0.010836303234100342, 0.008144681341946125, 0.034882236272096634, -0.0020002706442028284, -0.05358872935175896, 0.06913647800683975, 0.02516361139714718, 0.055914413183927536, -0.004600598011165857, 0.0022679909598082304, 0.02507915161550045, 0.04248107224702835, -0.012960920110344887, 0.03706444427371025, -0.01573835499584675, -0.02605775184929371, 0.006456325296312571, 0.04899008944630623, 0.0030735512264072895, 0.010340666398406029, 0.008794784545898438, -0.010100497864186764, -0.0027094969991594553, -0.029723066836595535, 0.049860645085573196, -0.03273041918873787, -0.019353579729795456, 0.035126667469739914, 0.025609472766518593, -0.06451466679573059, 0.019602147862315178, -0.09916292130947113, 0.03686843439936638, 0.016995081678032875, 0.024170158430933952, -0.031924497336149216, -0.07734300196170807, 0.07246958464384079, 0.06782349199056625, 0.054827332496643066, -0.02185674011707306, -0.03261691331863403, -0.015555433928966522, 0.03857370465993881, 0.03199845552444458, 0.019114384427666664, -0.041922830045223236, -0.015060355886816978, 0.004605509806424379, -0.011229951865971088, -0.002720220247283578, 0.03475230559706688, 0.03803800418972969, 0.05110081657767296, 0.006164758000522852, -0.0407019704580307, 0.016354981809854507, -0.07412902265787125, 0.0015601697377860546, -0.01574188843369484, -0.04894271492958069, -0.06432836502790451, -0.04617276415228844, -6.488032336136165e-33, 0.018467990681529045, -0.03776095062494278, 0.0010862675262615085, -0.009600159712135792, -0.009800419211387634, 0.04096004739403725, -0.03350682556629181, -0.020729294046759605, -0.02896130643785, 0.0020088888704776764, -0.006412987131625414, 0.004738346673548222, -0.013109604828059673, 0.014989183284342289, 0.05736272409558296, 0.009362703189253807, 0.025915874168276787, -0.011249532923102379, 0.028723612427711487, 0.02905227802693844, 0.021280406042933464, 0.04855185002088547, 0.014615979976952076, -0.05014216527342796, -0.07272180169820786, 0.04931925982236862, 0.055997297167778015, 0.013835429213941097, -0.018374528735876083, 0.013796776533126831, 0.0008054804638959467, -0.007963798940181732, 0.0019581192173063755, -0.021104756742715836, -0.0042722527869045734, -0.013590693473815918, -0.06354719400405884, 0.018153851851820946, -0.042658109217882156, -0.021631918847560883, -0.02920755371451378, -0.056527502834796906, 0.04876511171460152, -0.025865597650408745, -0.03599487245082855, -0.0017723898636177182, 0.024230090901255608, -0.012496324256062508, -0.03374522551894188, -0.02891462855041027, -0.030129287391901016, -0.00558138033375144, -0.007680030539631844, 0.025408722460269928, 0.018781639635562897, -0.017379697412252426, -0.0005528951878659427, 0.025878190994262695, -0.0033273440785706043, 0.0439731739461422, 0.013566495850682259, 0.025660578161478043, 0.023671412840485573, 0.012290258891880512, 0.03864733502268791, 0.01866510882973671, 0.0445818267762661, -0.0023553899955004454, -0.01926330290734768, 0.008415639400482178, -0.015744803473353386, 0.0666278526186943, 0.0048751323483884335, -0.023158224299550056, 0.05804169550538063, -0.032975904643535614, -0.09732913225889206, 0.05582134798169136, -0.03215153142809868, 0.00935282837599516, -0.026051688939332962, 0.0428953543305397, 0.02347072958946228, 0.019660377874970436, 0.027962952852249146, -0.016525305807590485, -0.02219243533909321, -0.030132904648780823, -0.0242337416857481, -0.04062371328473091, -0.0019995844922959805, 0.056461628526449203, -0.009561668150126934, -0.09313996136188507, 0.05825244262814522, 0.01620331220328808, 0.026606053113937378, -0.022784480825066566, 0.009801549836993217, -0.003350989893078804, -0.03538511320948601, -0.05592029169201851, 0.01429271325469017, -0.026976343244314194, 0.04125988483428955, -0.006503628566861153, 0.01414015144109726, -0.01538049802184105, 0.018962938338518143, -0.018351832404732704, -0.023955753073096275, -0.02694109082221985, 0.045415885746479034, 0.005997348576784134, -0.012913846410810947, -0.009233889169991016, 0.008579906076192856, 0.04142094776034355, 0.05179937928915024, 0.036774128675460815, 0.00035303019103594124, 0.0001600688701728359, -0.004578764550387859, 0.009434647858142853, -0.07344355434179306, -0.02703910320997238, -0.0502481609582901, 0.006806952878832817, 0.005807745736092329, -0.058036305010318756, -0.042275309562683105, 0.034751199185848236, 2.9718640348619374e-07, 0.032295625656843185, 0.05403554067015648, 0.05327657237648964, -0.0328269824385643, 0.019476165995001793, -0.0025192415341734886, 0.02530614845454693, 0.021282058209180832, -0.0875840038061142, -0.011646739207208157, 0.03822200000286102, -0.028746088966727257, 0.03809143975377083, -0.01840963214635849, -0.03535798192024231, 0.011039641685783863, -0.0010981393279507756, 0.03878353536128998, -0.010081826709210873, 0.014786877669394016, 0.04078277200460434, 0.09882912784814835, -0.004091427195817232, -0.01952449418604374, 0.07868041843175888, 0.039151325821876526, 0.0014759959885850549, 0.0023268703371286392, 0.04652995988726616, -0.025165803730487823, -0.07251740992069244, -0.027886828407645226, -0.015168590471148491, 0.009033411741256714, -0.01930391415953636, -0.03787342086434364, -0.015064592473208904, 0.026274360716342926, 0.024558095261454582, -0.00047975563211366534, 0.03725898638367653, 0.04661951959133148, 0.023710966110229492, 0.018279438838362694, -0.008104880340397358, -0.04150205850601196, -0.09649301320314407, 0.03818436339497566, 0.023122362792491913, -0.0006689432193525136, -0.021980799734592438, 0.01211667899042368, 0.05237475037574768, 0.04088873416185379, -0.01567656360566616, -0.031145310029387474, 0.03931168094277382, -0.009480351582169533, 0.05207401514053345, 0.06006046012043953, -0.035047583281993866, 0.031565021723508835, -0.02530643902719021, 0.0023722448386251926, 0.04068218171596527, -0.007994277402758598, 0.006469946354627609, 2.6101555890533785e-34, -0.01776476390659809, -0.02303435653448105, -0.005453275050967932, 0.015132233500480652, 0.05057353526353836, -0.0008104836451821029, 0.0029343580827116966, -0.006528680212795734, -0.02584335394203663, -0.04153018444776535, -0.042041242122650146]

['Tejas D. Kulkarni', 'Ardavan Saeedi', 'Simanta Gautam', 'Samuel J. Gershman']

1606.02396v1

Learning robust value functions given raw observations and rewards is now possible with model-free and model-based deep reinforcement learning algorithms. There is a third alternative, called Successor Representations (SR), which decomposes the value function into two components -- a reward predictor and a successor map. The successor map represents the expected future state occupancy from any given state and the reward predictor maps states to scalar rewards. The value function of a state can be computed as the inner product between the successor map and the reward weights. In this paper, we present DSR, which generalizes SR within an end-to-end deep reinforcement learning framework. DSR has several appealing properties including: increased sensitivity to distal reward changes due to factorization of reward and world dynamics, and the ability to extract bottleneck states (subgoals) given successor maps trained under a random policy. We show the efficacy of our approach on two diverse environments given raw pixel observations -- simple grid-world domains (MazeBase) and the Doom game engine.

Deep Successor Reinforcement Learning

http://arxiv.org/pdf/1606.02396v1

Title Deep Successor Reinforcement Learning Summary Learning robust value function given raw observation reward possible modelfree modelbased deep reinforcement learning algorithm third alternative called Successor Representations SR decomposes value function two component reward predictor successor map successor map represents expected future state occupancy given state reward predictor map state scalar reward value function state computed inner product successor map reward weight paper present DSR generalizes SR within endtoend deep reinforcement learning framework DSR several appealing property including increased sensitivity distal reward change due factorization reward world dynamic ability extract bottleneck state subgoals given successor map trained random policy show efficacy approach two diverse environment given raw pixel observation simple gridworld domain MazeBase Doom game engine Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0047506894916296005, 0.06638247519731522, -0.007088123355060816, -0.003773239441215992, -0.016015956178307533, -0.013669737614691257, -0.018909061327576637, -0.028850967064499855, -0.03467404097318649, 0.043055251240730286, -0.01732652820646763, 0.039135873317718506, -0.025339452549815178, 0.052633967250585556, 0.01391677651554346, -0.08276686817407608, 0.007050131447613239, -0.026740817353129387, -0.03546822443604469, -0.007046569604426622, -0.01572040654718876, -0.054788216948509216, -0.00242769462056458, 0.035243671387434006, -0.05249716341495514, -0.0002966606989502907, -0.0529635064303875, -0.0002534835657570511, 0.05050830543041229, -0.09123716503381729, 0.054014887660741806, -0.0414566770195961, 0.06643188744783401, 0.03935176134109497, 2.3130385216063587e-06, -0.017079779878258705, -0.010845526121556759, -0.027625834569334984, 0.0796116515994072, -0.05401800945401192, 0.002696618437767029, -0.009603002108633518, -0.04961026832461357, -0.0056300037540495396, -0.040146999061107635, -0.017490018159151077, 0.055943746119737625, -0.0038389668334275484, 0.024115467444062233, 0.01692749559879303, 0.011223740875720978, -0.03708847984671593, 0.03476288169622421, -0.009923241101205349, 0.04617923125624657, -0.049074962735176086, 0.010098225437104702, 0.02054084837436676, -0.023181462660431862, -0.025812312960624695, -0.032418712973594666, 0.006983185186982155, 0.03602073714137077, -0.014800036326050758, 0.030155574902892113, 0.04780397191643715, 0.0993615984916687, 0.011794738471508026, -0.035188939422369, 0.013781123794615269, -0.08317162096500397, 0.027590660378336906, 0.010563276708126068, 0.0210384763777256, -0.030313609167933464, -0.012418491765856743, -0.046255923807621, 0.050834666937589645, -0.043713584542274475, -0.002732147229835391, -0.03674258664250374, 0.09126307815313339, -0.008589335717260838, 0.011742348782718182, -0.014981310814619064, 0.060784149914979935, 0.0060118031688034534, 0.004447541665285826, -0.03765793889760971, 0.004605114459991455, 0.026717383414506912, -0.013046732172369957, 0.004221009556204081, 0.015155513770878315, -0.07106606662273407, 0.00852147489786148, -0.007096137385815382, -0.006345648318529129, 0.005876336712390184, -0.025199560448527336, 0.05904141813516617, -0.021883519366383553, -0.0058983080089092255, 0.04342016577720642, -0.014139758422970772, 0.02487117424607277, -0.07940038293600082, 0.03654709830880165, -0.008057907223701477, 0.020730040967464447, 0.010983575135469437, 0.019928263500332832, -0.012369429692626, 0.04201251268386841, 0.016822105273604393, -0.03181121498346329, 0.009028422646224499, 0.003807115601375699, -0.035537492483854294, -0.005335770547389984, -0.019987167790532112, 0.0894094780087471, -0.01878674514591694, 0.0039701699279248714, -0.028173208236694336, -0.00489329406991601, -0.03827535733580589, -0.00789941381663084, 0.02820313163101673, 0.02092846669256687, 0.025853771716356277, 0.0036352770403027534, -0.016661332920193672, 0.03776772320270538, 0.002607857109978795, 0.12434881180524826, 0.020600879564881325, 0.05305783078074455, -0.05417346954345703, 0.017581822350621223, 0.013681527227163315, -0.02121047116816044, 0.052974287420511246, -0.06282550096511841, -0.038876499980688095, -0.0856303870677948, -0.021867450326681137, 0.008715387433767319, 0.014965577982366085, 0.006676628720015287, -0.007201417814940214, 0.06827757507562637, -0.011465325020253658, -0.02249613031744957, 0.06550194323062897, -0.0008554719970561564, 0.006758227478712797, 0.03200651705265045, 0.050891757011413574, 0.05049516260623932, -0.002616504207253456, 0.030128415673971176, -0.005060945637524128, -0.005547243636101484, -0.01228171307593584, 0.03891569748520851, 0.008741726167500019, -0.036884158849716187, 0.004148117266595364, 0.06698707491159439, 0.03218161687254906, 0.005641900934278965, 0.0001604782446520403, -0.04574400931596756, 0.01506007183343172, 0.03283095359802246, -0.02069726772606373, -0.00890678446739912, 0.020832829177379608, -0.01053491048514843, -0.06554790586233139, -0.011292025446891785, -0.034359417855739594, 0.10664811730384827, 0.0360601507127285, -0.03244318068027496, -0.03589627519249916, 0.013862165622413158, -0.0179377943277359, -0.08597695082426071, 0.05066723749041557, -0.02091289311647415, 0.029356427490711212, -0.026924898847937584, 0.028750894591212273, 0.03209330886602402, -0.056064143776893616, -0.08582346886396408, -0.006739381235092878, 0.025904931128025055, -0.0254141204059124, -0.04585832357406616, 0.07088720798492432, -0.023537039756774902, -0.018495256081223488, -0.02386612817645073, -0.021469714120030403, -0.008485008031129837, -0.03153549134731293, -0.0025333219673484564, -0.025484886020421982, -0.0036882981657981873, 0.05127302557229996, -0.008982576429843903, -0.0654955580830574, -0.005275130271911621, 0.012230277061462402, 0.07075350731611252, -0.01955079287290573, -0.03142055124044418, 0.003623122116550803, 0.0193368811160326, 0.017337599769234657, 0.015553593635559082, 0.0018153416458517313, 0.00034746580058708787, 0.05274233967065811, 0.002435071161016822, 0.006485775578767061, -0.034517381340265274, 0.030775804072618484, -0.02405978925526142, 0.030574072152376175, 0.0052284845151007175, -0.007697420194745064, 0.0012561141047626734, -0.0876995250582695, -0.04952341690659523, 0.017728090286254883, -0.031723976135253906, 0.033706653863191605, 0.053528595715761185, -0.03872251883149147, 0.010458987206220627, 0.039086855947971344, -0.0078030782751739025, 0.0060903048142790794, 0.016838956624269485, -0.005900469142943621, 0.014486496336758137, -0.030434295535087585, -0.03651651740074158, 0.04871087893843651, -0.04887654632329941, -0.044478025287389755, -0.020006375387310982, 0.027269279584288597, 0.02523185685276985, -0.043756820261478424, 0.03224136680364609, -0.04766874387860298, -0.048647910356521606, 0.0007215985679067671, 0.04516284167766571, 0.056171320378780365, -0.0029391080606728792, 0.052181411534547806, 0.04485831409692764, -0.0006835042731836438, -0.0397145114839077, -0.001271505025215447, 0.00805852934718132, -0.032926175743341446, 0.019715577363967896, -0.0525524728000164, -0.026671800762414932, 0.05971943214535713, 0.011960319243371487, -0.02454315684735775, 0.02764793671667576, -0.005162493325769901, 0.03445015475153923, -0.05159025639295578, -0.015292848460376263, 0.007890217937529087, -0.018544834107160568, -0.0032044716645032167, 0.0008553371299058199, -0.033886514604091644, 0.019994959235191345, -0.0016572822351008654, 0.057759057730436325, -0.017854340374469757, -0.05810388922691345, 0.013945984654128551, -0.0408041812479496, 0.031103111803531647, 0.05836964771151543, 0.02095496840775013, 0.033255770802497864, -0.029177969321608543, 0.044606536626815796, -0.01733403652906418, 0.019292622804641724, -0.02799575962126255, -0.06102185696363449, 0.0033826783765107393, 0.013483094982802868, 0.04407960921525955, 0.024253956973552704, -0.004837529268115759, 0.014800945296883583, -0.05023319646716118, 0.018974928185343742, -0.010015410371124744, -0.06493311375379562, -0.042140595614910126, 0.03228776529431343, -0.012572942301630974, -0.0015123608754947782, -0.041540905833244324, -0.04058734327554703, 0.051525089889764786, 0.05057831108570099, -0.009150141850113869, 0.013866457156836987, -0.02358406037092209, 0.007461111526936293, 0.008269566111266613, 0.046160172671079636, 0.021886738017201424, -0.030391542240977287, -0.036246489733457565, -0.04166847839951515, -0.038382455706596375, -0.039958324283361435, -0.013015266507863998, -0.019434094429016113, -0.04173839092254639, -0.031578101217746735, 0.01582697220146656, -0.06780336052179337, -0.06478047370910645, 0.05240688845515251, 0.024068597704172134, 0.0048118093982338905, -0.04029732570052147, -0.010963925160467625, -0.002074906835332513, -0.015808088704943657, 0.015965523198246956, 0.031686946749687195, -0.009094085544347763, -0.03127424046397209, -0.017195653170347214, 0.031410109251737595, 0.06289350241422653, 0.04117089882493019, 0.005032402463257313, -0.009551746770739555, 0.05047817900776863, 0.056822989135980606, -0.007411042228341103, 0.013651450164616108, -0.10168665647506714, 0.06745275110006332, -0.013670855201780796, -0.01598111353814602, -0.029364045709371567, 0.031316887587308884, 0.025445593520998955, -0.060537777841091156, 0.0049102832563221455, -0.03421458229422569, -0.01138188038021326, -0.012847398407757282, 0.011990461498498917, -0.03580275550484657, 0.02903280220925808, 0.02119087614119053, 0.007083704695105553, 0.0046917409636080265, -0.006349102593958378, -0.019137995317578316, 0.007550620008260012, 0.011710765771567822, -0.025889767333865166, 0.05059005320072174, -0.0661860853433609, 0.04673269763588905, -0.0036476925015449524, -0.0415884368121624, -0.0022478527389466763, 0.023418918251991272, -0.0009365440928377211, -0.023616818711161613, -0.0511464923620224, 0.04361322522163391, 0.006982504390180111, -0.010950213298201561, 0.021186381578445435, 0.010851120576262474, 0.05940723046660423, -0.025066150352358818, -0.09677191823720932, -0.009748511016368866, 0.09954961389303207, 0.008366198278963566, -0.008124801330268383, -0.03951449319720268, -0.06422851979732513, -0.011701016686856747, 0.024107493460178375, 0.00914918351918459, 0.0756639614701271, 0.015315298922359943, 0.022846359759569168, 0.007133071776479483, 0.020915303379297256, 0.005908336490392685, 0.0028595130424946547, 0.02815486304461956, 0.00598545977845788, -0.01564186066389084, 0.032112326472997665, -0.06801652908325195, 0.02199324034154415, 0.0821787565946579, -0.020677512511610985, -0.03038981184363365, 0.02013191394507885, -0.05726338550448418, -0.04201635345816612, 0.022348804399371147, -0.06885746121406555, -0.02582010067999363, -0.03454415127635002, 0.015563391149044037, 0.013411940075457096, -0.0689542219042778, -0.013115820474922657, -0.03162482753396034, 0.05346156656742096, -0.013157379813492298, -0.05826573073863983, -0.03586481139063835, 0.0021731029264628887, -0.03385318070650101, -0.047408390790224075, 0.01652652584016323, 0.008731760084629059, -0.035348791629076004, 0.026174239814281464, 0.02693389542400837, -0.033130500465631485, -0.005647716578096151, -0.029930807650089264, -0.0278868917375803, -0.01141694001853466, -0.021564193069934845, 0.13669459521770477, 0.0039602005854249, 0.013848697766661644, -0.01268460601568222, 0.02607893757522106, 0.04604474455118179, -0.04781613498926163, 0.036304350942373276, -0.016037018969655037, 0.06021445617079735, 0.054923322051763535, -0.015490609221160412, 0.011574974283576012, -0.02319253981113434, 0.04913608357310295, -0.011573010124266148, 0.0013654290232807398, 0.019562924280762672, 0.011427909135818481, 0.009527303278446198, -0.07849152386188507, 0.08633299916982651, 0.013678335584700108, 0.02857501618564129, 0.00902050081640482, 0.006516399327665567, -0.0036797344218939543, 0.005970391910523176, -0.04685963690280914, 0.029203342273831367, 0.01248078141361475, 0.02595728635787964, 0.013555592857301235, -0.015368333086371422, 0.0717078298330307, -0.015197668224573135, -0.03741243854165077, -0.007973688654601574, 0.022802285850048065, 0.008099011145532131, -0.03414139896631241, 0.04209623485803604, 0.045038215816020966, 0.019966762512922287, 0.033717136830091476, 0.030165353789925575, 0.019981537014245987, -0.02568741701543331, 0.03419860824942589, -0.019718408584594727, -0.03009481355547905, 0.007967343553900719, -0.02116353251039982, -0.0870671346783638, -0.008583921007812023, 0.04665651544928551, 0.07686261087656021, 0.004886972717940807, 0.017013510689139366, 0.0003358959802426398, 0.017733337357640266, -0.04334167391061783, -0.0022427747026085854, 0.02834789641201496, -0.041519567370414734, 0.040642935782670975, -0.009518078528344631, -0.006544138770550489, -0.021274928003549576, 0.020281828939914703, 0.06112596392631531, 0.03657381981611252, -0.0505853146314621, 0.03115382231771946, -0.007960221730172634, 0.038426704704761505, 0.010677636601030827, 0.047779157757759094, 0.02830272540450096, -0.006155762821435928, -0.00544143607839942, -0.0030251292046159506, -0.019488228484988213, 0.05700920149683952, 0.03377499431371689, -0.003161749104037881, 0.04647548496723175, -0.030909962952136993, -0.04390660300850868, -0.046908434480428696, -0.034904394298791885, -0.057464588433504105, -0.004924111533910036, -0.03175107762217522, -0.04949195683002472, -6.116575019250368e-33, -0.007399692665785551, -0.009332436136901379, 0.013077841140329838, -0.028840521350502968, -0.029933877289295197, -0.030981987714767456, -0.0033524620812386274, -0.039562348276376724, 0.016943074762821198, 0.005347159691154957, -0.0018918925197795033, -0.012423299252986908, 0.011462326161563396, 0.04995924234390259, -0.00032884610118344426, -0.027867421507835388, 0.04296232759952545, 0.00970656331628561, -0.012647522613406181, 0.02535676583647728, 0.011822550557553768, 0.027991408482193947, 0.07523483783006668, -0.05435485020279884, -0.05233587324619293, 0.05092233046889305, -0.03269168362021446, -0.02093910425901413, -0.0040231249295175076, 0.023778358474373817, -0.007643443997949362, -0.015404409728944302, 0.0038141959812492132, -0.05622663348913193, -0.03149844706058502, -0.019049135968089104, -0.07051033526659012, -0.039910975843667984, -0.0660306066274643, 0.014836182817816734, -0.10340965539216995, -0.042588409036397934, 0.03913060203194618, 0.011083361692726612, -0.024154145270586014, 0.0002332952426513657, 0.05791002884507179, -0.024840515106916428, -0.011066202074289322, 0.01332863885909319, -0.027906235307455063, 0.020388862118124962, -0.011932484805583954, -0.048863962292671204, 0.0030896656680852175, 0.032305289059877396, -0.008236066438257694, -0.008451756089925766, -0.020395299419760704, 0.04181240126490593, 0.04043960198760033, 0.03414588049054146, 0.00906325038522482, 0.07424721866846085, 0.06922799348831177, 0.041487887501716614, 0.01260286383330822, -0.03755216300487518, -0.02196837216615677, -0.0301935076713562, -0.004372626077383757, 0.050983041524887085, 0.009493659250438213, 0.018998004496097565, 0.06236859783530235, -0.01448381319642067, -0.03936478868126869, 0.06021518260240555, -0.018451156094670296, 0.07220599800348282, -0.04814046993851662, 0.01585913635790348, -0.006545216776430607, 0.0026418501511216164, 0.020119093358516693, -0.018800871446728706, 0.02438223734498024, -0.056202519685029984, 0.029113993048667908, 0.008463879115879536, -0.017743127420544624, 0.0010564171243458986, 0.037652529776096344, -0.051070135086774826, 0.0429147407412529, 0.029741037636995316, -0.003513585776090622, 0.017038296908140182, 0.02190277725458145, 0.015798427164554596, -0.007281930651515722, -0.014985326677560806, 0.00040954098221845925, 0.017726976424455643, -0.018111862242221832, 0.03560682013630867, -0.04459119588136673, 0.07050073891878128, -0.0056777819991111755, 0.012607209384441376, 0.0024258452467620373, 0.004382023587822914, 0.025620728731155396, -0.0028881097678095102, 0.03061475045979023, -0.08696093410253525, 0.005016328766942024, 0.06288174539804459, 0.0010506954276934266, -0.03606732189655304, -0.018886564299464226, -0.010790341533720493, -0.02791430801153183, 0.04575086012482643, -0.04755236580967903, -0.008257472887635231, -0.10151490569114685, -0.032200027257204056, -0.047103650867938995, -0.07909578830003738, 0.0009633189183659852, 0.006280569359660149, 2.983838669479155e-07, -0.06877218931913376, 0.00104086147621274, 0.01494218036532402, -0.03346308693289757, 0.012979762628674507, 0.03848941624164581, -0.017720002681016922, 0.021125096827745438, -0.03608999773859978, -0.030273552983999252, 0.021456753835082054, -0.031081944704055786, 0.0018302053213119507, -0.017526648938655853, -0.024532584473490715, 0.02051239088177681, -0.0476859025657177, 0.060500700026750565, -0.010021750815212727, -0.008728238753974438, 0.021590426564216614, 0.0585731640458107, 0.030428851023316383, -0.015107459388673306, 0.07092823833227158, 0.03908917307853699, 0.009078320115804672, 0.002355678007006645, 0.034842558205127716, -0.035219307988882065, -0.03383700177073479, 0.05054154992103577, -0.017855843529105186, -0.052901070564985275, -0.029407259076833725, 0.016742145642638206, -0.012870298698544502, 0.03029562719166279, -0.012120548635721207, -0.04442821070551872, 0.03452768921852112, 0.02832077071070671, 0.06953912228345871, -0.01826212741434574, 0.040239494293928146, -0.005876709707081318, -0.012340154498815536, 0.004422420635819435, -0.01676350086927414, 0.01979774422943592, -0.002486360725015402, -0.00034665927523747087, -0.07399626076221466, -0.057515546679496765, 0.009418676607310772, 0.0371801033616066, -0.01986483298242092, -0.04098118841648102, 0.037170980125665665, 0.021814385429024696, -0.0006268799188546836, -0.0007391007384285331, -0.05482114851474762, 0.010860037058591843, 0.011736677959561348, -0.03780955448746681, -0.05237329751253128, 2.6268340630993716e-34, -0.008695295080542564, -0.02122657746076584, -0.023152705281972885, -0.051441553980112076, -0.025479834526777267, 0.034168630838394165, 0.04770468547940254, 0.016575096175074577, 0.05042747035622597, 0.045267291367053986, -0.02766563557088375]

['Yan Duan', 'John Schulman', 'Xi Chen', 'Peter L. Bartlett', 'Ilya Sutskever', 'Pieter Abbeel']

1611.02779v2

Deep reinforcement learning (deep RL) has been successful in learning sophisticated behaviors automatically; however, the learning process requires a huge number of trials. In contrast, animals can learn new tasks in just a few trials, benefiting from their prior knowledge about the world. This paper seeks to bridge this gap. Rather than designing a "fast" reinforcement learning algorithm, we propose to represent it as a recurrent neural network (RNN) and learn it from data. In our proposed method, RL$^2$, the algorithm is encoded in the weights of the RNN, which are learned slowly through a general-purpose ("slow") RL algorithm. The RNN receives all information a typical RL algorithm would receive, including observations, actions, rewards, and termination flags; and it retains its state across episodes in a given Markov Decision Process (MDP). The activations of the RNN store the state of the "fast" RL algorithm on the current (previously unseen) MDP. We evaluate RL$^2$ experimentally on both small-scale and large-scale problems. On the small-scale side, we train it to solve randomly generated multi-arm bandit problems and finite MDPs. After RL$^2$ is trained, its performance on new MDPs is close to human-designed algorithms with optimality guarantees. On the large-scale side, we test RL$^2$ on a vision-based navigation task and show that it scales up to high-dimensional problems.

RL$^2$: Fast Reinforcement Learning via Slow Reinforcement Learning

http://arxiv.org/pdf/1611.02779v2

Title RL2 Fast Reinforcement Learning via Slow Reinforcement Learning Summary Deep reinforcement learning deep RL successful learning sophisticated behavior automatically however learning process requires huge number trial contrast animal learn new task trial benefiting prior knowledge world paper seek bridge gap Rather designing fast reinforcement learning algorithm propose represent recurrent neural network RNN learn data proposed method RL2 algorithm encoded weight RNN learned slowly generalpurpose slow RL algorithm RNN receives information typical RL algorithm would receive including observation action reward termination flag retains state across episode given Markov Decision Process MDP activation RNN store state fast RL algorithm current previously unseen MDP evaluate RL2 experimentally smallscale largescale problem smallscale side train solve randomly generated multiarm bandit problem finite MDPs RL2 trained performance new MDPs close humandesigned algorithm optimality guarantee largescale side test RL2 visionbased navigation task show scale highdimensional problem Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.029053961858153343, 0.031220439821481705, -0.022526610642671585, -0.0188052449375391, -0.01906392350792885, 0.006721537094563246, 0.002386258915066719, -0.00878199189901352, -0.03018711879849434, -0.015467081218957901, 0.002808040240779519, 0.021843677386641502, -0.016497164964675903, 0.053887419402599335, 0.006730447523295879, -0.04560660570859909, 0.009557917714118958, -0.03789766505360603, 0.023760545998811722, -0.005118596833199263, 0.03208036720752716, -0.03502489998936653, -0.0030981642194092274, 0.011894676834344864, 0.005708360578864813, 0.048478398472070694, -0.03227238357067108, -0.015051146037876606, 0.009101251140236855, -0.12710829079151154, 0.04228318855166435, -0.019626179710030556, 0.07199768722057343, 0.0863412618637085, 2.2924393761059036e-06, -0.02816002257168293, -0.013216649182140827, -0.03302790969610214, 0.045890357345342636, -0.052834492176771164, 0.03437343239784241, -0.006659218110144138, -0.010536745190620422, 0.017056316137313843, -0.030908280983567238, -0.06957236677408218, 0.030214011669158936, 0.08213959634304047, -0.01394625660032034, 0.06790001690387726, 0.003852994181215763, -0.04858553409576416, -0.0001785151252988726, -0.03920185938477516, 0.060743845999240875, -0.021037952974438667, 0.014079872518777847, 0.008964836597442627, -0.019173717126250267, -0.04016774892807007, -0.02518194355070591, 0.007159384898841381, 0.02476184070110321, 0.002195073291659355, 0.0007294971728697419, 0.054068855941295624, 0.031089767813682556, -0.027915798127651215, -0.010251788422465324, 0.02988317608833313, -0.09129275381565094, 0.01318078488111496, 0.030879169702529907, -0.00888663437217474, -0.02404201030731201, -0.0785844698548317, -0.0033534022513777018, 0.04514197260141373, -0.025757938623428345, 0.010630201548337936, -0.0162394680082798, 0.018454736098647118, 0.013851293362677097, -0.018021466210484505, 0.009450127370655537, 0.01654943823814392, -0.004152119159698486, -0.0004742991295643151, -0.007706265430897474, -0.005625543184578419, 0.03487849235534668, -0.008144129998981953, -0.024576187133789062, 0.02222881279885769, -0.05921725928783417, 0.005070020444691181, -0.0006275385385379195, -0.011412661522626877, 0.024410990998148918, -0.02441842295229435, 0.05672256276011467, -0.052812110632658005, 0.019746635109186172, 0.018927711993455887, -0.029056455940008163, 0.04303986206650734, -0.05906762555241585, 0.047425542026758194, -0.0029490815941244364, 0.00931468978524208, -0.026611533015966415, 0.03115585260093212, -0.04245889559388161, 0.055227477103471756, 0.015232241712510586, -0.031009098514914513, -0.05966061353683472, -0.020153362303972244, -0.02438145875930786, -0.025259021669626236, -0.025540009140968323, 0.043876055628061295, -0.01781175471842289, 0.02613571286201477, -0.06821636110544205, 0.007710506673902273, -0.04469519481062889, 0.01864110305905342, 0.0023092220071703196, 0.023864340037107468, 0.03337908163666725, -0.0002803271927405149, -0.01189225260168314, 0.005219799466431141, 0.012498844414949417, 0.10515312850475311, 0.004504276439547539, 0.01706722564995289, -0.05343438684940338, -0.0003268359287176281, 0.04309264197945595, -0.03827419504523277, 0.022018153220415115, -0.10360009968280792, 0.02296573668718338, -0.04314735159277916, -0.04082506522536278, 0.044123630970716476, 0.01630556769669056, 0.0029515514615923166, -0.037267930805683136, 0.07030594348907471, -0.008120614103972912, -0.0013727850746363401, 0.023471269756555557, -0.029824240133166313, 0.014683879911899567, 0.04141128063201904, 0.04710192605853081, 0.008330649696290493, -0.01191973127424717, 0.021387699991464615, 0.006095855496823788, -0.008964985609054565, -0.010838834568858147, -0.01612747088074684, -0.013142413459718227, -0.04662969708442688, 0.0354347862303257, 0.07476358860731125, 0.02156681753695011, 0.004381506238132715, -0.03927689045667648, 0.00439101830124855, 0.03920387849211693, 0.0168084055185318, 0.06623134762048721, 0.006958301644772291, 0.012310216203331947, -0.017494024708867073, -0.03827836364507675, -0.03755266219377518, -0.01786334440112114, 0.07160741090774536, -0.035710472613573074, -0.02486397512257099, -0.05385218560695648, 0.01348775066435337, -0.032514538615942, -0.03159162774682045, 0.0596357136964798, -0.028403371572494507, 0.02716928720474243, -0.011499833315610886, 0.04632602259516716, -0.0018359418027102947, -0.04166946932673454, -0.11415749788284302, 0.03671348839998245, 0.07702638953924179, -0.05836344510316849, -0.03511035442352295, 0.04605827108025551, -0.039582423865795135, 0.015502448193728924, -0.02297106571495533, -0.01994149386882782, -0.05532101169228554, 0.00249609281308949, -0.011931635439395905, 0.040484342724084854, -0.007796106860041618, 0.021465249359607697, -0.03388148546218872, -0.023155810311436653, 0.02963259443640709, -0.04443930834531784, 0.06812233477830887, 0.01747017912566662, 0.05928484722971916, -0.02252316288650036, 0.07477162778377533, -0.021609017625451088, 0.019544411450624466, -0.010613295249640942, -0.028825001791119576, 0.055781662464141846, 0.007450842298567295, 0.0198352113366127, -0.06086157634854317, 0.007946349680423737, -0.021687978878617287, 0.013888468034565449, -0.013941946439445019, 0.00015877683472353965, -0.026721132919192314, -0.04812989756464958, -0.013660901226103306, 0.0004234286898281425, -0.019209792837500572, 0.031750842928886414, 0.05072503909468651, -0.0064533781260252, -0.029303675517439842, -0.034664690494537354, -0.009040534496307373, -0.01732109673321247, 0.01622687838971615, -0.018558021634817123, 0.023524809628725052, 0.020361701026558876, -0.05863731727004051, 0.017893031239509583, -0.0022392922546714544, 0.024637440219521523, -0.014414310455322266, 0.002823582850396633, -0.003711127210408449, -0.04451298341155052, -0.026006458327174187, 0.011926048435270786, -0.009705034084618092, -0.005722974427044392, 0.04060262814164162, 0.07465559244155884, 0.019934726879000664, -0.000354551273630932, 0.03092123195528984, -0.0006857208791188896, -0.01201329194009304, -0.03712797909975052, -0.014975357800722122, -0.022143999114632607, 0.008151332847774029, -0.022767258808016777, -0.04659975692629814, 0.06310614198446274, 0.040923990309238434, -0.024120282381772995, 0.04495038464665413, 0.03543943166732788, -0.015860410407185555, -0.020057663321495056, -0.032359689474105835, 0.016899071633815765, -0.026797045022249222, 0.05060514062643051, -0.008021238259971142, -0.03625059127807617, -0.05978958308696747, -0.0011927330633625388, 0.047765687108039856, -0.005103142000734806, -0.061863694339990616, -0.0020780470222234726, -0.046289294958114624, -0.0018757781945168972, 0.06601206958293915, 0.043485578149557114, 0.029370266944169998, 0.023403432220220566, 0.03500901162624359, -0.03547987341880798, 0.04312506318092346, -0.040301207453012466, -0.05664733424782753, -0.03781571611762047, 0.006659660022705793, 0.00454431539401412, 0.03629394993185997, -0.024022439494729042, 0.06568388640880585, -0.023931797593832016, 0.0027452120557427406, 0.03467269614338875, -0.07992452383041382, -0.028018878772854805, 0.04682072997093201, -0.03027929924428463, -0.004968817345798016, 0.002089932793751359, -0.018220016732811928, 0.04977524280548096, 0.06888405978679657, -0.010153386741876602, -0.0159575454890728, -0.034357551485300064, 0.017250986769795418, -3.676084088510834e-05, 0.03925637900829315, 0.04635336995124817, -0.027968507260084152, -0.011852029711008072, -0.01593945547938347, -0.020116765052080154, 0.0022476487793028355, -0.011270075105130672, 0.007212400436401367, 0.016379360109567642, -0.00875485222786665, -0.03333767130970955, -0.04532730579376221, -0.051607608795166016, 0.04732232913374901, -0.01766148768365383, -0.01630663126707077, -0.024985171854496002, -0.028605418279767036, -0.058589667081832886, 0.002785127144306898, 0.05173557996749878, 0.011007923632860184, -0.047959618270397186, -0.02732061594724655, -0.01046556793153286, 0.02594848908483982, 0.0927073210477829, 0.008850298821926117, 0.024387668818235397, -0.008698701858520508, 0.082037553191185, 0.021428585052490234, 0.048657309263944626, 0.02246282622218132, -0.09409067034721375, 0.044330038130283356, -0.007651404943317175, -0.011135198175907135, 0.0006742214900441468, 0.0451127327978611, -0.004235014785081148, -0.06402573734521866, -0.01723613403737545, 0.05334959179162979, -0.02216879464685917, -0.07619323581457138, -0.03500617668032646, -0.026000017300248146, 0.034528207033872604, 0.023684049025177956, 0.06558313965797424, -0.010676510632038116, -0.013331437483429909, -0.019461361691355705, 0.021137641742825508, -0.021508723497390747, -0.03572217375040054, 0.03414003551006317, -0.09494690597057343, 0.027866482734680176, -0.028187837451696396, -0.09748145937919617, -0.06164525821805, -0.0038489808794111013, -0.029194524511694908, -0.013453317806124687, -0.043176837265491486, 0.06719733774662018, -0.014464443549513817, -0.028809351846575737, 0.026116278022527695, -0.013864102773368359, 0.06509699672460556, 0.04471680894494057, -0.0721365436911583, 0.032309964299201965, 0.049138572067022324, 0.004362283740192652, -0.04883331060409546, -0.03720004856586456, -0.02581905387341976, 0.03114894963800907, 0.007772531826049089, -0.024430129677057266, 0.031160123646259308, 0.018580272793769836, -0.032513413578271866, -0.017109254375100136, 0.04955339431762695, 0.01622728258371353, 0.02880714274942875, 0.02326119691133499, 0.041804540902376175, -0.009828906506299973, -0.009155812673270702, -0.03080972284078598, -0.0073548369109630585, 0.031980711966753006, -0.01600462570786476, -0.05006961151957512, -0.041256412863731384, -0.07685358822345734, 0.017283814027905464, -0.013766526244580746, -0.06935382634401321, -0.017353525385260582, -0.016654115170240402, 0.017002282664179802, 0.002392339985817671, -0.07539522647857666, -0.03924621269106865, -0.01848573423922062, 0.09548076242208481, -0.00474330922588706, 0.011073858477175236, 0.017551245167851448, 0.028063541278243065, -0.039501793682575226, -0.025323549285531044, -0.019383760169148445, 0.013287780806422234, -0.05079181119799614, 0.024345921352505684, 0.0038246256299316883, -0.01794784516096115, -0.00822541769593954, -0.031939003616571426, -0.0546988770365715, -0.028683461248874664, 0.010304517112672329, 0.08440516889095306, -0.0001333752879872918, 0.05212239548563957, -0.03524261340498924, 0.0045923409052193165, 0.03775801882147789, -0.030523354187607765, 0.028717586770653725, 0.011231405660510063, 0.0224568173289299, 0.014531521126627922, -0.014907638542354107, 0.023743370547890663, -0.04405781626701355, 0.025262387469410896, -0.021259376779198647, -0.0031663088593631983, -0.018209310248494148, 0.009263969957828522, 0.00026856950717046857, -0.029848909005522728, 0.07510171830654144, 0.04450248181819916, -0.010390336625277996, -0.022944655269384384, 0.019012343138456345, 0.020713115110993385, 0.0047953627072274685, -0.05230022966861725, 0.008961197920143604, 0.012037609703838825, 0.07051938027143478, 0.021472156047821045, -0.04450428858399391, 0.08542963117361069, -0.05212394893169403, -0.0233317781239748, 0.014895569533109665, 0.03925517573952675, 0.056299176067113876, -0.03705037012696266, 0.043446313589811325, 0.018483158200979233, 0.03604232519865036, 0.027595000341534615, 0.04247959330677986, -0.009154889732599258, 0.036735761910676956, 0.05491282790899277, 0.026243751868605614, -0.04127678647637367, -0.012248384766280651, 0.016905808821320534, -0.08164386451244354, -0.0014251128304749727, 0.05132671073079109, 0.05610783398151398, -0.014253349974751472, -0.015187234617769718, -0.021944181993603706, 0.03063197433948517, -0.03795488923788071, 0.0029461178928613663, -0.07191520929336548, 0.012973735108971596, 0.04378306865692139, 0.0284558292478323, -0.004290890879929066, 0.02356981672346592, 0.04333794489502907, 0.03911444917321205, 0.014970688149333, 0.005655799061059952, 0.02361331693828106, 0.006749690044671297, 0.014837677590548992, 0.042612407356500626, 0.041716381907463074, 0.000602543877903372, -0.02271774224936962, 0.014653104357421398, -0.0020052928011864424, 0.009724872186779976, 0.03150947764515877, 0.040258850902318954, -0.03532281145453453, 0.06130150705575943, -0.012027519755065441, 0.0009645006502978504, 0.011996529065072536, -0.03036651201546192, -0.047955505549907684, 0.010349918156862259, -0.020265718922019005, -0.040332552045583725, -6.454591725907179e-33, 0.036832768470048904, -0.007887589745223522, 0.011986895464360714, -0.06381965428590775, -0.051155611872673035, 0.0014864843105897307, 0.004132186062633991, -0.025899460539221764, -0.003027866827324033, 0.008323375135660172, -0.0019938391633331776, -0.0413939394056797, -0.004519232548773289, 0.02314009517431259, 0.05102567747235298, -0.00728618772700429, -0.007716016378253698, 0.006218690425157547, 0.011016515083611012, 0.0033296544570475817, 0.034491900354623795, 0.03122108429670334, 0.014606621116399765, -0.04256811738014221, -0.0647556260228157, 0.026408856734633446, 0.0009563590283505619, -0.012440292164683342, -0.06487467139959335, 0.05290817841887474, 0.00879456102848053, -0.0137070557102561, 0.0020761697087436914, -0.06979242712259293, -0.023870712146162987, 0.0035653410013765097, -0.09358645230531693, -0.05893664062023163, -0.05442783236503601, 0.021564707159996033, -0.06962063908576965, 0.04162667691707611, 0.07542944699525833, -0.001723859109915793, -0.0011441025417298079, 0.025411155074834824, 0.05229170247912407, -0.006846735253930092, -0.004287043586373329, -0.019486723467707634, -0.03849614039063454, 3.122313501080498e-05, 0.02816224843263626, -0.02015995979309082, 0.027036167681217194, -0.01219907682389021, -0.019947439432144165, -0.004643292631953955, -0.018677206709980965, -0.014731897972524166, -0.005611617583781481, 0.023143460974097252, -0.02015717141330242, 0.08451928198337555, 0.05996249243617058, 0.0323491245508194, 0.0008879499509930611, -0.011302764527499676, 0.032994434237480164, 0.006160686258226633, 0.011069070547819138, 0.0416613332927227, 0.03926840424537659, 0.0062463111244142056, 0.09010385721921921, -0.0403449721634388, -0.04805298522114754, 0.008717143908143044, 0.02836093120276928, 0.06641107052564621, 0.015352156013250351, -0.00873490422964096, -0.022583475336432457, 0.024693600833415985, -0.007700882852077484, 0.024480219930410385, -0.021526696160435677, -0.049417998641729355, 0.030029332265257835, 0.035668302327394485, 0.027273083105683327, -0.010550781153142452, 0.02368401549756527, -0.003289366839453578, 0.02360006608068943, -0.019010160118341446, 0.018986158072948456, 0.01428196020424366, 0.004790049511939287, -0.010159536264836788, -0.043729666620492935, -0.024400152266025543, -0.01348230428993702, -0.03603748232126236, -0.02837442047894001, 0.047604721039533615, -0.00022969637939240783, 0.014883107505738735, -0.01654778979718685, 0.0008649292285554111, -0.009998294524848461, 0.01880788803100586, 0.034905701875686646, 0.012634914368391037, 0.04223494976758957, -0.05344786494970322, -0.002399496268481016, 0.0564759187400341, -0.0075410595163702965, -0.08662743866443634, -0.04931355640292168, 0.007139279041439295, -0.022357342764735222, 0.03225558623671532, -0.05506587401032448, -0.00340731767937541, -0.09407510608434677, -0.003177463077008724, -0.03682290390133858, -0.07824092358350754, 0.005441893823444843, 0.0179530568420887, 2.973002324324625e-07, -0.10515907406806946, 0.018206899985671043, 0.0434182807803154, -0.012759401462972164, 0.013205226510763168, 0.03237353637814522, -0.0035476412158459425, 0.028223270550370216, -0.012225055135786533, 0.034713856875896454, 0.0268443264067173, 0.008598042652010918, -0.024851009249687195, -0.01843571476638317, -0.03230385482311249, -0.00995283480733633, -0.026501726359128952, 0.03934387117624283, -0.023522228002548218, -0.019458875060081482, -0.036197811365127563, 0.09437549114227295, 0.06005774438381195, -0.02973807416856289, 0.0784006267786026, -0.005042816046625376, -0.0008143680752255023, -0.003119812812656164, 0.027999432757496834, -0.03543674945831299, 0.008070003241300583, 0.07176170498132706, -0.029835548251867294, -0.025715980678796768, 0.003733633551746607, 0.033544644713401794, -0.0492871068418026, 0.021993979811668396, -0.0154452845454216, -0.023377619683742523, 0.025221996009349823, 0.04587852582335472, 0.01886976882815361, -0.0018890652572736144, 0.04642585664987564, -0.049921996891498566, -0.004487424157559872, -0.009295732714235783, 0.021176567301154137, -0.004857144318521023, 0.020034540444612503, 0.0036822969559580088, -0.0297206100076437, -0.018455011770129204, 0.008317050524055958, -0.0013567948481068015, -0.003981288522481918, -0.05829010531306267, 0.0461653433740139, 0.055990006774663925, 0.004878549370914698, 0.008205260150134563, -0.06314097344875336, 0.0557045042514801, 0.05722898244857788, -0.037264902144670486, -0.04365478828549385, 2.5874194160920638e-34, 0.00661951070651412, -0.028430098667740822, -0.031477149575948715, -0.03095504827797413, -0.0010068946285173297, 0.032294996082782745, -0.0020240426529198885, 0.034211404621601105, 0.05053466930985451, -0.0036501113791018724, -0.04401741549372673]

['Jasmine Collins', 'Jascha Sohl-Dickstein', 'David Sussillo']

1611.09913v3

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show experimentally that all common RNN architectures achieve nearly the same per-task and per-unit capacity bounds with careful training, for a variety of tasks and stacking depths. They can store an amount of task information which is linear in the number of parameters, and is approximately 5 bits per parameter. They can additionally store approximately one real number from their input history per hidden unit. We further find that for several tasks it is the per-task parameter capacity bound that determines performance. These results suggest that many previous results comparing RNN architectures are driven primarily by differences in training effectiveness, rather than differences in capacity. Supporting this observation, we compare training difficulty for several architectures, and show that vanilla RNNs are far more difficult to train, yet have slightly higher capacity. Finally, we propose two novel RNN architectures, one of which is easier to train than the LSTM or GRU for deeply stacked architectures.

Capacity and Trainability in Recurrent Neural Networks

http://arxiv.org/pdf/1611.09913v3

Title Capacity Trainability Recurrent Neural Networks Summary Two potential bottleneck expressiveness recurrent neural network RNNs ability store information task parameter store information input history unit show experimentally common RNN architecture achieve nearly pertask perunit capacity bound careful training variety task stacking depth store amount task information linear number parameter approximately 5 bit per parameter additionally store approximately one real number input history per hidden unit find several task pertask parameter capacity bound determines performance result suggest many previous result comparing RNN architecture driven primarily difference training effectiveness rather difference capacity Supporting observation compare training difficulty several architecture show vanilla RNNs far difficult train yet slightly higher capacity Finally propose two novel RNN architecture one easier train LSTM GRU deeply stacked architecture Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.023925350978970528, 0.01983645185828209, 0.009100564755499363, 0.0378272607922554, -0.008427752181887627, -0.021360011771321297, 0.03861137479543686, -0.03598586469888687, -0.02964172326028347, -0.004948351997882128, -0.04585633799433708, -0.05377557873725891, 0.015707507729530334, 0.03036889061331749, 0.012821054086089134, -0.04432181641459465, 3.991636185673997e-05, -0.010548589751124382, -0.005835017189383507, 0.019864123314619064, 0.01696617901325226, -0.01176907867193222, -0.01016823947429657, 0.03667234629392624, -0.005910028237849474, 0.011288205161690712, -0.011140765622258186, -0.018859948962926865, -0.01346325408667326, -0.08410169929265976, 0.028691213577985764, 0.0028672651387751102, 0.05753078684210777, 0.04242873936891556, 2.214226014984888e-06, 0.0040902006439864635, 0.009357687085866928, -0.04036986082792282, -0.030046500265598297, 0.016388731077313423, 0.03364788740873337, -0.014599191024899483, -0.003061328548938036, 0.03830645605921745, -0.007661545183509588, -0.02445870079100132, 0.034088876098394394, 0.07710036635398865, 0.008478393778204918, 0.08384755998849869, 0.004787765443325043, -0.053547732532024384, 0.04120321571826935, -0.07556556910276413, -0.0022030379623174667, -0.030763745307922363, 0.003813758259639144, -0.026196051388978958, 0.025435075163841248, -0.016205957159399986, 0.00434705289080739, 0.021372107788920403, 0.05923961102962494, 0.005379344802349806, 0.001686401548795402, 0.037194229662418365, 0.038342367857694626, 0.012463539838790894, -0.013253942131996155, 0.0295750480145216, -0.04542116820812225, 0.038958143442869186, -0.009852636605501175, -0.01845267228782177, -0.044160787016153336, -0.05899829417467117, -0.022809365764260292, 0.023866066709160805, -0.006471254397183657, 0.021137390285730362, -0.0345635786652565, 0.053020551800727844, 0.06857217848300934, 0.012468031607568264, 0.00691591901704669, -0.0037644768599420786, -0.005664375144988298, -0.010157023556530476, -0.010819579474627972, -0.05070023238658905, 0.016456641256809235, -0.02727224864065647, 0.011937621980905533, 0.04549963399767876, -0.006691576447337866, 0.007470111828297377, -0.01996520347893238, -0.0698389932513237, 0.02150726690888405, -0.04922383278608322, 0.06291592121124268, -0.00481386249884963, -0.012857657857239246, -0.0036347205750644207, -0.022046690806746483, 0.08107443153858185, -0.06659351289272308, -0.02475026808679104, -0.0231174286454916, 0.013238185085356236, -0.03664466366171837, -0.0021476633846759796, -0.02958698198199272, 0.040247078984975815, -0.008519187569618225, -0.009857370518147945, -0.07868005335330963, 0.013914084061980247, -0.028211703523993492, -0.010420572943985462, 0.0134433563798666, 0.022649569436907768, -0.051151975989341736, 0.025115232914686203, -0.018211599439382553, -0.0020765464287251234, -0.027794281020760536, 0.024120530113577843, 0.02204836718738079, -0.05826406925916672, 0.004066849127411842, 0.021474631503224373, 0.015734078362584114, -0.023133868351578712, -0.011513905599713326, 0.038767021149396896, 0.033701054751873016, 0.0165693536400795, -0.057075805962085724, 0.007934295572340488, -0.00743759423494339, -0.07445075362920761, 0.003921126946806908, -0.05167684704065323, 0.03398437425494194, -0.0508827269077301, -0.027345972135663033, 0.015340954065322876, 0.017188776284456253, 0.02536432258784771, -0.012189316563308239, 0.04039386659860611, 0.019759442657232285, -0.04962918162345886, 0.055401142686605453, 0.010343446396291256, -0.006029120180755854, 0.02833903580904007, 0.04821363463997841, 0.08473561704158783, -0.01643771305680275, -0.012084518559277058, 0.0056941919028759, 0.00021508079953491688, 0.010812482796609402, -0.02019719034433365, -0.015076873824000359, -0.01856973022222519, 0.004830310586839914, 0.06502536684274673, 0.018436362966895103, 0.035071924328804016, -0.005342639517039061, -0.044090647250413895, 0.01063352171331644, 0.038188736885786057, 0.052259091287851334, 0.08297619968652725, 0.03224732726812363, -0.029771778732538223, 0.025125300511717796, -0.03400552645325661, -0.029914379119873047, 0.06198985502123833, 0.00634894659742713, -0.004713964182883501, -0.013484781607985497, -0.02055852673947811, -0.05045664310455322, -0.026770897209644318, -0.00811023823916912, -0.037091076374053955, 0.008793159388005733, -0.04967893287539482, 0.05113062635064125, 0.0031661393586546183, -0.058787908405065536, 0.011294766329228878, -0.005702565889805555, -0.017084676772356033, -0.0019039695616811514, -0.006226898171007633, -0.002544197952374816, 0.016200529411435127, 0.011633752845227718, -0.0209480132907629, -0.017307542264461517, -0.00955494400113821, -0.023342562839388847, 0.014755899086594582, 0.01526216883212328, 0.02166694961488247, 0.053906314074993134, -0.05140659958124161, 0.01133874710649252, -0.024864748120307922, -0.0293500367552042, 0.07327351719141006, -0.050751134753227234, 0.03771112114191055, 0.03300991654396057, 0.016135497018694878, -0.05460374429821968, 0.02013186551630497, -0.045761413872241974, -0.025586185976862907, 0.026017289608716965, 0.043077174574136734, 0.029124658554792404, -0.002186007099226117, 0.021817002445459366, 0.0016985738184303045, 0.03382529690861702, -0.06388332694768906, -0.006367838010191917, -0.033413246273994446, -0.11693280190229416, 0.007800658233463764, 0.0009052780806086957, 0.04887068644165993, 0.03903096914291382, 0.05733558163046837, -0.03496319055557251, -0.06841991096735, 0.07109259814023972, -0.04685052111744881, 0.023216644302010536, -0.03693888336420059, -0.0027380739338696003, 0.03046581894159317, 0.014277339912950993, 0.02621169574558735, 0.03226838633418083, -0.03823672607541084, 0.014987644739449024, -0.008220035582780838, -0.0014901201939210296, 0.017765803262591362, -0.038686178624629974, -0.03768115118145943, -0.010981987230479717, -0.04542476683855057, 0.004300727043300867, -0.012428157962858677, -0.007923543453216553, -0.005079658702015877, -0.04312065988779068, -0.03298821672797203, 0.031504206359386444, -0.022073917090892792, 0.018039055168628693, -0.02895398624241352, 0.014631303027272224, 0.03957757726311684, -0.03129835054278374, -0.06678018718957901, 0.04502379521727562, -0.03230167180299759, 0.009396391920745373, 0.045224592089653015, 0.08518613874912262, -0.02093745768070221, -0.029058368876576424, -0.02595406025648117, 0.023495711386203766, 0.00923573412001133, 0.026707349345088005, -0.04692265763878822, 0.02587743103504181, -0.008965179324150085, 0.013301355764269829, 0.04066798463463783, -0.023452090099453926, -0.09077169746160507, 0.00010606484283925965, -0.026785995811223984, 0.043851952999830246, 0.03745221346616745, 0.019498584792017937, -0.012762634083628654, 0.020408056676387787, 0.03299405798316002, 0.0012938836589455605, 0.03843759000301361, -0.013476941734552383, -0.013704929500818253, 0.007134344428777695, 0.02684013731777668, -0.017476432025432587, 0.06283706426620483, -0.010533032938838005, 0.046924203634262085, -0.01903463900089264, -0.008002635091543198, 0.01132325828075409, -0.0077217272482812405, -0.008908027783036232, -0.013973013497889042, -0.012070290744304657, -0.021148690953850746, -0.015048264525830746, -0.01788075640797615, -0.010791059583425522, 0.010187763720750809, 0.0020286140497773886, -0.0001886667450889945, -0.04940740019083023, -0.01939174346625805, 0.04205603897571564, 0.035829734057188034, -0.002171694068238139, 0.020218659192323685, -0.03978990763425827, -0.004316835198551416, -0.005478298757225275, -0.01745755784213543, 0.000189937578397803, 0.01156210619956255, -0.013994152657687664, -0.0091415299102664, -0.06720136106014252, -0.06291086971759796, -0.038427744060754776, 0.001434468780644238, 0.0037377297412604094, 0.019123200327157974, -0.009290759451687336, -0.04070550575852394, 0.009698607958853245, 0.001180281862616539, 0.016053570434451103, 0.054855093359947205, -0.007889844477176666, -0.006902660243213177, 0.004516777582466602, 0.008008119650185108, 0.010998034849762917, 0.04768531024456024, -0.011187934316694736, 0.04380915313959122, 0.012615014798939228, 0.0313003808259964, 0.006692382972687483, 0.02399391122162342, -0.12079500406980515, -0.013678493909537792, -0.014447399415075779, -0.012627680785953999, -0.004215043969452381, 0.032601792365312576, 0.032211270183324814, -0.10605907440185547, 0.006754582282155752, 0.06557069718837738, -0.031785670667886734, -0.04701340198516846, -0.011678720824420452, 0.04297124966979027, -0.023221397772431374, 0.009705232456326485, 0.007503347471356392, -0.02423829771578312, 0.01233617402613163, -0.0038864596281200647, 0.01340724341571331, -0.03674305975437164, -0.0620737224817276, -0.01689990796148777, -0.09277763962745667, 0.00980458501726389, -0.015196023508906364, -0.04308988153934479, -0.03169030323624611, -0.017673227936029434, -0.02309965156018734, -0.0011970014311373234, 0.001430160948075354, 0.005149432457983494, 0.022086728364229202, -0.028285395354032516, 0.046386681497097015, -0.09318897873163223, -0.004352976102381945, 0.018701618537306786, -0.08211466670036316, 0.006374649703502655, 0.03251431882381439, 0.0261594969779253, -0.031026406213641167, -0.04452763497829437, 0.005828813649713993, 0.003071408485993743, 0.0319691002368927, -0.013544410467147827, 0.036677177995443344, 0.039391133934259415, -0.03820761665701866, -0.010276377201080322, 0.033583059906959534, -0.01654929853975773, 0.029227744787931442, -0.005363977048546076, 0.0648801177740097, 0.02625652216374874, 0.0038014214951545, -0.034648437052965164, -0.009275288321077824, 0.04837533086538315, 0.03384343534708023, 0.03938992694020271, -0.007179155945777893, -0.04067721217870712, 0.03079390525817871, -0.008149061352014542, -0.1266833394765854, 0.017943955957889557, 0.012351183220744133, 0.03325555846095085, -0.03446178883314133, -0.08433323353528976, -0.025106007233262062, -0.03983531892299652, 0.046480532735586166, 0.011238710954785347, 0.0023253934923559427, 0.05308118835091591, 0.012167095206677914, -0.059971000999212265, -0.0012894186656922102, 0.025902964174747467, 0.020467769354581833, -0.05525164306163788, 0.006311553530395031, 0.016303766518831253, -0.0007630801992490888, 0.006600128952413797, -0.060767631977796555, -0.1030275821685791, -0.0034326910972595215, 0.014199821278452873, 0.04134708270430565, 0.0026946880389004946, 0.0035371219273656607, -0.006557495333254337, -0.02654734067618847, 0.024163411930203438, -0.04457790404558182, -0.040405549108982086, 0.006321104709059, 0.06612055003643036, 0.034892525523900986, 0.006459125783294439, 0.025975767523050308, -0.04399169608950615, 0.057684265077114105, 0.004358282312750816, -0.03363005816936493, -0.01440008170902729, 0.0232473686337471, -0.018259314820170403, -0.01777130365371704, 0.03959979489445686, 0.036559026688337326, 0.03372904285788536, -0.031054871156811714, 0.03167860954999924, -0.023862339556217194, 0.046467699110507965, -0.052552781999111176, 0.018048999831080437, 0.05559362471103668, 0.0020235467236489058, 0.012735318392515182, -0.032340157777071, 0.11738836765289307, -0.0389057993888855, -0.008853884413838387, 0.04452555999159813, -0.008443549275398254, 0.02231370471417904, -0.030166855081915855, 0.05489088222384453, -0.05518117547035217, -0.030249016359448433, -0.0010784560581669211, 0.04565024375915527, -0.023846611380577087, 0.051593419164419174, 0.002390150912106037, 0.004406119231134653, -0.004046318586915731, 0.022783691063523293, -0.023134499788284302, -0.02021905779838562, -0.02101968228816986, -0.010036196559667587, 0.0381564125418663, -0.008563786745071411, -0.038118015974760056, -0.01540933083742857, 0.035360146313905716, -0.06134151294827461, 0.039985816925764084, -0.02943607047200203, 0.007007276173681021, 0.0345706045627594, 0.014559172093868256, -0.029151039198040962, 0.007316915784031153, 0.06097371131181717, 0.03831857070326805, 0.02476516179740429, 0.023079484701156616, 0.049941640347242355, -0.017896834760904312, 0.014150569215416908, -0.0268403347581625, 0.023633766919374466, 0.013916551135480404, 0.01121541764587164, -0.008491460233926773, -0.023099955171346664, 0.042285796254873276, -0.0007716037216596305, 0.0531187430024147, -0.022879479452967644, 0.01058129034936428, -0.01833208091557026, 0.02395308017730713, 0.019760414958000183, -0.0033704855013638735, 0.016403835266828537, 0.01360675971955061, 0.01586386002600193, -0.055888596922159195, -6.46372311296116e-33, 0.012807469815015793, 0.019378069788217545, 0.010147521272301674, -0.035421766340732574, -0.03945891186594963, 0.04652653634548187, -0.040728237479925156, -0.04180566966533661, -0.03344999998807907, -0.033279139548540115, -0.019830580800771713, -0.010576019994914532, 0.010262293741106987, 0.04423509165644646, 0.04897303879261017, -0.022438855841755867, 0.04937072843313217, 0.005960025824606419, 0.035720355808734894, 0.010007445700466633, 0.07479120790958405, 0.02634303830564022, 0.05683380737900734, -0.05473489686846733, -0.03575057536363602, -0.01881847344338894, -0.015536005608737469, 0.012315875850617886, 0.007931893691420555, 0.02317172847688198, -0.02848953753709793, 0.017191780731081963, 0.03400103747844696, -0.07209105044603348, -0.026458686217665672, 0.008151018992066383, -0.07431000471115112, -0.08795984089374542, -0.02976171299815178, 0.021320492029190063, -0.08083592355251312, 0.0021360041573643684, 0.06272171437740326, -0.00022638574591837823, -0.004386221524327993, 0.02393091470003128, -0.019871367141604424, -0.016762645915150642, -0.022945735603570938, -0.050977613776922226, -0.00798665452748537, 0.018145479261875153, 0.0065725455060601234, -0.004211003426462412, 0.015113714151084423, -0.011127952486276627, -0.029235277324914932, 0.002356077078729868, -0.12951304018497467, -0.05392630398273468, -0.024468354880809784, 0.06576970219612122, -0.010455294512212276, 0.03850676491856575, 0.018520331010222435, 0.04457501694560051, 0.03957250714302063, 0.027954665943980217, -0.04438897967338562, 0.041112467646598816, -0.024731826037168503, 0.03631085157394409, 0.07425852119922638, -0.0009245173423551023, 0.1376490443944931, -0.05791874974966049, -0.05571303144097328, -0.0006712406175211072, 0.07419677823781967, 0.06862373650074005, 0.006482850760221481, 0.010473786853253841, -0.04017700254917145, -0.0016322042793035507, 0.01003324519842863, 0.02004172094166279, -0.025927355512976646, -0.04406481608748436, 0.029971053823828697, 0.0277022123336792, 0.058202169835567474, 0.019503775984048843, -0.012401032261550426, -0.007634372916072607, 0.05489974841475487, 0.006130116526037455, 0.06163310259580612, 0.015907419845461845, 0.023669779300689697, -0.027827292680740356, -0.05710570141673088, -0.008545937016606331, -0.0011041683610528708, 0.03701993450522423, 0.027465106919407845, 0.03330737724900246, 0.028927667066454887, 0.05189637839794159, -0.023643333464860916, -0.042440835386514664, -0.026418454945087433, 0.03347478806972504, 0.023821646347641945, 0.05664025619626045, 0.04044470563530922, -0.053590018302202225, -0.0027532547246664762, 0.07287922501564026, -0.02755969762802124, -0.018524710088968277, -0.016290398314595222, -0.01941921003162861, 0.046283356845378876, 0.019695010036230087, -0.015580257400870323, -0.025551706552505493, -0.06293460726737976, -0.0024823821149766445, 0.017135560512542725, -0.03324538469314575, -0.0026509100571274757, 0.04362095147371292, 2.8979550847907376e-07, -0.05759330466389656, -0.03560444340109825, 0.05603368580341339, -0.02719568833708763, 0.032788120210170746, 0.016268856823444366, -0.003629721701145172, 0.04301848262548447, -0.04595048725605011, 0.011994678527116776, -0.006919465027749538, -0.010612783953547478, 0.03101545013487339, -0.008075712248682976, -0.08812928199768066, -0.03630534186959267, -0.08223917335271835, 0.04485902190208435, 0.01410671416670084, 0.002369497437030077, 0.04214421287178993, 0.1331900656223297, 0.03481733053922653, -0.016052881255745888, 0.025849567726254463, -0.04700307175517082, -0.0038001681677997112, 0.0024814775679260492, 0.02721676602959633, -0.002492492087185383, 0.012188426218926907, 0.07144498825073242, -0.021919678896665573, -0.03251563385128975, -0.023394891992211342, 0.04510578140616417, -0.03446820378303528, 0.041410189121961594, -0.00686617149040103, -0.059008799493312836, 0.03680884465575218, -0.01162870042026043, 0.013900023885071278, 0.01679271273314953, 0.026101004332304, -0.027269111946225166, -0.04418250173330307, -0.00016842916375026107, 0.038166336715221405, 0.02797774411737919, 0.025034207850694656, -0.004375649616122246, 0.000551025674212724, -0.027106009423732758, -0.008197600021958351, -0.06214257702231407, -0.010854847729206085, -0.08106160163879395, 0.021315673366189003, 0.003240961581468582, -0.022517485544085503, 0.020008163526654243, -0.08650299161672592, -0.019180335104465485, 0.08651316910982132, -0.014732724986970425, -0.01916598714888096, 2.1952745006577487e-34, 0.003971985075622797, -0.04097900167107582, -0.023916006088256836, 0.03456847742199898, -0.001523102866485715, 0.003649431746453047, -0.033925753086805344, 0.010056081227958202, 0.029655946418642998, -0.053448501974344254, -0.052530042827129364]

['Mohammad Taha Bahadori', 'Krzysztof Chalupka', 'Edward Choi', 'Robert Chen', 'Walter F. Stewart', 'Jimeng Sun']

1702.02604v2

In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically study its properties. In a large-scale analysis of Electronic Health Records (EHR), our causally-regularized model outperforms its L1-regularized counterpart in causal accuracy and is competitive in predictive performance. We perform non-linear causality analysis by causally regularizing a special neural network architecture. We also show that the proposed causal regularizer can be used together with neural representation learning algorithms to yield up to 20% improvement over multilayer perceptron in detecting multivariate causation, a situation common in healthcare, where many causal factors should occur simultaneously to have an effect on the target variable.

Causal Regularization

http://arxiv.org/pdf/1702.02604v2

Title Causal Regularization Summary application domain healthcare want accurate predictive model also causally interpretable pursuit model propose causal regularizer steer predictive model towards causallyinterpretable solution theoretically study property largescale analysis Electronic Health Records EHR causallyregularized model outperforms L1regularized counterpart causal accuracy competitive predictive performance perform nonlinear causality analysis causally regularizing special neural network architecture also show proposed causal regularizer used together neural representation learning algorithm yield 20 improvement multilayer perceptron detecting multivariate causation situation common healthcare many causal factor occur simultaneously effect target variable Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.02947417087852955, 0.08376093208789825, -0.018450533971190453, -0.04846975579857826, 0.028199339285492897, 0.00529453856870532, 0.01475520059466362, 0.037952154874801636, 0.017821740359067917, 0.05523843318223953, 0.08522357791662216, 0.033800411969423294, -0.02397766336798668, 0.05173458531498909, 0.02230899967253208, -0.021289143711328506, 0.03221544250845909, 0.049979645758867264, 0.028678806498646736, -0.007285804953426123, 0.009548281319439411, -0.0544549897313118, 0.020214706659317017, 0.06678678840398788, -0.04830747842788696, 0.0357581190764904, 0.027369486168026924, 0.0033245468512177467, -0.024258192628622055, -0.06738630682229996, 0.006835406646132469, -0.019033120945096016, 0.012611670419573784, 0.021430175751447678, 2.271209496029769e-06, -0.043032173067331314, -0.0093327471986413, -0.0030992431566119194, -0.008771832101047039, -0.07644258439540863, -0.07295456528663635, -0.05990835279226303, 0.06047525256872177, -0.001783274463377893, 0.008377260528504848, -0.013961771503090858, 0.029188819229602814, 0.09347373992204666, 0.01923942193388939, 0.07040379196405411, -0.02466375008225441, -0.0355679951608181, 0.02219933457672596, -0.01365639641880989, 0.02779187075793743, -0.04515903443098068, 0.03677565976977348, -0.004363763611763716, -0.023820122703909874, -0.08098969608545303, -0.041571345180273056, 0.00017045059939846396, 0.035981953144073486, 0.05015247315168381, 0.06854520738124847, 0.0046544685028493404, 0.06627839058637619, -0.0003567470994312316, -0.0093166409060359, 0.05529823899269104, 0.0005747355171479285, -0.0063895671628415585, 0.03505986928939819, 0.00925592053681612, 0.015550968237221241, 0.024137383326888084, -0.04182858020067215, -0.052403368055820465, -0.009388459846377373, -0.017204340547323227, -0.008291860111057758, 0.04431239888072014, 0.04969017580151558, 0.00790935754776001, -0.01717381179332733, 0.016605732962489128, -0.010854831896722317, -0.016905147582292557, -0.025318074971437454, 0.017917361110448837, 0.05816487595438957, 0.026249384507536888, -0.000942335813306272, 0.03520950302481651, -0.08156238496303558, -0.0006642078515142202, 0.015096509829163551, -0.029914595186710358, 0.06580168753862381, -0.035464365035295486, 0.03886746987700462, 0.005490973126143217, 0.016637444496154785, -0.0020647530909627676, 0.007636719848960638, 0.02916845679283142, -0.0827086940407753, 0.0443979911506176, -0.004319160711020231, 0.04283491522073746, -0.01868654228746891, -0.009744001552462578, 0.019269973039627075, 0.02796264924108982, 0.07052932679653168, 0.0304927546530962, -0.07413128763437271, -0.005648529622703791, -0.016559435054659843, -0.03817956522107124, 0.002454472938552499, 0.05090881884098053, 0.009198538959026337, 0.007816159166395664, -0.023018212988972664, -0.00017797596228774637, -0.06417426466941833, 0.06292217969894409, -0.046693094074726105, 0.019697127863764763, 0.0069955275394022465, 0.006977058481425047, 0.0180249884724617, -0.015815556049346924, -0.017325537279248238, 0.08349592983722687, 0.0481940321624279, 0.010058374144136906, -0.052153632044792175, -0.030849670991301537, 0.03074268437922001, -0.015631424263119698, -0.02724083699285984, -0.025803830474615097, -0.0067032030783593655, 0.0017041449900716543, -0.012459523975849152, -0.04757491871714592, -0.010839125141501427, -0.04904841259121895, -0.04921304062008858, 0.019744200631976128, -0.028341108933091164, -0.027016600593924522, 0.03605927526950836, -0.005590382963418961, 0.008922634646296501, 0.02283313311636448, 0.02642609365284443, -0.029796568676829338, -0.025757091119885445, -0.02850700542330742, 0.00018105712661053985, -0.005014433525502682, 0.05065669119358063, -0.046095818281173706, -0.008795223198831081, -0.07140026241540909, 0.01673663780093193, 0.038816165179014206, -0.028596412390470505, -0.009632415138185024, -0.003535127267241478, 0.029080132022500038, 0.009878262877464294, -0.007724432274699211, 0.04013305529952049, 0.009167232550680637, -0.003278168383985758, -0.03955545648932457, -0.04024270176887512, 0.02595067396759987, 0.01409291010349989, 0.01815248839557171, -0.026377767324447632, -0.07553227245807648, -0.046209320425987244, -0.036288052797317505, -0.014004587195813656, -0.042017146944999695, 0.01650538109242916, -0.04466749355196953, -0.016448216512799263, -0.028652839362621307, 0.08514483273029327, -0.010576986707746983, -0.006245868280529976, 0.004778602160513401, 0.03708450868725777, 0.011405332945287228, -0.00046485362690873444, -0.028537122532725334, -0.02541615441441536, -0.002105993451550603, -0.0024187390226870775, -0.02664162963628769, -0.020427929237484932, -0.05762571468949318, -0.04307399317622185, -0.09477211534976959, 0.006493133492767811, 0.009492366574704647, 0.01816139928996563, -0.00825462955981493, -0.01920727826654911, 0.03385571017861366, 0.04641605541110039, 0.0023532549384981394, -0.042631614953279495, -0.012937511317431927, -0.0006778763490729034, 0.05846968665719032, 0.010409840382635593, 0.03280869498848915, -0.03312481567263603, 0.004247766919434071, 0.006732541136443615, 0.04872114956378937, 0.027488624677062035, 0.028380023315548897, -0.002832685364410281, 0.010631827637553215, 0.00875854678452015, -0.07990556955337524, -0.06362088769674301, 0.009416244924068451, -0.02905328758060932, 0.0010548054706305265, -0.019320497289299965, -0.00830067042261362, 0.04895889014005661, 0.013370159082114697, -0.00953062903136015, -0.07023650407791138, 0.03816918656229973, -0.04189496859908104, -0.010867364704608917, 0.021922875195741653, -0.007454233709722757, 0.03198488801717758, 0.021482426673173904, -0.023160604760050774, -0.007578076329082251, 0.0008350862190127373, -0.0012466193875297904, 0.0320332832634449, -0.05902193486690521, 0.06843843311071396, 0.0029471623711287975, 0.0030635236762464046, -0.055783458054065704, -0.058412108570337296, -0.026261795312166214, 0.041048094630241394, -0.062114931643009186, 0.004214955028146505, 0.015475223772227764, 0.012744324281811714, -0.037232886999845505, 0.007466387469321489, -0.05341019108891487, -0.0300045907497406, 0.04617372155189514, 0.05134982243180275, -0.04035206139087677, -0.008464471437036991, 0.020049486309289932, 0.04649142920970917, -0.023463990539312363, 0.022525716572999954, 0.02265624701976776, 0.011031520552933216, 0.018422409892082214, -0.009866839274764061, -0.06991124898195267, 0.030931327491998672, 0.07140932232141495, -0.0346335843205452, -0.00608285516500473, -0.044106461107730865, 0.03656215965747833, -0.015422078780829906, -0.01179139968007803, -0.04302224516868591, -0.055981095880270004, -0.01221933402121067, -0.031184814870357513, 0.0401347279548645, -0.03898843377828598, 0.0005300258635543287, -0.011936042457818985, 0.039716288447380066, -0.04088433086872101, 0.0037467842921614647, -0.025246012955904007, 0.01836128532886505, -0.024948179721832275, 0.004346157424151897, -0.01091316994279623, 0.07988180965185165, 0.07956574857234955, 0.01108870655298233, -0.013105602003633976, 0.029606027528643608, 3.126340379822068e-05, -0.024411482736468315, -0.08612877130508423, -0.004375943448394537, -0.03821899741888046, 0.04794105887413025, -0.00640026805922389, -0.06124322861433029, 0.03391014039516449, 0.07838408648967743, 0.07623565196990967, 0.03480769693851471, -0.03333234041929245, -0.01208126824349165, -0.02419399842619896, 0.007625591475516558, 0.0009899224387481809, -0.009647063910961151, -0.03022724576294422, -0.003193821059539914, 0.011233896017074585, -0.012410181574523449, 0.015071372501552105, 0.011447061784565449, -0.010366780683398247, 0.022027846425771713, 0.025564169511198997, -0.011435627937316895, -0.053355854004621506, -0.047576211392879486, 0.029543152078986168, -0.010510221123695374, -0.005744786001741886, 0.02396228536963463, -0.004451921675354242, -0.007778918836265802, -0.01803920790553093, 0.039489295333623886, -0.04418082907795906, 0.0038065165281295776, 0.011166893877089024, -0.007260323967784643, 0.014914494939148426, -0.07027865201234818, -0.010952684096992016, -0.01847739890217781, 0.04821129888296127, -0.025514809414744377, -0.018148411065340042, -0.013033982366323471, -0.07482486218214035, 0.043897368013858795, -0.04598031938076019, -0.0061407615430653095, 0.016555069014430046, 0.012962568551301956, 0.00816264282912016, -0.05465183034539223, 0.0565674714744091, 0.012458140961825848, 0.0015352563932538033, -0.06248139962553978, 0.011830784380435944, -0.0008116044336929917, -0.055949922651052475, 0.003166947513818741, -0.01812897063791752, -0.03268488124012947, -0.0018279612995684147, -0.008389675058424473, -0.02619229257106781, -0.04723973572254181, -0.047742150723934174, 0.040536317974328995, 0.037112221121788025, -0.0012223604135215282, 0.01106778159737587, -0.011861784383654594, 0.005194202531129122, -0.03826982527971268, -0.013038668781518936, -0.0526522621512413, -0.03796963766217232, -0.012735105119645596, 0.029852120205760002, -0.014507735148072243, 0.016998019069433212, -0.046442750841379166, -0.0060111284255981445, -0.004203148186206818, -0.022348245605826378, 0.019155209884047508, 0.056579988449811935, 0.02897953987121582, -0.05267520248889923, 0.005297491792589426, -0.031502798199653625, 0.0811457633972168, 0.035493239760398865, -0.017447886988520622, 0.10284408181905746, 0.0660579651594162, -0.024953918531537056, -0.019343268126249313, 0.06427944451570511, -0.0112953782081604, 0.04304060712456703, -2.1961541278869845e-05, 0.07095922529697418, -0.06003880500793457, -0.014119477942585945, -0.010840228758752346, -0.02554955892264843, 0.01975960098206997, -0.010993323288857937, -0.004714463837444782, -0.010596905834972858, -0.07052664458751678, 0.01822127029299736, 0.013771056197583675, -0.005996907129883766, -0.0043192170560359955, -0.010967777110636234, 0.04696999490261078, -0.07019012421369553, -0.02828270010650158, 0.0006365068256855011, -0.03211507201194763, 6.61104786559008e-05, 0.03546324744820595, 0.06354624778032303, 0.013672004453837872, -0.003977878950536251, -0.02328789047896862, 0.005106917582452297, 0.057633355259895325, 0.017724039033055305, -0.00828707218170166, -0.004365820903331041, -0.008476345799863338, -0.02534998022019863, -0.02064918354153633, -0.02613404579460621, -0.018220262601971626, 0.020192300900816917, -0.01468671951442957, 0.0547771230340004, 0.006724334321916103, 0.019419528543949127, -0.03163722902536392, -0.05090374872088432, -0.041743453592061996, -0.020006943494081497, -0.026418456807732582, -0.05285727605223656, 0.026741432026028633, -0.008807262405753136, -0.028357842937111855, 0.014228052459657192, 0.001755597535520792, 0.05641716346144676, -0.02148406021296978, -0.013375936076045036, -0.0024018390104174614, 0.03566070273518562, 0.008294805884361267, 0.020340446382761, 0.058561261743307114, -0.009802784770727158, 0.00959195289760828, -0.009335006587207317, 0.005485315807163715, -0.002790082711726427, 0.010251299478113651, -0.013658804818987846, 0.010169325396418571, 0.0546162873506546, 0.02242104709148407, -0.02161809802055359, -0.1114106997847557, -0.004174360539764166, -0.09604551643133163, -0.05680667608976364, 0.0782703310251236, -0.029912708327174187, 0.031694747507572174, 0.011154112406075, 0.017004864290356636, 0.022857055068016052, 0.018073303624987602, 0.047883041203022, 0.02158006839454174, -0.03587176278233528, 0.04163278639316559, -0.010443796403706074, 0.06154376268386841, -0.03590613976120949, -0.0546761229634285, -0.035906851291656494, -0.007542615290731192, 0.045838892459869385, -0.034745749086141586, 0.06873127818107605, 0.003711329773068428, 0.0017352672293782234, 0.02784746326506138, 0.02603915147483349, -0.003991258796304464, 0.05745268240571022, -0.024592656642198563, 0.05521605536341667, 0.04566063731908798, -0.024479757994413376, -0.0274480152875185, -0.009662872180342674, 0.08346603810787201, 0.04854292795062065, 0.02583024650812149, -0.06093023717403412, -0.0011930424952879548, -0.031262706965208054, -0.007702498231083155, 0.06989783048629761, 0.03778165206313133, -0.059564922004938126, 0.01154017448425293, -0.03132447972893715, -0.0032246168702840805, 0.053358014672994614, -0.07277094572782516, 0.04844287782907486, 0.0006293590413406491, 0.02076908014714718, -0.04186481237411499, -0.05943909287452698, -0.008422835730016232, 0.015533669851720333, -0.012931166216731071, -0.01786917634308338, -0.014008140191435814, -0.011726497672498226, -6.341118317486426e-33, 0.024244314059615135, -0.014049638994038105, -0.03515671193599701, -0.040213290601968765, 0.025169966742396355, 0.02685295045375824, -0.05228392034769058, -0.01483810693025589, 0.04062085598707199, -0.011692770756781101, -0.005254362244158983, 0.026639731600880623, -0.0008493221248500049, 0.05025859549641609, 0.07533203810453415, -0.04187183454632759, 0.009199477732181549, 0.014390635304152966, 0.06226326897740364, 0.029049349948763847, 0.0074288505129516125, 0.08319654315710068, 0.019129056483507156, -0.09517824649810791, 0.004745163954794407, 0.03324950113892555, 0.006688481662422419, -0.02859315276145935, -0.05577390640974045, 0.018611112609505653, -0.0004380216123536229, 0.015038269571959972, 0.03826646879315376, -0.03993649408221245, 0.028761232271790504, 0.011151771061122417, -0.01783127896487713, -0.027517948299646378, -0.0073475707322359085, -0.02394990809261799, -0.03278213366866112, -0.04491903632879257, 0.039519913494586945, -0.015039436519145966, -0.03689968213438988, 0.03768371790647507, 0.03465847671031952, 0.005117989610880613, -6.140324694570154e-05, -0.04981978237628937, -0.028115972876548767, 0.019202925264835358, -0.05090416595339775, 0.058718398213386536, -0.03047790378332138, 0.029621731489896774, -0.05324632674455643, 0.0453224778175354, 0.0018604432698339224, -0.01370390597730875, -0.0360071063041687, -0.00036907821777276695, -0.014698099344968796, 0.016712145879864693, 0.017209192737936974, 0.04676825553178787, 0.0015062416205182672, 0.00316191790625453, -0.054849639534950256, 0.0241572055965662, -0.046543851494789124, 0.03814274072647095, 0.04591941833496094, 0.016369905322790146, 0.03852764517068863, -0.0862388163805008, -0.10860159993171692, 0.04319098964333534, 0.005723047070205212, 0.033270593732595444, 0.009200992062687874, -0.02437327429652214, -0.04252487048506737, -0.005985660944133997, -0.004173144698143005, -0.03563375771045685, -0.0296192429959774, -0.02444574609398842, 0.0067811403423547745, -0.01347065158188343, 0.054949693381786346, 0.011105811223387718, 0.02311616763472557, -0.06826994568109512, 0.05293926224112511, 0.0166852455586195, 0.03995543345808983, -0.02407589741051197, 0.011563144624233246, -0.041802797466516495, -0.033793818205595016, 0.003767765127122402, -0.03527588024735451, -0.00342329079285264, 0.07952157407999039, 0.013934028334915638, 0.021352456882596016, -0.06066280975937843, 0.011382078751921654, -0.023330792784690857, 0.01271241158246994, -0.06584005802869797, 0.014139043167233467, -0.01045577134937048, 0.04502307251095772, 0.025954557582736015, -0.02214725874364376, 0.08849024027585983, 0.028830422088503838, 0.010210123844444752, -0.015318975783884525, -0.06478627026081085, 0.014218739233911037, 0.003920546267181635, -0.051266271620988846, -0.026133667677640915, -0.040153540670871735, 0.009828848764300346, -0.011764959432184696, -0.08461842685937881, -0.009489631280303001, -0.03121004067361355, 2.970231491872255e-07, 0.03323967754840851, 0.031084584072232246, -0.002426996361464262, -0.012884062714874744, 0.005134917329996824, -0.022992631420493126, -0.007118063513189554, 0.009399184957146645, -0.06217572093009949, 0.04667635262012482, 0.06365963071584702, -0.03686737269163132, 0.04884533956646919, -0.03149452060461044, -0.028822949156165123, -0.0057221464812755585, -0.004400890786200762, 0.017115840688347816, -0.005313945468515158, 0.029285570606589317, 0.07714581489562988, 0.02847074717283249, 0.002710913307964802, -0.031168492510914803, 0.05187720060348511, 0.05092136934399605, 0.008388244546949863, -0.007295174989849329, 0.03057098388671875, -0.024997366592288017, -0.011089005507528782, -0.014803105033934116, -0.004132286179810762, 0.04899663105607033, -0.020510416477918625, 0.030806316062808037, -0.004336624406278133, 0.06452032923698425, -0.0638452097773552, -0.0030532616656273603, 0.0038748220540583134, -0.030887311324477196, 0.05493009090423584, 0.0077933939173817635, 0.04901444539427757, -0.0113301370292902, -0.10246147960424423, 0.03985631838440895, 0.007284484803676605, 0.03985213488340378, 0.061861228197813034, -1.733017597871367e-05, 0.026833156123757362, -0.010474086739122868, -0.006088578142225742, 0.015657979995012283, 0.02437947317957878, -0.01550635788589716, -0.025914456695318222, 0.056683577597141266, 0.002027475507929921, -0.03341103345155716, 0.01146536786109209, -0.0008601497393101454, 0.04277428239583969, 0.0012810835614800453, 0.004969580564647913, 2.915756569618326e-34, 0.015385513193905354, -0.014894910156726837, 0.010157834738492966, -0.023266086354851723, 0.03233209252357483, -0.04665292054414749, 0.004656083881855011, 0.047015272080898285, 0.024395905435085297, -0.051138292998075485, 0.006302803289145231]

['Dario Garcia-Gasulla', 'Ferran Parés', 'Armand Vilalta', 'Jonatan Moreno', 'Eduard Ayguadé', 'Jesús Labarta', 'Ulises Cortés', 'Toyotaro Suzumura']

1703.01127v4

Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within a trained CNN model (in the case of image data), and reusing it for other purposes is a field of interest, as it provides access to the visual descriptors previously learnt by the CNN after processing millions of images, without requiring an expensive training phase. Contributions to this field (commonly known as feature representation transfer or transfer learning) have been purely empirical so far, extracting all CNN features from a single layer close to the output and testing their performance by feeding them to a classifier. This approach has provided consistent results, although its relevance is limited to classification tasks. In a completely different approach, in this paper we statistically measure the discriminative power of every single feature found within a deep CNN, when used for characterizing every class of 11 datasets. We seek to provide new insights into the behavior of CNN features, particularly the ones from convolutional layers, as this can be relevant for their application to knowledge representation and reasoning. Our results confirm that low and middle level features may behave differently to high level features, but only under certain conditions. We find that all CNN features can be used for knowledge representation purposes both by their presence or by their absence, doubling the information a single CNN feature may provide. We also study how much noise these features may include, and propose a thresholding approach to discard most of it. All these insights have a direct application to the generation of CNN embedding spaces.

On the Behavior of Convolutional Nets for Feature Extraction

http://arxiv.org/pdf/1703.01127v4

Title Behavior Convolutional Nets Feature Extraction Summary Deep neural network representation learning technique training deep net capable generating descriptive language unprecedented size detail machine learning Extracting descriptive language coded within trained CNN model case image data reusing purpose field interest provides access visual descriptor previously learnt CNN processing million image without requiring expensive training phase Contributions field commonly known feature representation transfer transfer learning purely empirical far extracting CNN feature single layer close output testing performance feeding classifier approach provided consistent result although relevance limited classification task completely different approach paper statistically measure discriminative power every single feature found within deep CNN used characterizing every class 11 datasets seek provide new insight behavior CNN feature particularly one convolutional layer relevant application knowledge representation reasoning result confirm low middle level feature may behave differently high level feature certain condition find CNN feature used knowledge representation purpose presence absence doubling information single CNN feature may provide also study much noise feature may include propose thresholding approach discard insight direct application generation CNN embedding space Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.032952629029750824, 0.01611396297812462, -0.01034631859511137, 0.10258033126592636, -0.02511817403137684, 0.008014094084501266, 0.06135148927569389, 0.025373611599206924, -0.04846315085887909, -0.0306550282984972, -0.015558541752398014, 0.02333213947713375, -0.027563640847802162, 0.058921780437231064, 0.025731228291988373, -0.04099631682038307, 0.01465984620153904, 0.04781461879611015, 0.0041937935166060925, -0.012692002579569817, 0.0034298794344067574, -0.0236173328012228, 0.0315852090716362, 0.04296768829226494, -0.05304355174303055, 0.023057444021105766, -0.003356005996465683, -0.018992381170392036, 0.02262764982879162, 0.008517248556017876, 0.05929192155599594, 0.0266986396163702, 0.01917911320924759, 0.0518912635743618, 2.4151763682311866e-06, -0.024781513959169388, -0.030358081683516502, -0.02440553717315197, 0.017875228077173233, -0.015898138284683228, 0.022696396335959435, -0.00780143029987812, -0.009740641340613365, -0.04365931451320648, -0.03543582558631897, -0.03394957259297371, 0.037052400410175323, 0.08297237008810043, -0.03672211989760399, 0.022243596613407135, -0.014042051509022713, -0.050926074385643005, -0.008270121179521084, 0.0199542585760355, 0.007253206335008144, -0.010174572467803955, -0.005572119727730751, -0.027623478323221207, -0.05831022933125496, -0.02550399862229824, -0.023893043398857117, 0.02586008422076702, 0.023116057738661766, -0.001418798347003758, 0.015050939284265041, 0.05111318454146385, -0.034027162939310074, -0.056980229914188385, 0.01469918992370367, 0.07358333468437195, -0.05599741265177727, 0.03484442085027695, -0.005778162740170956, 0.002497231587767601, -0.03503374382853508, -0.025568092241883278, -0.010311589576303959, 0.03140528127551079, 0.012083308771252632, 0.020009707659482956, -0.08186041563749313, 0.05427303537726402, -0.01334751769900322, 0.019405754283070564, -0.06167888641357422, -0.021768011152744293, -0.026120521128177643, 0.028594637289643288, -0.013506571762263775, -0.048458032310009, 0.022635791450738907, -0.020189205184578896, 0.016447260975837708, -0.00419175811111927, 0.03226916491985321, -0.030224816873669624, -0.026420343667268753, -0.08063910156488419, 0.06748855859041214, -0.05954945459961891, 0.045852310955524445, -0.037909653037786484, -0.1211213767528534, 0.03732778877019882, -0.02597919851541519, 0.06838395446538925, -0.054791416972875595, 0.04105740785598755, -0.020429234951734543, 0.0045892829075455666, -0.053856927901506424, -0.009184291586279869, 0.027323052287101746, 0.0372578389942646, 0.02314355969429016, -0.024438252672553062, -0.03884071856737137, -0.04866817593574524, -0.042878806591033936, 0.008461670018732548, -0.0461588017642498, 0.08536235243082047, -0.024710120633244514, -0.01935381256043911, 0.017962010577321053, 0.007452887482941151, -0.0337345227599144, 0.019908329471945763, 0.02458971180021763, -0.02937167137861252, 0.027796972543001175, 0.01729605346918106, 0.026189185678958893, -0.0011409271974116564, 0.04166960343718529, 0.04811795428395271, -0.0016165641136467457, -0.015596172772347927, -0.04068842902779579, -0.01604871265590191, 0.002201235154643655, -0.02215324528515339, 0.021474722772836685, -0.07473938912153244, 0.016507821157574654, -0.03848737105727196, -0.032651033252477646, -0.005448116455227137, -0.020445356145501137, -0.018897855654358864, -0.012023667804896832, 0.08830205351114273, -0.06709902733564377, -0.006193740293383598, 0.10145916044712067, -0.008852300234138966, 0.063906729221344, 0.013067318126559258, 0.031596217304468155, 0.038036465644836426, 0.009900822304189205, -0.047040339559316635, -0.008273076266050339, -0.011296273209154606, -0.027769645676016808, -0.02998739294707775, -0.05129387602210045, -0.01137927733361721, -0.0038513101171702147, -0.012627793475985527, 0.009752034209668636, 0.027340473607182503, 0.004657849669456482, -0.04262242466211319, 0.0012608905090019107, 0.09095354378223419, 0.027448508888483047, 0.0398077555000782, 0.015509634278714657, 0.04662896692752838, 0.018729189410805702, -0.004505195189267397, -0.0186246819794178, 0.041131142526865005, 0.006069561000913382, -0.0407961942255497, -0.04613786190748215, 0.014501533471047878, -0.025627871975302696, -0.05692518875002861, 0.0134976701810956, -0.0443311482667923, 0.016684282571077347, 0.007139415480196476, 0.04852888360619545, -9.289551962865517e-05, 0.028388611972332, -0.008824453689157963, 0.02924192324280739, 0.02252805419266224, -0.048021528869867325, -0.08301413804292679, 0.02063792198896408, 0.01029521320015192, -0.03114793635904789, -0.02758883871138096, -0.005026769358664751, -0.001963417511433363, 0.022689618170261383, -0.03172457963228226, 0.008409376256167889, 0.0025193283800035715, 0.028019243851304054, -0.04558953270316124, -0.018065836280584335, -0.037035804241895676, -0.006914922036230564, 0.00860162079334259, -0.018041150644421577, 0.014856774359941483, 0.02188926935195923, 0.04099754989147186, -0.02029772475361824, 0.042238324880599976, 0.047405973076820374, -0.025996528565883636, 0.044336412101984024, 0.048866938799619675, 0.01094912551343441, 0.00869201309978962, 0.0039904192090034485, -0.025179775431752205, 0.06959045678377151, -0.023132970556616783, -0.01160457730293274, 0.018828991800546646, -0.011902060359716415, 0.020771820098161697, 0.021601999178528786, -0.011170929297804832, 0.03919621929526329, 0.025363923981785774, -0.04171079024672508, -0.020410941913723946, 0.013464687392115593, 0.021856041625142097, 0.023490821942687035, -0.027936572209000587, -0.015495575964450836, -0.012463328428566456, 0.0423462837934494, -0.012088377960026264, 0.03600030764937401, 0.002481167670339346, -0.009178158827126026, -0.022345278412103653, -0.018204044550657272, 0.03984500840306282, -0.040004998445510864, -0.0070436866953969, 0.025316881015896797, -0.07790150493383408, -0.011218228377401829, -0.012688220478594303, 0.0398951955139637, -0.014313745312392712, 0.03466077893972397, -0.027495259419083595, -0.0030784273985773325, -0.005680030677467585, -0.05102472007274628, -0.0213630273938179, -0.012578768655657768, 0.024722013622522354, -0.040608424693346024, -0.03666193410754204, 0.04627760499715805, -0.013449759222567081, -0.022067096084356308, 0.0571979284286499, 0.01443473156541586, -0.006412365008145571, -0.04705088958144188, -0.035330358892679214, 0.025574294850230217, 0.03915206715464592, 0.019231926649808884, -0.07670416682958603, -0.003146675182506442, -0.006900262553244829, 0.003263680264353752, 0.054396431893110275, -0.00504878768697381, -0.07427949458360672, -0.0020153236109763384, -0.04325888305902481, -0.04632571339607239, 0.08812591433525085, 0.04983332008123398, 0.06858618557453156, 0.009267603978514671, 0.06188589334487915, -0.01475533377379179, 0.007310533430427313, -0.040123749524354935, 0.0035283479373902082, 0.013972427695989609, 0.019029077142477036, -0.0252525694668293, 0.010754482820630074, 0.005889419931918383, 0.03939659520983696, 0.01844070293009281, -0.022993871942162514, -0.0293557271361351, -0.024000216275453568, -0.05267573520541191, 0.02752157300710678, -0.004147401545196772, 0.0596199631690979, 0.022293079644441605, -0.05694922059774399, 0.04279555380344391, 0.06026981770992279, -0.016781579703092575, 0.0288552176207304, -0.05939961224794388, 0.01330976840108633, 0.09972135722637177, 0.022869596257805824, 0.038717903196811676, 0.021478137001395226, -0.031171590089797974, 0.002909197472035885, -0.0061104679480195045, -0.007333260960876942, -0.05941430479288101, 0.038205210119485855, -0.00679616117849946, -0.02813330478966236, -0.037794969975948334, -0.014972880482673645, -0.0620228610932827, -0.024112720042467117, 0.0016800581943243742, -0.010506579652428627, -0.03281201049685478, -0.014956247992813587, 0.02432441897690296, 0.005473236087709665, -0.011042032390832901, 0.029593579471111298, -0.0070459418930113316, 0.007059766910970211, -0.02463645301759243, 0.022456668317317963, 0.05323999747633934, 0.024838553741574287, -0.04224713519215584, 0.03847743943333626, 0.00012723304098472, 0.06160261854529381, -0.08159876614809036, 0.016014032065868378, -0.10081898421049118, 0.0322149433195591, -0.0023662270978093147, 0.01644115336239338, 0.002446565078571439, 0.02453148178756237, 0.031352605670690536, -0.07684371620416641, -0.005020986311137676, 0.0416029617190361, 0.0005753689329139888, -0.09292171895503998, 0.0294208787381649, 0.01938750594854355, -0.04946863278746605, 0.010648578405380249, 0.013953451998531818, -0.0227520689368248, -0.0007373387343250215, -0.015599106438457966, -0.005578808486461639, 0.003621146082878113, -0.007903831079602242, 0.004258476663380861, -0.04585728794336319, 0.07078318297863007, -0.014765565283596516, -0.017535731196403503, -0.05702421814203262, 0.019547702744603157, -0.002868977375328541, -0.009627735242247581, -0.010280129499733448, -0.0003580588672775775, 0.04993966966867447, -0.029146580025553703, 0.019776079803705215, -0.026697801426053047, -0.021843712776899338, 0.056349191814661026, -0.04637659341096878, -0.003981117624789476, 0.0346020944416523, 0.03390853479504585, -0.05101789906620979, -0.04166443273425102, -0.020267793908715248, -0.011772118508815765, 0.04752977937459946, -0.012703906744718552, 0.09195686131715775, 0.019858958199620247, -0.007669380400329828, 0.0050802710466086864, 0.06143203377723694, -0.01088527962565422, 0.01402049046009779, 0.016493186354637146, -0.0030702040530741215, -0.02943931519985199, 0.0005796484183520079, -0.08679398149251938, -0.006586270872503519, 0.01870410144329071, -0.023263169452548027, 0.01611368916928768, -0.027552032843232155, -0.03526315093040466, 0.004284425172954798, 0.010010452941060066, -0.02730683796107769, -0.022670386359095573, 0.015311956405639648, 0.020672863349318504, -0.04545522481203079, -0.0391572043299675, -0.015093176625669003, -0.00910988636314869, 0.0226594228297472, 0.005425862967967987, -0.0593743659555912, 0.01619720831513405, 0.0002794746251311153, -0.07165873795747757, 0.011594520881772041, 0.07321243733167648, 0.03424018993973732, -0.015258271247148514, 0.01590403914451599, 0.06285510957241058, -0.02910637855529785, -0.020594637840986252, -0.04212944582104683, -0.05074060335755348, -0.020658371970057487, 0.02147255279123783, 0.032450344413518906, 0.0076338378712534904, 0.027263548225164413, -0.023086220026016235, -0.03903248906135559, -0.00026833772426471114, -0.008367099799215794, 0.012030169367790222, -0.04154066741466522, 0.03639901801943779, -0.058782946318387985, -0.0136598264798522, -0.002039983868598938, -0.018124990165233612, 0.08548347651958466, 0.006238850764930248, -0.09279818832874298, -0.05693890154361725, -0.022999662905931473, 0.03901185095310211, -0.014317886903882027, 0.09014377743005753, 0.04235729202628136, -0.01703868992626667, -0.03410499542951584, 0.011278484016656876, 0.019009506329894066, 0.003061878029257059, -0.03618913143873215, 0.007948325015604496, 0.006573156453669071, -0.001327654579654336, 0.008700289763510227, -0.008033216930925846, 0.05825260654091835, -0.029430272057652473, -0.011706645600497723, 0.019958417862653732, -0.021594390273094177, -0.0014015716733410954, -0.03929074853658676, 0.027226829901337624, -0.015011054463684559, 0.032992225140333176, 0.026492714881896973, 0.04303598776459694, 0.0009471210651099682, 0.001410106080584228, 0.011914405971765518, 0.02155526541173458, -0.058969538658857346, 0.045634232461452484, 0.023445094004273415, 0.0030433114152401686, -0.03445674106478691, 0.015868008136749268, 0.04027748107910156, -0.08013222366571426, 0.008794380351901054, -0.006540699861943722, 0.02174973487854004, -0.01722806878387928, 0.03628495708107948, -0.03478482365608215, 0.0004991169553250074, 0.05184116214513779, 0.012014824897050858, -0.02329430542886257, -0.04358680546283722, 0.03761202096939087, 0.02604703977704048, -0.008089682087302208, -0.04060402140021324, -0.006841947790235281, -0.034240178763866425, 0.04566223919391632, 0.005263089202344418, 0.030592693015933037, 5.422826870926656e-05, 0.010618608444929123, 0.016399288550019264, -0.030845899134874344, 0.01609203778207302, -0.018707478418946266, 0.05656200647354126, 0.0024053507950156927, 0.03334715962409973, 0.0484841950237751, 0.012276938185095787, -0.07405760884284973, -0.01182430051267147, -0.03451215475797653, 0.031383026391267776, -0.003702801652252674, -0.058138657361269, -6.838876257554339e-33, 0.04182276129722595, -0.03650690242648125, -0.019306238740682602, -0.0018886319594457746, -0.026072075590491295, 0.028979090973734856, -0.004952876828610897, -0.024721458554267883, -0.04323599115014076, 0.04134215787053108, -0.010391502641141415, -0.004857437685132027, 0.0324864499270916, 0.028155909851193428, 0.022956985980272293, -0.008226379752159119, -0.008021130226552486, -0.055152542889118195, 0.04762115702033043, 0.02532203309237957, 0.037749502807855606, 0.03189612179994583, 0.08481566607952118, -0.08040475845336914, -0.03264933452010155, 0.013643317855894566, -0.009336444549262524, -0.03725740686058998, 0.011976121924817562, 0.03127863630652428, -0.01806010492146015, 0.011525915935635567, 0.027056023478507996, -0.030609749257564545, -0.02321188896894455, -0.04258380085229874, -0.053618185222148895, -0.0036402149125933647, -0.0735192820429802, 0.045758895576000214, -0.06499295681715012, -0.0006990288966335356, 0.09833662956953049, -0.035251177847385406, -0.043481696397066116, -0.03376782685518265, 0.07848221063613892, -0.02787899598479271, -0.011556090787053108, -0.042635902762413025, -0.08240459114313126, 0.03773973882198334, -0.007335433270782232, -0.005073985550552607, 0.0510542206466198, -0.001996363280341029, -0.003248882247135043, 0.01026004459708929, -0.05980361998081207, 0.0250275619328022, 0.013066401705145836, 0.04311846196651459, 0.047572363168001175, 0.05310438200831413, 0.036567751318216324, 0.04641632363200188, 0.04132711887359619, 0.005919461138546467, -0.022908944636583328, 0.017441632226109505, 0.018705446273088455, 0.11794916540384293, 0.0352153517305851, 0.007636222522705793, 0.08890742808580399, -0.0993821993470192, -0.04722023382782936, -0.029277540743350983, -0.00663940142840147, 0.020086344331502914, -0.03931770846247673, 0.0029039091896265745, -0.014730366878211498, -0.003534487448632717, 0.03237064927816391, 0.010017313063144684, 0.002983159152790904, -0.03266606479883194, 0.026035647839307785, -0.017506146803498268, -0.01583714596927166, 0.035217586904764175, -0.01738113909959793, -0.03457468003034592, 0.051961734890937805, -0.02525552362203598, 0.006264856085181236, 0.049124740064144135, 0.028696363791823387, -0.02595701813697815, -0.0360083170235157, -0.05107475072145462, -0.014796166680753231, -0.008619959466159344, 0.023600805550813675, 0.05044427141547203, 0.031016333028674126, 0.05024498328566551, -0.009318583644926548, 0.001177133177407086, 0.016082320362329483, -0.045014508068561554, 0.030939919874072075, 0.04604468122124672, -0.008996186777949333, -0.03572046384215355, 0.007046456448733807, 0.04323265701532364, 0.01758708246052265, -0.030171900987625122, -0.05547088012099266, -0.02035653032362461, 0.015995969995856285, 0.04767336696386337, -0.06727470457553864, -0.013268014416098595, -0.07452227175235748, -0.005198436789214611, 0.03535301983356476, -0.029935196042060852, -0.010973956435918808, 0.04340096563100815, 3.043318201889633e-07, -0.024226974695920944, 0.008297968655824661, 0.013112560845911503, -0.016607724130153656, 0.010070458054542542, 0.028531525284051895, 0.010779744945466518, 0.019072191789746284, -0.015386296436190605, -0.036859240382909775, 0.04317307844758034, -0.007052215747535229, 0.014441462233662605, 0.022299055010080338, -0.034119442105293274, 0.010752820409834385, -0.018273500725626945, -0.02521720714867115, -0.04123431444168091, 0.013051257468760014, 0.06480992585420609, 0.09899960458278656, 0.020785611122846603, -0.03127618879079819, 0.08582930266857147, -0.03851880878210068, 0.003013045759871602, -0.012503372505307198, 0.04485941678285599, -0.010268816724419594, -0.01723851077258587, 0.02836797572672367, -0.014300542883574963, 0.008814840577542782, -0.03928472474217415, 0.000690879242029041, 0.03403415158390999, 0.0367218554019928, -0.05374017730355263, -0.0038724576588720083, 0.00020734277495648712, -0.00037601948133669794, 0.018295055255293846, -0.03992949798703194, 0.06693466007709503, -0.002695784205570817, -0.0051389699801802635, -0.06448059529066086, 0.02547534927725792, 0.022671451792120934, 0.03826283663511276, -0.020819662138819695, 0.02356773428618908, 0.007997313514351845, 0.01406126283109188, -0.022779690101742744, -0.040822237730026245, -0.0767035111784935, 0.038792021572589874, -0.01642797514796257, -0.05931450426578522, 0.015934376046061516, -0.009814153425395489, -0.038156185299158096, 0.06859296560287476, 0.036704909056425095, -0.03473757952451706, 2.8050732154063493e-34, -0.038645628839731216, 0.0035279965959489346, 0.013608734123408794, -0.001485511427745223, -0.0716557651758194, 0.015107650309801102, 0.02693232335150242, 0.03408133238554001, -0.027775442227721214, -0.012759356759488583, -0.052562590688467026]

['Aditya Grover', 'Manik Dhar', 'Stefano Ermon']

1705.08868v2

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.

Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models

http://arxiv.org/pdf/1705.08868v2

Title FlowGAN Combining Maximum Likelihood Adversarial Learning Generative Models Summary Adversarial learning probabilistic model recently emerged promising alternative maximum likelihood Implicit model generative adversarial network GAN often generate better sample compared explicit model trained maximum likelihood Yet GANs sidestep characterization explicit density make quantitative evaluation challenging bridge gap propose FlowGANs generative adversarial network perform exact likelihood evaluation thus supporting adversarial maximum likelihood training trained adversarially FlowGANs generate highquality sample attain extremely poor loglikelihood score inferior even mixture model memorizing training data opposite true trained maximum likelihood Results MNIST CIFAR10 demonstrate hybrid training attain high heldout likelihood retaining visual fidelity generated sample Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.003950317390263081, 0.07688191533088684, 0.0009166643721982837, -0.004617008846253157, -0.0009049780201166868, -0.018247541040182114, 0.03817833214998245, -0.009871242567896843, -0.035942502319812775, 0.002297213999554515, -0.03915375843644142, -0.0024538380093872547, -0.005245716776698828, 0.07906213402748108, 0.07487092167139053, -0.08514614403247833, 0.0027484004385769367, 0.02820718102157116, -0.01837427169084549, -0.03170928359031677, -0.0005434883642010391, -0.004724533297121525, -0.01476504746824503, 0.030529674142599106, 0.015208184719085693, -0.012045173905789852, -0.015779200941324234, 0.017845144495368004, 0.03186119347810745, -0.01705487072467804, 0.014333536848425865, 0.009223063476383686, 0.0288249384611845, 0.03474552556872368, 2.6427285320096416e-06, -0.020426630973815918, 0.0030177433509379625, 0.02017749845981598, 0.00911735463887453, 0.038818903267383575, 0.009927158243954182, -0.007259368430823088, -0.014868294820189476, 0.033315446227788925, -0.02349998988211155, -0.10220649838447571, 0.04695625975728035, 0.04643388092517853, -0.0040672095492482185, 0.028480425477027893, -0.015122554264962673, -0.0522797517478466, 0.07151959091424942, -0.06078682839870453, 0.028289327397942543, -0.06274614483118057, 0.011107728816568851, 0.026417169719934464, -0.06446530669927597, -0.05177700147032738, -0.01961834914982319, 0.04713502898812294, 0.07978492230176926, 0.0044809384271502495, 0.03467927128076553, 0.10476044565439224, 0.022379647940397263, 0.010685183107852936, -0.0048257773742079735, 0.04132501408457756, -0.05753292143344879, 0.022333234548568726, -0.024152498692274094, -0.03260305896401405, -0.030876338481903076, 0.013982945121824741, -0.052746064960956573, -0.0062846653163433075, -0.01944773457944393, 0.00024833891075104475, -0.0771854817867279, 0.031150056049227715, 0.049053359776735306, 0.0449652299284935, -0.04250318557024002, -0.07061748206615448, 0.008499071933329105, 0.045753758400678635, -0.035907093435525894, -0.020483404397964478, -0.03987765312194824, -0.05991476774215698, 0.027239298447966576, -0.00953639391809702, 0.00484510138630867, -0.03161321580410004, -0.008454919792711735, -0.0003608801052905619, 0.0056916712783277035, -0.0015827729366719723, 0.06846357136964798, -0.025574160739779472, -0.015864603221416473, 0.013386600650846958, -0.01625128462910652, 0.034693289548158646, -0.025917425751686096, 0.028492676094174385, -0.015336823649704456, 0.0021967687644064426, -0.00011680283932946622, -0.0022470264229923487, 0.036118555814027786, 0.004215114284306765, -0.039349351078271866, -0.04860030487179756, -0.0582878477871418, -0.029641438275575638, 0.01346178725361824, 0.027850018814206123, -0.008516809903085232, 0.07375705987215042, -0.05782531946897507, -0.03299985080957413, -0.012050940655171871, -0.04093138873577118, -0.01633482798933983, 0.025014307349920273, 0.042890023440122604, -0.015690913423895836, 0.011086768470704556, 0.009583065286278725, -0.027953406795859337, 0.0012724008411169052, -0.0015173208666965365, 0.08929413557052612, -0.025021595880389214, 0.01753617450594902, -0.023482536897063255, 0.024258874356746674, 0.0013406308135017753, -0.0737895667552948, 0.03477231785655022, -0.05790499970316887, 0.012469911947846413, -0.05275338515639305, 0.0056393942795693874, -0.029871122911572456, -0.021757295355200768, -0.035437341779470444, 0.040473103523254395, 0.058731742203235626, 0.05951777100563049, -0.02905915677547455, 0.04207717254757881, 0.01641850359737873, 0.05517898499965668, -0.003857650328427553, 0.036568399518728256, 0.0787392258644104, -0.00838007777929306, -0.004856858868151903, 0.012260278686881065, 0.00814511626958847, 0.0029251636005938053, -0.005240307655185461, -0.01222502812743187, -0.03465934470295906, -0.03772618621587753, 0.028927577659487724, 0.05115220695734024, 0.03773944824934006, -0.04141455888748169, -0.05010019242763519, 0.051888272166252136, -0.018663819879293442, 0.05682036653161049, 0.012733160518109798, 0.0473196879029274, 0.004518458619713783, 0.009828107431530952, 0.021669182926416397, -0.023771915584802628, 0.06654948741197586, -0.0021470545325428247, 0.00010466545791132376, 0.05423663556575775, 0.051147229969501495, -0.045315951108932495, -0.06896612793207169, 0.033288370817899704, -0.009692558087408543, -0.05322756618261337, 0.005998002830892801, 0.05528879165649414, -0.00562052708119154, -0.024514151737093925, -0.09444812685251236, 0.02916029281914234, -0.012724011205136776, -0.021520031616091728, -0.02835932746529579, 0.02542799897491932, 0.0024007544852793217, 0.03248406574130058, 0.02724679373204708, -0.008093617856502533, -0.009813282638788223, -0.06409875303506851, -0.0012934345286339521, 0.021206043660640717, 0.0019719195552170277, 0.034492433071136475, -0.04625089466571808, -0.021583134308457375, -0.03323173522949219, 0.032708656042814255, 0.07321358472108841, -0.0008294470026157796, 0.005867993459105492, 0.028897948563098907, -0.019151775166392326, -0.03545961529016495, 0.02963521145284176, -0.08772127330303192, 0.026600616052746773, 0.06947576254606247, 0.01369006559252739, 0.026806795969605446, -0.027545776218175888, -0.030132876709103584, 0.01860899291932583, 0.026869744062423706, -0.04283067211508751, -0.043511535972356796, 0.02398631162941456, -0.040383413434028625, -0.012509515509009361, -0.007933924905955791, -0.04605698212981224, 0.030932456254959106, -0.019472535699605942, -0.044538870453834534, -0.017628496512770653, 0.017084607854485512, 0.03679400682449341, -0.0200345478951931, -0.042828332632780075, -0.000633141549769789, 0.02327778749167919, 0.01769127883017063, -0.02851308137178421, 0.06791770458221436, -0.022484993562102318, -0.005932973697781563, 0.010611921548843384, 0.03787054121494293, 0.01446842122823, -0.018982315436005592, 0.025637153536081314, 0.02357175573706627, 0.00813684519380331, -0.006946686189621687, -0.020543653517961502, -0.00779516389593482, -0.014621029607951641, 0.02431649900972843, 0.010678660124540329, 0.051545750349760056, 0.006556781940162182, -0.010380402207374573, 0.03880903497338295, 0.005209732335060835, -0.005299942567944527, 0.035501036792993546, -0.05198221281170845, 0.05132783576846123, -0.01700172945857048, -0.05038219690322876, 0.007482469081878662, 0.00765406945720315, 0.05821260064840317, -0.036364976316690445, -0.002614679979160428, -0.0009762359550222754, 0.03082968108355999, 0.02183600701391697, -0.03983137384057045, 0.006436991970986128, 0.046134352684020996, -0.0002505169250071049, 0.027500955387949944, -0.05181403085589409, -0.06972454488277435, -0.01661388948559761, -0.01790524646639824, 0.03497762233018875, 0.07538329809904099, 0.018366405740380287, -0.02689219079911709, -0.003120415611192584, 0.031983956694602966, -0.048020314425230026, -0.002092239912599325, 0.0031996213365346193, -0.013471327722072601, 0.031741365790367126, -0.047766923904418945, -0.0386027954518795, 0.010828535072505474, 0.06332231312990189, 0.028994407504796982, -0.021326014772057533, 0.03770994022488594, 0.0008104594307951629, -0.03489037975668907, -0.002796259941533208, 0.03577793017029762, -0.0027481121942400932, -0.011014601215720177, -0.04150719195604324, -0.029947390779852867, 0.033635154366493225, -0.011195085942745209, -0.006998902186751366, 0.017244437709450722, -0.025502333417534828, 0.007631989195942879, 0.027032310143113136, 0.0477268248796463, 0.02761400304734707, 0.040020063519477844, -0.015269259922206402, -0.06607901304960251, 0.025052573531866074, 0.059766750782728195, -0.022304506972432137, 0.003747188951820135, -0.0006808502366766334, -0.019674498587846756, -0.025631088763475418, -0.01010940782725811, -0.05728800967335701, -0.034970540553331375, 0.07435884326696396, 0.03129008039832115, -0.0031769415363669395, -0.044139280915260315, -0.040129780769348145, -0.0027952452655881643, 0.0036186175420880318, 0.0377240851521492, -0.029510924592614174, -0.003713659942150116, -0.003647200996056199, 0.09060946851968765, 0.03254526108503342, -0.04861604422330856, -0.0009998992318287492, -0.005940430331975222, 0.050309423357248306, 0.06263866275548935, -0.05269342660903931, 0.061503078788518906, -0.07605944573879242, -0.023529037833213806, -0.03796224296092987, 0.04614666476845741, -0.0035331007093191147, 0.03828348591923714, 0.06602118909358978, -0.028286892920732498, 0.010064640082418919, 0.03634293004870415, -0.02297070622444153, -0.03872884437441826, 0.005495271645486355, 0.04388407617807388, 0.031038880348205566, 0.015580127947032452, 0.021693091839551926, -0.03767677769064903, -2.6573610739433207e-05, -0.02062251605093479, 0.01620500534772873, 0.017395824193954468, -0.01390735525637865, 0.028526516631245613, -0.06404042989015579, 0.053637150675058365, 0.02182961255311966, -0.028563300147652626, -0.04246510937809944, -0.01159884873777628, 0.0060418350622057915, -0.052027132362127304, 0.009350964799523354, -0.007428002078086138, 0.017417998984456062, 0.029154062271118164, 0.05020992457866669, 0.03114938549697399, -0.06923235207796097, 0.027133041992783546, -0.06398192048072815, 0.012791215442121029, 0.09419649094343185, 0.024302702397108078, -0.0163707472383976, 0.001183413784019649, 0.00858042761683464, -0.002789000514894724, -0.014705469831824303, 0.015299627557396889, 0.07813684642314911, 0.042046770453453064, 0.024435706436634064, 0.010450848378241062, 0.07750862836837769, 0.012369629926979542, 0.010536570101976395, 0.022652126848697662, -0.025801759213209152, 0.00924586970359087, -0.02708006277680397, -0.05365551635622978, 0.015378224663436413, 0.016797810792922974, 0.01216870453208685, 0.029863543808460236, 0.003333090338855982, -0.011828870512545109, -0.049049343913793564, 0.05680536478757858, -0.02248161844909191, -0.04422582685947418, 0.029158227145671844, 0.026019185781478882, -0.0947173461318016, -0.07586158812046051, -0.012447427958250046, -0.043805673718452454, 0.03057084046304226, 0.010105262510478497, -0.0055786906741559505, -0.04804884269833565, -0.03903248533606529, -0.015988511964678764, -0.02651136741042137, 0.02943670004606247, 0.02787677012383938, 0.005638544913381338, -0.026923345401883125, 0.04576548561453819, -0.030785242095589638, -0.015025932341814041, 0.058125074952840805, -0.04158483073115349, -0.028965016826987267, -0.05040730535984039, 0.04559163376688957, 0.0004130940942559391, 0.03509746491909027, -0.04469669610261917, 0.0015732872998341918, 0.02418600767850876, 0.05763692781329155, 0.011638757772743702, -0.018050016835331917, 0.038751475512981415, 0.030267033725976944, -0.0018059902358800173, -0.00855320505797863, 0.0067059374414384365, 0.04917791113257408, 0.007202749140560627, -0.028504468500614166, -0.02839742787182331, -0.0013788299402222037, 0.043187130242586136, -0.036548271775245667, 0.032679926604032516, -0.0324833020567894, -0.019101742655038834, -0.04996591806411743, 0.0071956864558160305, 0.004655022639781237, -0.01689152792096138, -0.03976612165570259, -0.02895195595920086, 0.07815392315387726, 0.009996095672249794, 0.002300606807693839, 0.025036446750164032, 0.043553151190280914, 0.004764578305184841, -0.09428391605615616, -0.037164974957704544, 0.020780842751264572, 0.030308488756418228, -0.03786740079522133, 0.002343121450394392, -0.004941680934280157, -0.023477043956518173, -0.007464129477739334, 0.03192245960235596, -0.031019313260912895, 0.02204887568950653, 0.005867940839380026, 0.01487751305103302, -0.011923600919544697, 0.01264357939362526, -0.05900518596172333, -0.038598403334617615, -0.06649906933307648, 0.04805614426732063, 0.10351122170686722, -0.005366475787013769, 0.021828385069966316, -0.025532115250825882, 0.028488365933299065, -0.04086558520793915, 0.021353015676140785, 0.003050611587241292, -0.030476581305265427, 0.031043989583849907, -0.0019280511187389493, 0.03220687806606293, -0.07462111115455627, 0.08574719727039337, 0.053099919110536575, 0.05243925750255585, -0.04178713634610176, -0.009547055698931217, -0.009919695556163788, -0.02234000898897648, 0.028452590107917786, 0.022778620943427086, 0.008242323063313961, 0.03524523228406906, -0.02098027430474758, -0.04457421228289604, -0.06878652423620224, 0.014688587747514248, 0.03535450994968414, 0.02015390247106552, 0.004155877511948347, 0.03126462548971176, -0.014367911964654922, -0.024507081136107445, -0.031774427741765976, 0.04609081894159317, 0.03537715598940849, -0.014901317656040192, -0.04138900339603424, -7.224421506892756e-33, -0.015840359032154083, -0.022314928472042084, -0.009769477881491184, -0.08434682339429855, -0.03678452968597412, 0.014643879607319832, -0.06921152770519257, -0.039898015558719635, -0.015456607565283775, -7.543826359324157e-05, -0.007300422061234713, 0.019898569211363792, -0.00828983448445797, 0.025541672483086586, -0.005930804181843996, 0.001752954674884677, 0.030203968286514282, -0.02711825631558895, 0.01827731914818287, 0.025128405541181564, 0.0007901813369244337, 0.005419129505753517, 0.032854657620191574, -0.0568218007683754, -0.04008407145738602, 0.008804797194898129, -0.05521848052740097, -0.04303954541683197, -0.050066858530044556, 0.009496213868260384, -0.001187518355436623, 0.0005275780567899346, -0.005091573111712933, 0.01445892732590437, -0.03487119451165199, -0.09881819039583206, -0.04513673484325409, 0.02223772369325161, -0.044274233281612396, -0.00026729117962531745, -0.10277170687913895, -0.036366354674100876, 0.04201677814126015, -0.03181568905711174, 0.014142869040369987, -0.03896569088101387, 0.043984852731227875, -0.02446410432457924, -0.03301934152841568, -0.04715711623430252, -0.017003744840621948, 0.030521780252456665, -0.03793076053261757, -0.03140788897871971, -0.02068805694580078, -0.0032013754826039076, 0.016999684274196625, 0.007271283306181431, -0.0678514689207077, 0.03064761683344841, -0.005806320812553167, 0.030230527743697166, 0.041838862001895905, 0.02237037383019924, 0.0574837364256382, 0.04572494700551033, 0.0040761204436421394, -0.07986979931592941, -0.04845666140317917, 0.017096685245633125, 0.009305521845817566, 0.0448434092104435, 0.020656973123550415, 0.05461999401450157, 0.07317685335874557, -0.023806998506188393, -0.07922112941741943, 0.07397011667490005, -0.017249351367354393, 0.05392041429877281, 0.0013397317379713058, 0.036251500248909, -0.0024113261606544256, -0.00033471337519586086, 0.00901260506361723, -0.1421363353729248, -0.0036510657519102097, -0.010982741601765156, 0.024408072233200073, 0.010910416021943092, -0.013668244704604149, -0.060063499957323074, 0.00589579064399004, -0.038036081939935684, -0.026910532265901566, 0.00723604578524828, -0.02787613496184349, 0.014057441614568233, -0.012019208632409573, 0.0017585351597517729, -0.06741997599601746, 0.009718578308820724, 0.030764734372496605, 0.0365092009305954, -0.003496067365631461, 0.033845968544483185, 0.04015497490763664, 0.014151197858154774, 0.024075902998447418, -0.007050769869238138, -0.06311827152967453, 0.008958353661000729, 0.046473484486341476, -0.0013614566996693611, 0.0027314124163240194, -0.030033931136131287, -0.026281703263521194, -7.087336416589096e-05, 0.001762955216690898, -0.016019288450479507, -0.03521323204040527, 0.01428383681923151, -0.0016958899796009064, 0.030730200931429863, -0.05782245472073555, 0.010098793543875217, -0.03304562717676163, -0.03841809928417206, 0.1050475612282753, -0.05291455239057541, -0.038471415638923645, -0.017548926174640656, 3.119347411484341e-07, 0.0063704997301101685, -0.040784385055303574, 0.002304061083123088, 0.01574045419692993, 0.014101910404860973, 0.028238419443368912, -0.040471818298101425, 0.015096308663487434, -0.024062946438789368, -0.018384236842393875, -0.004582911264151335, 0.04886878281831741, 0.03748942166566849, 0.009801768697798252, -0.0030043316073715687, 0.03167097270488739, 0.013002784922719002, 0.038041502237319946, 0.00038624004810117185, -0.023417487740516663, -0.006026043556630611, 0.08836749941110611, 0.017225846648216248, -0.021817002445459366, 0.08532741665840149, -0.00312757957726717, 0.04147050902247429, 0.010315577499568462, 0.027423545718193054, 0.039749085903167725, -0.011113831773400307, 0.05570467561483383, 0.00018630284466780722, -0.025780867785215378, -0.028545714914798737, -0.032480303198099136, 0.0401880219578743, 0.02559175342321396, 0.02549748867750168, -0.015077163465321064, -0.018672915175557137, 0.004113613162189722, 0.036311786621809006, -0.04062528535723686, 0.05323435366153717, 0.000554707192350179, -0.04072330519556999, -0.004970932379364967, -0.029127197340130806, 0.037545543164014816, 0.06310619413852692, 0.02110159583389759, -0.03399965912103653, 0.0038965423591434956, -0.0038837986066937447, -0.014933338388800621, -0.004632601048797369, -0.007739017717540264, -0.02945956215262413, -0.05863447114825249, -0.05022052675485611, -0.005250045098364353, -0.015348203480243683, -0.008968757465481758, 0.03111535869538784, 0.02906823717057705, -0.05538679659366608, 2.8992879396810536e-34, -0.02384883351624012, 0.03663162514567375, -0.009177513420581818, -0.006046326830983162, -0.008363567292690277, -0.01460239663720131, 0.01637188531458378, 0.0009408390033058822, -0.005351646337658167, -0.005725149065256119, -0.04403960332274437]

['Chris J. Maddison', 'Dieterich Lawson', 'George Tucker', 'Nicolas Heess', 'Mohammad Norouzi', 'Andriy Mnih', 'Arnaud Doucet', 'Yee Whye Teh']

1705.09279v3

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.

Filtering Variational Objectives

http://arxiv.org/pdf/1705.09279v3

Title Filtering Variational Objectives Summary used surrogate objective maximum likelihood estimation latent variable model evidence lower bound ELBO produce stateoftheart result Inspired consider extension ELBO family lower bound defined particle filter estimator marginal likelihood filtering variational objective FIVOs FIVOs take argument ELBO exploit model sequential structure form tighter bound present result relate tightness FIVOs bound variance particle filter estimator considering generic case bound defined logtransformed likelihood estimator Experimentally show training FIVO result substantial improvement training model architecture ELBO sequential data Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.006874850019812584, 0.0401766411960125, 0.0023397665936499834, -0.037960510700941086, 0.028556382283568382, -0.05808863043785095, 0.02238357998430729, 0.009222697466611862, -0.05419144779443741, 0.01739583909511566, 0.027890967205166817, 0.025587838143110275, -0.010478954762220383, 0.09561523050069809, 0.0010524546960368752, -0.10670018196105957, 0.027140066027641296, -0.007312394212931395, 0.01032878365367651, -0.022699259221553802, 0.025967692956328392, -0.023088818415999413, 0.018328992649912834, 0.05976541340351105, 0.024268733337521553, 0.033189598470926285, 0.0013030526461079717, 0.011973604559898376, 0.026869894936680794, -0.011881240643560886, 0.03432237729430199, -0.015585541725158691, 0.02097289077937603, -0.0076017058454453945, 2.7590792797127506e-06, -0.02323593944311142, -0.044518765062093735, -0.00690695783123374, -0.014474290423095226, 0.0027636787854135036, 0.051513317972421646, 0.03558238968253136, 0.023497745394706726, -0.0007163753034546971, 0.025663111358880997, -0.007170255295932293, 0.003602673765271902, -0.011495730839669704, 0.014901922084391117, 0.016362503170967102, -0.02247585542500019, -0.012082996778190136, -0.011216936632990837, -0.020808441564440727, 0.07097732275724411, -0.022114424034953117, 0.018226798623800278, -0.0014357862528413534, 0.03508028760552406, -0.0008269724203273654, -0.05081517994403839, 0.048966992646455765, 0.02939637564122677, 0.0072896420024335384, 0.033891044557094574, 0.03264468163251877, 0.04093415290117264, -0.00487730884924531, 0.009079480543732643, 0.022275015711784363, -0.006398437544703484, 0.0001679890847299248, -0.0023215909022837877, -0.030047643929719925, -0.03535693511366844, 0.05313564091920853, -0.005893617402762175, 0.0011963536962866783, -0.050428058952093124, 0.010432201437652111, -0.004305877722799778, 0.03807106241583824, 0.006071909796446562, 0.012496902607381344, 0.006217643618583679, 0.05070905014872551, 0.027784157544374466, 0.014455621130764484, 0.03187484294176102, -0.06399598717689514, -0.07396915555000305, -0.0197921022772789, 0.051409948617219925, -0.02340308576822281, -0.05997079983353615, -0.029990235343575478, -0.024799633771181107, 0.001988104311749339, 0.025114333257079124, -0.01789700612425804, 0.047859154641628265, -0.012050916440784931, 0.06250610202550888, 0.005819154903292656, 0.01577339507639408, -0.0037790259812027216, -0.043641347438097, 0.0007120197988115251, -0.052950967103242874, 0.0069761453196406364, -0.02782975696027279, 0.006146373227238655, 0.008181666024029255, 0.013724795542657375, -0.02944173291325569, 0.0023426262196153402, -0.08399000018835068, 9.83907375484705e-05, 0.019426999613642693, -0.04697725176811218, 5.772404620074667e-05, 0.038372740149497986, 0.008598544634878635, -0.018538514152169228, -0.008912194520235062, 0.04376310110092163, -0.03815462067723274, 0.022351255640387535, -0.0009616382303647697, 0.020852673798799515, 0.022757895290851593, 0.024396171793341637, -8.822150994092226e-05, -0.029818929731845856, 0.02158280648291111, -0.026543037965893745, 0.05556034296751022, -0.004350067116320133, -0.003975976724177599, 0.004509069956839085, 0.016680147498846054, -0.011195860803127289, -0.045384034514427185, -0.04147608205676079, -0.008476492948830128, -0.05249107629060745, 0.012272985652089119, -0.01428170781582594, 0.026470977813005447, -0.04007677733898163, 0.0028501534834504128, 0.049961671233177185, -0.021740540862083435, -0.010060126893222332, 0.051098909229040146, -0.00769974896684289, 0.05574239790439606, 0.02580242045223713, 0.010259849950671196, 0.017711132764816284, -0.02662966400384903, 0.010694966651499271, -0.013997750356793404, -0.035890642553567886, -0.01954636164009571, 0.006168147549033165, -0.08149705827236176, -0.036416471004486084, -0.021386675536632538, 0.0101445522159338, 0.004657125100493431, -0.040111370384693146, -0.006660154089331627, -0.024672331288456917, 0.0610724538564682, 0.0003650166909210384, -0.005768464878201485, -0.07691490650177002, 0.029303472489118576, 0.015097077004611492, -0.02659948542714119, -0.024187423288822174, 0.02825801633298397, 0.034531671553850174, -0.07698049396276474, -0.010197913274168968, -0.012599911540746689, -0.007419066037982702, -0.0278758704662323, -0.07636286318302155, -0.009947610087692738, 0.026089267805218697, -0.005792262032628059, 0.004743460565805435, 0.05915043130517006, -0.02624686248600483, -0.0020793424919247627, 0.009917744435369968, 0.04199085384607315, 0.001924868323840201, -0.025571469217538834, -0.06343419849872589, 0.054768308997154236, -0.041224006563425064, 0.00531544117256999, -0.014797153882682323, -0.0427909791469574, -0.01820996217429638, 0.0092886658385396, -0.05433260649442673, 0.02267325110733509, 0.022368265315890312, 0.04189881682395935, -0.0010162111138924956, -0.018381671980023384, 0.01409480907022953, 0.017907923087477684, 0.006757362280040979, -0.024606654420495033, -0.004525728523731232, 0.03753215819597244, 0.008031493984162807, -0.03247939795255661, 0.05438856780529022, -0.0005560838035307825, 0.020237822085618973, 0.03531128540635109, 0.015261523425579071, 0.06096148118376732, -0.01633937656879425, 0.03449749946594238, 0.019883736968040466, 0.06638256460428238, -0.04382352903485298, 0.004422815516591072, 0.03310117498040199, 0.09730181843042374, -0.022107619792222977, 0.008113447576761246, -0.016051732003688812, 0.06635060906410217, 0.0010603269329294562, -0.023117203265428543, -0.012003661133348942, -0.03120969980955124, 0.010736513882875443, -0.0025036586448550224, -0.004598001949489117, 0.010349973104894161, 0.02395150437951088, -0.012359993532299995, 0.011527448892593384, -0.003339779796078801, 0.006144121289253235, 0.04140986129641533, 0.0020232941024005413, 0.0413510762155056, -0.006526908837258816, -0.04679436609148979, 0.0034272577613592148, -0.010250765830278397, -0.023790238425135612, -0.050229232758283615, 0.025121891871094704, 0.03762878477573395, -0.01247335784137249, 0.042010027915239334, -0.05004141107201576, 0.04473653435707092, 0.01234717108309269, -0.03291125223040581, 0.022000698372721672, 0.0039093876257538795, -0.010925614275038242, 0.030106546357274055, 0.027983684092760086, 0.057634204626083374, -0.03879017382860184, -0.026010895147919655, -0.021223455667495728, -0.00024088450300041586, -0.04653492569923401, -0.05774601176381111, -0.008886554278433323, -0.03841882571578026, 0.030985206365585327, 0.033460237085819244, -0.04754161089658737, 0.01927279308438301, 0.0639243796467781, -0.0366191565990448, 0.0022088750265538692, 0.0029815523885190487, -0.0474272184073925, -0.007155747152864933, -0.045842476189136505, 0.0410994254052639, 0.04014187678694725, 0.032425496727228165, 0.016062505543231964, 0.033510468900203705, 0.0008031369070522487, -0.03590238839387894, 0.04304913431406021, -0.06808651983737946, 0.026741156354546547, 0.006696572061628103, -0.01146769616752863, 0.03019949421286583, 0.020115811377763748, 0.0034293662756681442, 0.04127884656190872, -0.022950641810894012, 0.1063796803355217, -0.0224627535790205, -0.02781555987894535, -0.061209529638290405, 0.027838988229632378, -0.05623100697994232, 0.03372645750641823, -0.036162931472063065, -0.006603194400668144, 0.005897435359656811, 0.06745515763759613, 0.0006265686242841184, 0.007509957533329725, 0.009822637774050236, 0.06616667658090591, -0.016656145453453064, 0.07986396551132202, 0.029732467606663704, -0.03900324925780296, 0.0328802764415741, 0.001004256191663444, 0.024159152060747147, 0.038785260170698166, -0.007478530518710613, -0.0664665699005127, -0.03705395758152008, 0.008209132589399815, 0.036218464374542236, 0.021272599697113037, -0.047527991235256195, 0.013654441572725773, 0.08015204966068268, 0.025991545990109444, -0.00882552657276392, 0.010153536684811115, -0.04693209007382393, 0.05164889246225357, -0.05932614952325821, 0.0479389913380146, -0.02415732853114605, -0.02634570375084877, -0.014476999640464783, 0.010925840586423874, 0.04583302140235901, -0.0767434760928154, 0.009356793016195297, -0.03746536374092102, 0.04135451465845108, 0.03218718245625496, 0.008996959775686264, -0.0038952042814344168, -0.028199367225170135, -0.005991173442453146, -0.023465396836400032, -0.034287307411432266, 0.005139871034771204, 0.06775607168674469, 0.10088206827640533, -0.06278789043426514, 0.0042179180309176445, 0.040643710643053055, -0.0110239889472723, -0.00425269128754735, -0.012696394696831703, -0.014075120911002159, 0.026286380365490913, 0.015037641860544682, 0.008677530102431774, 0.043968021869659424, -0.0030440203845500946, 0.028566982597112656, 0.05464758723974228, 0.0034622065722942352, 0.012966175563633442, -0.027262112125754356, 0.02004534937441349, 0.06364935636520386, 0.01857048086822033, -0.09233339130878448, -0.0342002771794796, -0.09372171014547348, 0.01479764562100172, -0.06725408136844635, -0.04133911058306694, 0.03788042813539505, 0.004787965212017298, -0.02684294991195202, 0.038601916283369064, -0.00684119900688529, -0.05855675786733627, 0.007963395677506924, -0.11344648152589798, -0.0028208002913743258, 0.03727103769779205, 0.03331341594457626, -0.024567386135458946, -0.02829550951719284, -0.004171702545136213, -0.007303653750568628, -0.035926736891269684, -0.04581219702959061, 0.03904830664396286, -0.025820637121796608, 0.01918601244688034, -0.023201797157526016, 0.10216958820819855, -0.02085103839635849, -0.008161586709320545, 0.005163903813809156, -0.017303576692938805, -0.02485208585858345, 0.0027871625497937202, -0.020724039524793625, 0.02936282567679882, -0.010493357665836811, 0.029644956812262535, 0.01104818657040596, -0.023338310420513153, 0.0019612698815762997, -0.006982393562793732, -0.016552159562706947, 0.04554497450590134, -0.02968996949493885, -0.008254723623394966, -0.03185131773352623, -0.07425857335329056, -0.10361616313457489, -0.02311593107879162, -0.00639561889693141, 0.04467523843050003, -0.02366558089852333, 0.06943680346012115, -0.029623398557305336, -0.05653056874871254, -0.0017160024726763368, -0.00954666081815958, 0.019751304760575294, 0.03660840913653374, -0.026197491213679314, 0.04530761390924454, -0.018713191151618958, 0.019576296210289, -0.0637306272983551, -0.010236365720629692, -0.11446674168109894, -0.032676734030246735, 0.03860810771584511, 0.10764999687671661, 0.020445233210921288, -0.005045181605964899, -0.0427435040473938, 0.016910690814256668, 0.012713062576949596, -0.007817971520125866, 0.07454043626785278, -0.0018300922820344567, 0.04385800287127495, -0.0033372798934578896, 0.02519155666232109, 0.01286039873957634, 0.02816823683679104, 0.04057067632675171, -0.020862901583313942, -0.007413437590003014, -0.006046950817108154, -0.09383062273263931, 0.03094768337905407, 0.01434767059981823, 0.04199371114373207, -0.010660677216947079, -0.06371354311704636, -0.0699601098895073, 0.015491004101932049, 0.013808961026370525, 0.002452147426083684, -0.02709198370575905, 0.010787660256028175, 0.020173635333776474, 0.024952175095677376, 0.008285341784358025, -0.010770708322525024, 0.0006543435156345367, 0.0068459538742899895, -0.05221977457404137, 0.041578106582164764, -0.029878562316298485, 0.011732899583876133, -0.006349226459860802, 0.03359254449605942, 0.04467468708753586, 0.017516499385237694, 0.026750657707452774, 0.04440818354487419, 0.004477194044739008, 0.047514479607343674, -0.024104217067360878, -0.007547167129814625, -0.04533062502741814, -0.031992681324481964, -0.04961748421192169, 0.007197505794465542, -0.08812360465526581, 0.05938820168375969, 0.04912872612476349, -0.033018313348293304, 0.053364623337984085, -0.06123623624444008, 0.029156995937228203, -0.06122039258480072, 0.07445167750120163, 0.01385410875082016, 0.05423230305314064, 0.04331175982952118, 0.0016820564633235335, -0.008440944366157055, -0.0127125708386302, 0.05468658357858658, 0.05200224369764328, 0.04137643426656723, -0.01383599080145359, -0.030815543606877327, -0.023401258513331413, 0.01869061402976513, 0.01641782373189926, 0.05367528274655342, -0.05404065176844597, 0.014536985196173191, -0.009967541322112083, 0.0010573328472673893, -0.020237479358911514, -0.04996310546994209, 0.037761565297842026, -0.000599327904637903, -0.029624834656715393, -0.006785285193473101, -0.06279643625020981, -0.02597702294588089, -0.03918038681149483, -0.053933076560497284, 0.019886868074536324, 0.04088081419467926, -0.018367959186434746, -7.408088091104923e-33, -0.0628221407532692, -0.018236584961414337, -0.08153736591339111, -0.01783246546983719, -0.02906924858689308, 0.0002116883551934734, -0.003023819299414754, -0.031947966665029526, 0.04113125056028366, -0.026000861078500748, 0.020536212250590324, 0.0011855234624817967, 0.009825082495808601, -0.03933754563331604, 0.03955438360571861, 0.031884681433439255, 0.04043544828891754, 0.0031239097006618977, 0.052247315645217896, -0.039259206503629684, 0.021625230088829994, 0.05032172426581383, 0.008038992993533611, 0.021049892529845238, 0.023381048813462257, 0.048230718821287155, -0.06325626373291016, -0.03316551446914673, -0.05183650553226471, 0.03360697254538536, 0.010252545587718487, -0.02130957879126072, -0.01353165227919817, -0.013514543883502483, -0.015830427408218384, -0.1039951965212822, 0.017000483348965645, -0.008228402584791183, -0.041739948093891144, -0.01707261987030506, -0.03130948916077614, -0.012547733262181282, 0.09268424659967422, 0.01649763062596321, 0.014962321147322655, 0.01622628979384899, 0.03744172677397728, -0.05827435478568077, -0.009062495082616806, -0.007678017020225525, -0.007192350458353758, 0.007632769178599119, -0.017850393429398537, 0.01894707977771759, 0.02458205260336399, 0.03230902552604675, -0.040306366980075836, -0.02822224609553814, -0.01753857731819153, -0.0011956903617829084, 0.026658931747078896, 0.07304836064577103, -0.004979395307600498, 0.026995379477739334, 0.059494007378816605, 0.0019847326911985874, 0.022425062954425812, -0.04588659480214119, -4.8365727707277983e-05, -0.03212358430027962, 0.04430721700191498, 0.04300213232636452, 0.027977492660284042, -0.02315054088830948, 0.08793240040540695, -0.05620430037379265, -0.04506769776344299, 0.05982467904686928, -0.03737110272049904, 0.09452897310256958, -0.008036196231842041, 0.02741296961903572, -0.024076906964182854, 0.014271702617406845, -0.014235385693609715, -0.0927482545375824, -0.016067082062363625, -0.04214496910572052, 0.04083293303847313, -0.02800605446100235, -0.06929253786802292, -0.05225563049316406, 0.0007030218839645386, -0.00725375534966588, 0.025433626025915146, -0.04545138403773308, -0.0031287851743400097, -0.020185258239507675, 0.019954264163970947, 0.012902923859655857, -0.06325880438089371, -0.01195389125496149, 0.04500361531972885, -0.03244848921895027, 0.00039926113095134497, -0.005679748021066189, -0.03705848753452301, -0.003112050471827388, -0.01826702244579792, 0.0018381312256678939, -0.038564085960388184, -0.05619408190250397, 0.009790166281163692, 0.08811066299676895, 0.08825121074914932, -0.03668290004134178, -0.0045373328030109406, 0.07570405304431915, 0.046633802354335785, -0.024935346096754074, -0.021551648154854774, -0.01950124092400074, 0.019630752503871918, 0.048468440771102905, -0.052132606506347656, -0.009693118743598461, -0.015676116570830345, -0.025709684938192368, -0.00485521275550127, 0.007946865633130074, -0.021780885756015778, -0.029997875913977623, 3.2536848948439e-07, -0.008349897339940071, 0.018782692030072212, -0.04719219356775284, 0.020899465307593346, -0.01373874768614769, -0.006587605457752943, -0.00704050762578845, -0.01904856227338314, -0.023305265232920647, -0.007614633534103632, 0.04037420079112053, -0.011979931965470314, 0.026468686759471893, -0.008146833628416061, -0.034298792481422424, -0.06336182355880737, -0.011400800198316574, 0.02069041319191456, -0.01405404880642891, -0.03206039220094681, 0.07120122760534286, 0.052289534360170364, 0.05279050022363663, -0.0246929582208395, 0.042974088340997696, 0.029062194749712944, 0.04141782224178314, -0.044608984142541885, -0.04685308039188385, -0.004673605784773827, -0.012080556713044643, -0.00044284964678809047, -0.019388092681765556, -0.01206924393773079, -0.02247822843492031, -0.0031712630297988653, 0.010438695549964905, 0.047015588730573654, -0.04063137248158455, 0.019889703020453453, 0.03391912952065468, 0.0855899229645729, -0.005098738707602024, 0.0006991667323745787, 0.05592268705368042, 0.01012060884386301, 0.00573804322630167, -0.01582658849656582, -0.026511427015066147, 0.05413507670164108, 0.07181347161531448, -0.031311240047216415, -0.02902175486087799, -0.023254062980413437, -0.03267618641257286, 0.0007060361676849425, -0.03063921071588993, 0.028329793363809586, -0.028429850935935974, -0.04409489408135414, -0.016908233985304832, 0.009654364548623562, -0.03510813042521477, 0.0022341967560350895, -0.011601557955145836, -0.0037611625157296658, -0.051857005804777145, 4.023280025902978e-34, 0.012063184753060341, 0.013843062333762646, -0.03525261580944061, 0.01418565958738327, -0.05135396495461464, -0.0035205488093197346, -0.06628666073083878, 0.03969321772456169, -0.011414936743676662, -0.013073613867163658, -0.03441626578569412]

['Jiaxin Shi', 'Shengyang Sun', 'Jun Zhu']

1705.10119v3

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of noisy estimation and computational infeasibility when applied to models with high-dimensional latent variables. In this paper, we present a new approach named Kernel Implicit Variational Inference that addresses these challenges. As far as we know, for the first time implicit variational inference is successfully applied to Bayesian neural networks, which shows promising results on both regression and classification tasks.

Kernel Implicit Variational Inference

http://arxiv.org/pdf/1705.10119v3

Title Kernel Implicit Variational Inference Summary Recent progress variational inference paid much attention flexibility variational posterior One promising direction use implicit distribution ie distribution without tractable density variational posterior However existing method implicit posterior still face challenge noisy estimation computational infeasibility applied model highdimensional latent variable paper present new approach named Kernel Implicit Variational Inference address challenge far know first time implicit variational inference successfully applied Bayesian neural network show promising result regression classification task Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.010575110092759132, 0.08029486238956451, -0.028552521020174026, 0.009393423795700073, 0.014080696739256382, -0.04454711452126503, -0.006002450827509165, -0.004905517678707838, -0.012617061845958233, 0.03260224685072899, -0.00027383549604564905, 0.05595364049077034, 0.03977024555206299, 0.04732508212327957, 0.06032135710120201, -0.04817724600434303, -0.022052142769098282, -0.026213128119707108, 0.011632549576461315, -0.018579112365841866, 0.007826426066458225, -0.026981104165315628, 0.007108584046363831, 0.017910439521074295, -0.09026707708835602, 0.029400868341326714, -0.012932751327753067, 0.006252341903746128, 0.022793659940361977, 0.003835147712379694, 0.05417732521891594, 0.012202716432511806, 0.01122168730944395, -0.014249150641262531, 2.183637889174861e-06, -0.02462136745452881, -0.010328433476388454, -0.0030025970190763474, 0.022145483642816544, 0.004013196565210819, 0.030530326068401337, 0.024219779297709465, -0.004660938400775194, -0.02451968565583229, -0.008141870610415936, -0.01699124462902546, 0.0701824426651001, 0.1453711837530136, -0.007419545669108629, -0.0052910540252923965, -0.022231174632906914, -0.03468812629580498, -0.00913466326892376, -0.024744367226958275, 0.059929296374320984, -0.025709770619869232, 0.025008492171764374, 0.028529370203614235, -0.045266903936862946, 0.003582962090149522, -0.01988385058939457, 0.07088392227888107, 0.07055690884590149, -0.03409171104431152, 0.018658485263586044, 0.08494455367326736, 0.026916123926639557, 0.0038649961352348328, 0.006909252144396305, 0.040335457772016525, -0.010796214453876019, -0.006832079496234655, 0.027688564732670784, -0.03654497489333153, -0.004652070347219706, 0.061834488064050674, -0.0018554509151726961, -0.014720091596245766, 0.011041241697967052, -0.006002840586006641, 0.015001358464360237, 0.046970151364803314, 0.03446384519338608, 0.02356910891830921, 0.04459332302212715, 0.03800482302904129, 0.005285570397973061, -0.004225392825901508, 0.027977509424090385, -0.009909313172101974, -0.09011753648519516, -0.011618786491453648, -0.006591562181711197, -0.006934648845344782, -0.005145140923559666, -0.027905698865652084, -0.00996033102273941, -0.02230777032673359, 0.014922301284968853, -0.06900493800640106, 0.017095031216740608, 0.013827409595251083, -0.015974782407283783, -0.05781334638595581, -0.01561805047094822, 0.013975064270198345, -0.01967240497469902, 0.016253279522061348, -0.010692584328353405, 0.024856822565197945, 0.0070785582065582275, 0.011703647673130035, 0.0009543286287225783, 0.012019455432891846, 0.040260642766952515, 0.00027135852724313736, -0.04527597874403, 0.03976055979728699, -0.0067748758010566235, -0.05402876064181328, 0.000628259964287281, 0.10083315521478653, -0.01593824289739132, 0.03150144964456558, -0.017019327729940414, -0.014856253750622272, -0.03571121767163277, 0.062493398785591125, -0.024637404829263687, -0.00343028805218637, 0.0005698937457054853, 0.010098019614815712, 0.014082356356084347, 0.00816003791987896, -0.0029067641589790583, 0.015450340695679188, -0.02201750874519348, 0.04330844432115555, -0.03810866177082062, 0.02386617287993431, -0.048167020082473755, -0.015681639313697815, -0.01912016049027443, -0.0993281751871109, -0.014578308910131454, -0.0015915421536192298, 0.007293961010873318, -0.006848243530839682, -0.0007468045805580914, -0.025696024298667908, -0.026403725147247314, 0.038970183581113815, 0.07917077094316483, -0.03367753326892853, 0.15084901452064514, -0.022544240579009056, 0.002415029564872384, 0.046445149928331375, 0.020150361582636833, 0.026763787493109703, -0.01213734969496727, 0.030460648238658905, -0.0655994713306427, 0.002618058118969202, 0.008533243089914322, -0.021520886570215225, -0.08310410380363464, -0.04696417227387428, -0.012859850190579891, 0.016409127041697502, 0.0394350029528141, 0.015580604784190655, 0.023532921448349953, -0.04019666463136673, 0.028006592765450478, 0.06155095621943474, -0.023041464388370514, -0.018201757222414017, 0.022936798632144928, 0.004695224110037088, -0.007629175204783678, -0.0374525748193264, 0.007775073405355215, 0.03150055184960365, -0.02592967450618744, -0.01764620654284954, 0.022129980847239494, -0.05624303221702576, -0.01070490013808012, -0.08067309856414795, 0.03477584943175316, 0.00814276933670044, -0.03403425216674805, -0.022355403751134872, 0.09219545125961304, -0.03827633336186409, 0.02179969847202301, 0.005303327925503254, 0.037050846964120865, 0.013403798453509808, -0.033326052129268646, -0.01710144616663456, 0.0489656999707222, -0.09550096094608307, -0.07181372493505478, -0.016653316095471382, 0.009858905337750912, 0.020553935319185257, -0.03903289511799812, -0.07458869367837906, 0.030050702393054962, -0.03362102434039116, 0.030073529109358788, -0.00965447723865509, -0.021133791655302048, -0.005438024178147316, 0.0513467900454998, -0.006859034299850464, -0.041304100304841995, 0.024982009083032608, 0.05576488748192787, -0.00849806796759367, 0.02674412727355957, 0.0004216146480757743, -0.037205446511507034, 0.02894040010869503, 0.04254642874002457, 0.008782539516687393, 0.023795444518327713, -0.010740886442363262, -0.008371664211153984, -0.01917634904384613, 0.012446783483028412, -0.03343119099736214, -0.061498064547777176, -0.03539210185408592, -0.016514858230948448, -0.03508475050330162, 0.024661291390657425, 0.0019871476106345654, 0.03620515763759613, -0.03357180580496788, -0.05210261791944504, -0.015863606706261635, 0.04915735125541687, 0.014011356979608536, -0.02089550346136093, -0.002089387970045209, 0.000527386786416173, 0.02807893231511116, 0.021510383114218712, -0.028049709275364876, 0.0009574569412507117, -0.029331805184483528, 0.02664904296398163, 0.02330455370247364, 0.03732558339834213, 0.042417652904987335, -0.020038897171616554, -0.002877150196582079, -0.023146117106080055, -0.031476449221372604, 0.017846789211034775, -0.03016667813062668, 0.01947909966111183, 0.004463118501007557, 0.025500010699033737, -0.0473533533513546, 0.01137709803879261, -0.0019777114503085613, -0.0517088882625103, -0.02227127179503441, 0.03086213767528534, 0.019476398825645447, -0.0026251627132296562, 0.012293773703277111, 0.10284042358398438, 0.003776348428800702, -0.06505170464515686, 0.014016970992088318, 0.019041355699300766, 0.04243200272321701, -0.020828738808631897, -0.02308857999742031, -0.016505392268300056, 0.050547923892736435, 0.04142230004072189, -0.017786331474781036, 0.026546679437160492, 0.007339192554354668, -0.03794257715344429, 0.0190255269408226, 0.01160495262593031, -0.04036200791597366, -0.05241354554891586, -0.05483805760741234, 0.08975336700677872, 0.034020956605672836, 0.020207174122333527, -0.005089235492050648, 5.483570203068666e-05, 0.02215704880654812, -0.030148765072226524, 0.017485421150922775, -0.03458217531442642, -0.033980902284383774, 0.012336822226643562, -0.0533280223608017, -0.030720528215169907, 0.0026519617531448603, 0.07049635052680969, 0.022941675037145615, -0.017209239304065704, 0.06752347201108932, -0.027139754965901375, -0.010627790354192257, -0.06500264257192612, 0.0692787617444992, -0.01362612098455429, -0.00171450967900455, -0.016382679343223572, -0.039643000811338425, 0.024416062980890274, 0.008467155508697033, 0.025068728253245354, 0.04171774536371231, -0.026953458786010742, 0.04535367339849472, -0.020481066778302193, 0.02622918225824833, -0.015939565375447273, 0.04146099090576172, -0.0036392880138009787, -0.017431510612368584, 0.024907713755965233, -0.019703315570950508, -0.011961842887103558, 0.05023382231593132, -0.009331772103905678, 0.04276420921087265, 0.02042318880558014, 0.014225696213543415, -0.0497015081346035, -0.046320054680109024, 0.04243556410074234, 0.012884831055998802, -0.0361752025783062, -0.032377276569604874, 0.016390379518270493, -0.00787336751818657, -0.014080775901675224, 0.015379778109490871, -0.022202711552381516, -0.020831437781453133, 0.017756331712007523, 0.046544115990400314, 0.060746196657419205, 0.013257701881229877, -0.04223852604627609, -0.0016365641495212913, 0.007488659583032131, 0.006903626956045628, -0.002949401969090104, 0.024865593761205673, -0.052513252943754196, 0.024404507130384445, -0.030317867174744606, 0.037156667560338974, 0.01839151419699192, 0.03784436732530594, 0.029844211414456367, 0.0038420886266976595, 0.001342220464721322, 0.061230577528476715, -0.032212600111961365, -0.0757664293050766, -0.0018234699964523315, -0.03296903893351555, 0.006292030680924654, -0.012051834724843502, 0.020850682631134987, 0.011363185942173004, 0.004970633890479803, -0.016473431140184402, -0.02062179520726204, -0.002797930035740137, -0.037745654582977295, 0.02209082432091236, -0.021050764247775078, 0.044318150728940964, 0.008408891037106514, -0.04158574342727661, 0.0014212599489837885, -0.08229900896549225, 0.026811333373188972, -0.013572817668318748, -0.03722979500889778, -0.06208186596632004, 0.012216635048389435, 0.006391905713826418, 0.046951450407505035, 0.012088822200894356, -0.034159671515226364, 0.0405057892203331, -0.07134749740362167, -0.019963720813393593, -0.0008393027237616479, 0.018024848774075508, -0.06556286662817001, -0.01953599788248539, -0.008872576989233494, -0.0871492400765419, -0.046628691256046295, -0.04544268175959587, 0.065493643283844, 0.020705774426460266, -0.003733439138159156, -0.01484798826277256, 0.0386667400598526, -0.01183877419680357, 0.025337588042020798, -0.015130328014492989, 0.052482664585113525, -0.013752958737313747, 0.0021020781714469194, -0.04050607606768608, 0.006139281205832958, 0.020875539630651474, -0.013163695111870766, -0.018710514530539513, -0.035755012184381485, 0.004645404405891895, -0.010962266474962234, -0.027044355869293213, 0.0815514624118805, -0.02319749817252159, 0.01542880479246378, -0.013391304761171341, -0.10964749753475189, -0.048068586736917496, 0.039720673114061356, -0.03154734894633293, 0.030622750520706177, -0.020908067002892494, 0.020220668986439705, 0.009839128702878952, -0.041140105575323105, -0.07665573805570602, 0.03427022323012352, 0.07727416604757309, 0.014680257067084312, 0.016402646899223328, -0.015734994783997536, 0.008786172606050968, -0.03342653438448906, -0.03559008240699768, -0.0025599764194339514, -0.07505367696285248, -0.05603335425257683, -0.026135358959436417, 0.047717805951833725, -0.008084992878139019, 0.006548458710312843, -0.04487728700041771, -0.04120388254523277, 0.09698276966810226, 0.0008695855503901839, 0.05898205190896988, 0.02732238732278347, 0.016935735940933228, 0.016030332073569298, 0.012396104633808136, 0.02782375179231167, -0.014132337644696236, 0.0674980878829956, -0.024686723947525024, -0.051502205431461334, 0.028463585302233696, -0.05282558128237724, -0.030317397788167, -0.056087471544742584, 0.022411243990063667, 0.030664633959531784, -0.04277266561985016, -0.07871222496032715, -0.02540634199976921, 0.013169757090508938, -0.03251984715461731, -0.01556807104498148, 0.009897692129015923, 0.028803031891584396, 0.08347182720899582, -0.057896245270967484, -0.07160674035549164, 0.05519142001867294, 0.02797624096274376, -0.03851737454533577, 0.0023047944996505976, 0.07496568560600281, 0.016652557998895645, -0.008698361925780773, 0.014009695500135422, -0.020083509385585785, -0.0683794617652893, 0.006108202040195465, 0.019180815666913986, 0.0038918079808354378, 0.03328916057944298, -0.0051858313381671906, 0.027536185458302498, -0.057933397591114044, -0.022747153416275978, -0.03139558434486389, -0.02643081545829773, -0.06825833022594452, 0.014175977557897568, 0.03242238610982895, -0.04559091478586197, 0.028463831171393394, -0.016788775101304054, 0.025346122682094574, -0.06477036327123642, 0.07537906616926193, 0.014839842915534973, -0.0012736632488667965, 0.07569026947021484, -0.005867134779691696, 0.0024998527951538563, 0.0358293391764164, 0.0006749780150130391, 0.04308086633682251, 0.000738865346647799, -0.0637320950627327, -0.007157054729759693, -0.016095958650112152, 0.04498240351676941, 0.04954111948609352, 0.027339063584804535, -0.01817515678703785, 0.0342535600066185, 0.0349741205573082, -0.06951572746038437, 0.02731912024319172, -0.003952536266297102, 0.023386530578136444, 0.020015183836221695, -0.03200434148311615, 0.034138794988393784, -0.01738571561872959, -0.05357372760772705, -0.05788383260369301, -0.0282016359269619, -0.022946149110794067, -0.025269100442528725, -0.06868467479944229, -6.226910959780379e-33, -0.005414183251559734, -0.04299916699528694, -0.0882672443985939, -0.01411115750670433, -0.04781027510762215, 0.06421886384487152, -0.07025399059057236, -0.005385282915085554, 0.02652069553732872, 0.012556590139865875, 0.008789877407252789, 0.03254809230566025, 0.009090018458664417, 0.013418166898190975, 0.062419332563877106, -0.012423724867403507, 0.02495308592915535, -0.01508856937289238, 0.05605081468820572, 0.030902422964572906, 0.04132299870252609, 0.03024163842201233, 0.027592195197939873, -0.02631189487874508, 0.025789177045226097, 0.014608420431613922, -0.026914874091744423, -0.009855194948613644, 0.004379869904369116, 0.012805275619029999, -0.041449472308158875, 0.03266644477844238, 0.02209467627108097, 0.04817245528101921, 0.013558154925704002, -0.03286517411470413, -0.03967060148715973, -0.0336206816136837, -0.04946684092283249, 0.03860423341393471, -0.04493904486298561, 0.01589784398674965, 0.06290167570114136, 0.036579374223947525, -0.029723940417170525, -0.010038531385362148, 0.05774374678730965, 0.016295870766043663, 0.02905026264488697, 0.007440431509166956, -0.0008671898394823074, 0.027020752429962158, -0.011286999098956585, 0.025587555021047592, 0.009909999556839466, 0.0045080529525876045, -0.011258115991950035, -0.04617908224463463, 0.01006558258086443, -0.00042708072578534484, -0.016478581354022026, -0.018818428739905357, 0.03220605477690697, 0.05395219847559929, 0.03597711771726608, 0.01160154677927494, -0.008998986333608627, -0.06189309433102608, -0.025015676394104958, -0.0721728727221489, -0.01961784064769745, 0.06196456030011177, -0.024750806391239166, 0.008687594905495644, 0.0674632266163826, -0.038334861397743225, -0.040107402950525284, 0.04975011199712753, 0.00436472799628973, -0.020373808220028877, 0.019502276554703712, -0.008725924417376518, -0.01721123978495598, -0.010740124620497227, -0.017786145210266113, -0.06741117686033249, 0.004817894659936428, -0.03352011367678642, 0.013812936842441559, -0.00887752790004015, 0.007232297211885452, -0.04304730147123337, 0.03726821020245552, -0.025614449754357338, 0.06725630164146423, -0.020423611626029015, 0.029314855113625526, 0.04505780339241028, 0.03220934793353081, -0.02983725629746914, -0.07509291172027588, -0.0016138667706400156, -0.004253707360476255, -0.000502389797475189, 0.02442522719502449, 0.02201828919351101, -0.04632570222020149, -0.0012928757350891829, 0.020006481558084488, -0.017958998680114746, -0.014781498350203037, -0.06431242823600769, -0.02273954264819622, 0.1015072613954544, 0.038962267339229584, -0.03296820819377899, -0.02161421999335289, 0.053304772824048996, 0.029083551838994026, 0.013480226509273052, 0.014484505169093609, -0.02144307643175125, 0.0280813779681921, 0.0005514643853530288, -0.05862494930624962, 0.02186943031847477, -0.0033363676629960537, -0.05522102490067482, -0.0326310433447361, -0.08214914798736572, -0.007463294547051191, -0.021398015320301056, 2.7445670980341674e-07, 0.02320854738354683, -0.03670406714081764, -0.026692871004343033, -0.0003373719519004226, 0.01416497491300106, 0.01538364589214325, 0.010398821905255318, -0.0008346250979229808, -0.03690072149038315, -0.03284325823187828, 0.03146439418196678, -0.023016002029180527, 0.017045993357896805, 0.00753774493932724, 0.00261699128895998, -0.07889112830162048, -0.020972946658730507, 0.029876641929149628, 0.003376337932422757, 0.009922969155013561, 0.08217784762382507, 0.06552352756261826, 0.017385415732860565, -0.029438383877277374, 0.03488386049866676, 0.02558925561606884, 0.03814889118075371, 0.018437065184116364, -0.012501833960413933, -0.022738231346011162, 0.028934022411704063, -0.004246243275702, 0.041232604533433914, 0.033339448273181915, -0.033643219619989395, 0.02927289344370365, 0.028325917199254036, 0.030430028215050697, -0.0016074231825768948, -0.027770930901169777, -0.006594019941985607, 0.04087333008646965, 0.05502545088529587, -0.02816716954112053, 0.037658121436834335, -0.0016946885734796524, -0.04909912496805191, -0.00965787097811699, -0.00048203649930655956, 0.04824640974402428, 0.06285152584314346, -0.008043384179472923, -0.00777808204293251, 0.003612034022808075, 0.008954305201768875, -0.013394810259342194, -0.028098879382014275, -0.06377964466810226, 0.0046580275520682335, 0.01921306923031807, -0.053105678409338, -0.01081794872879982, 0.008966567926108837, -0.041180968284606934, 0.0801856592297554, 0.02129623293876648, 0.0006663725362159312, 2.5941153717056833e-34, 0.002122911624610424, 0.031094295904040337, -0.02434171363711357, 0.0007481052307412028, -0.006213523913174868, 0.0018548667430877686, 0.03333854675292969, 0.0041854907758533955, 0.013640059158205986, -0.05259772017598152, -0.05570998787879944]

['Julien Perez', 'Tomi Silander']

1705.10993v1

Partially observable environments present an important open challenge in the domain of sequential control learning with delayed rewards. Despite numerous attempts during the two last decades, the majority of reinforcement learning algorithms and associated approximate models, applied to this context, still assume Markovian state transitions. In this paper, we explore the use of a recently proposed attention-based model, the Gated End-to-End Memory Network, for sequential control. We call the resulting model the Gated End-to-End Memory Policy Network. More precisely, we use a model-free value-based algorithm to learn policies for partially observed domains using this memory-enhanced neural network. This model is end-to-end learnable and it features unbounded memory. Indeed, because of its attention mechanism and associated non-parametric memory, the proposed model allows us to define an attention mechanism over the observation stream unlike recurrent models. We show encouraging results that illustrate the capability of our attention-based model in the context of the continuous-state non-stationary control problem of stock trading. We also present an OpenAI Gym environment for simulated stock exchange and explain its relevance as a benchmark for the field of non-Markovian decision process learning.

Non-Markovian Control with Gated End-to-End Memory Policy Networks

http://arxiv.org/pdf/1705.10993v1

Title NonMarkovian Control Gated EndtoEnd Memory Policy Networks Summary Partially observable environment present important open challenge domain sequential control learning delayed reward Despite numerous attempt two last decade majority reinforcement learning algorithm associated approximate model applied context still assume Markovian state transition paper explore use recently proposed attentionbased model Gated EndtoEnd Memory Network sequential control call resulting model Gated EndtoEnd Memory Policy Network precisely use modelfree valuebased algorithm learn policy partially observed domain using memoryenhanced neural network model endtoend learnable feature unbounded memory Indeed attention mechanism associated nonparametric memory proposed model allows u define attention mechanism observation stream unlike recurrent model show encouraging result illustrate capability attentionbased model context continuousstate nonstationary control problem stock trading also present OpenAI Gym environment simulated stock exchange explain relevance benchmark field nonMarkovian decision process learning Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.024732718244194984, 0.01664862409234047, -0.02197991870343685, -0.03774814307689667, 0.022393692284822464, -0.009015173651278019, 0.01819654554128647, -0.02713029459118843, -0.014965947717428207, 0.0020225439220666885, -0.015060298144817352, 0.005750337149947882, -0.061916615813970566, 0.08552317321300507, 0.02859872579574585, -0.04588259756565094, 0.040953129529953, -0.013659107498824596, 0.006827433127909899, 0.018088001757860184, 0.038390081375837326, -0.07492181658744812, 0.017429621890187263, 0.017321281135082245, 0.005087070632725954, -0.021485943347215652, -0.04327423498034477, -0.045240893959999084, 0.026744389906525612, -0.07421544194221497, 0.04585718736052513, -0.045667946338653564, 0.0263195987790823, 0.018171845003962517, 2.4832270355545916e-06, -0.02864566259086132, 0.00462650740519166, -0.03498188778758049, 0.034658875316381454, -0.05711144953966141, -0.0012695721816271544, -0.02478092722594738, 0.009296664036810398, 0.032625239342451096, -0.03959309682250023, -0.013168028555810452, 0.05562412366271019, 0.07990042120218277, 0.03931634500622749, 0.07922715693712234, 0.014496819116175175, -0.018202003091573715, 0.04416941851377487, -0.0471305325627327, 0.028173303231596947, -0.08693166822195053, 0.017487285658717155, -0.02790803648531437, -0.01640891656279564, -0.03952859342098236, -0.07327418029308319, 0.013257239945232868, 0.04657841846346855, 0.00755429919809103, 0.005304161924868822, 0.013066139072179794, 0.04164307191967964, 0.025804974138736725, -0.022267388179898262, 0.03004862181842327, -0.03505054488778114, 0.00412072753533721, 0.04995636269450188, -0.011306065134704113, -0.010085816495120525, 0.002062635263428092, -0.01695229671895504, 0.052927013486623764, -0.02347216010093689, 0.02738122269511223, -0.010047012008726597, 0.08999089896678925, -0.008829331956803799, -0.0012632664293050766, -0.0006578864413313568, 0.032827746123075485, -0.05362619832158089, -0.021660588681697845, 0.0056415642611682415, -0.015923161059617996, -0.005577548872679472, -0.04914701357483864, 0.010646925307810307, 0.036838483065366745, -0.005005378741770983, 0.0003735134669113904, -0.02164594829082489, -0.030080167576670647, -0.027581965550780296, -0.07083351165056229, 0.007956216111779213, 0.028610600158572197, -0.011301753111183643, 0.02382073923945427, -0.04129061475396156, 0.05407223850488663, -0.06894716620445251, 0.005931689403951168, -0.0037788799963891506, 0.03907625377178192, -0.037135928869247437, 0.020935729146003723, -0.0225518848747015, 0.07917729765176773, 0.015268532559275627, -0.025652803480625153, -0.06719304621219635, 0.029302673414349556, -0.05265997722744942, 0.028112558647990227, 0.01217283122241497, 0.04092288017272949, -0.02521381713449955, 0.020947108045220375, -0.06609374284744263, -0.0026027446147054434, -0.019809819757938385, 0.04010002315044403, 0.012099746614694595, 0.019206296652555466, 0.007581715006381273, 0.01766202785074711, -0.021216794848442078, 0.0468185655772686, -0.032172687351703644, 0.11298030614852905, 0.02217479981482029, 0.01168777234852314, -0.06295768916606903, -0.0055909124203026295, 0.0399727001786232, -0.03161214292049408, 0.017107926309108734, -0.010059067979454994, -0.044787973165512085, -0.04594138637185097, -0.05805616453289986, 0.021861281245946884, 0.01907893270254135, -0.01848667301237583, 0.005412047263234854, 0.07033742219209671, 0.05769374594092369, -0.07988161593675613, -0.003941548056900501, -0.018916621804237366, -0.005255451425909996, 0.054794732481241226, 0.037020113319158554, 0.01661989837884903, 0.023657403886318207, 0.03013555146753788, 0.022877709940075874, -0.03216566517949104, 0.0828499048948288, -0.023098058998584747, -0.028537306934595108, -0.004531266167759895, 0.028777537867426872, -0.02231275849044323, 0.05404093116521835, -0.005807020235806704, 0.009753525257110596, -0.03006661869585514, 0.04796891286969185, -0.02878142148256302, -0.00222783163189888, -0.012514526955783367, -0.002935253083705902, -0.013206414878368378, -0.050634004175662994, 0.00921999104321003, -0.020339161157608032, 0.07812652736902237, 0.003664138028398156, 0.014071328565478325, -0.023769505321979523, -0.024309497326612473, -0.06259714812040329, -0.024122172966599464, 0.051229845732450485, -0.05373376980423927, 0.019662246108055115, 0.0077174087055027485, 0.040884096175432205, -0.015560886822640896, -0.057136084884405136, 0.002053089439868927, -0.018198514357209206, 0.05801612138748169, -0.027665477246046066, -0.05671505257487297, 0.019035499542951584, -0.01760787144303322, -0.014197210781276226, -0.05936465784907341, 0.015538382343947887, -0.06910813599824905, -0.020097404718399048, 0.003227595705538988, 0.0007934526656754315, 0.007132635917514563, -0.04870333895087242, -0.06262169778347015, -0.004208759870380163, 0.017708178609609604, 0.014577586203813553, 0.022355392575263977, -0.08158457279205322, 0.03418019413948059, -0.016613192856311798, 0.07850166410207748, 0.002336291829124093, 0.011950653046369553, -0.017659353092312813, -0.038330789655447006, 0.012042309157550335, 0.000674819340929389, 0.02454553358256817, -0.025638943538069725, 0.036163490265607834, 0.006066740956157446, -0.007085385266691446, -0.025603894144296646, -0.023997655138373375, 0.040296345949172974, -0.0885680615901947, -0.000617258541751653, 0.011053374968469143, 0.009260347113013268, 0.05228755623102188, 0.006407781038433313, -0.014479790814220905, -0.09574916958808899, 0.044308748096227646, 0.004923299420624971, 0.051736876368522644, -0.015324464067816734, -0.017946090549230576, 0.048328373581171036, 0.022759130224585533, 0.017146633937954903, 0.021143192425370216, -0.05074801295995712, 0.02299349568784237, -0.016278347000479698, 0.04184189811348915, -0.0068009039387106895, -0.03503276780247688, 0.0214236993342638, 0.02739960141479969, -0.03303941711783409, 0.009510267525911331, 0.006661489140242338, -0.03417779877781868, 0.016496840864419937, 0.01746267080307007, 0.0011089729377999902, 0.014248421415686607, -0.0057052928023040295, 0.010044076479971409, 0.020949507132172585, 0.007495560683310032, 0.003089373931288719, -0.072482630610466, -0.055607449263334274, 0.05355262756347656, -0.009048395790159702, -0.026807544752955437, 0.010450745932757854, 0.04082905128598213, 0.033158078789711, -0.002450990956276655, -0.011217883788049221, 0.002966562518849969, 0.011671638116240501, -0.0013330354122444987, -0.03566921874880791, -0.014117470942437649, 0.02279789000749588, 0.025380007922649384, 0.06420667469501495, -0.032079920172691345, 0.01924518495798111, -0.020201077684760094, -0.025706404820084572, -0.004448814317584038, 0.08176131546497345, 0.029402561485767365, 0.035228025168180466, -0.023843184113502502, 0.026584304869174957, -0.02774897776544094, 0.05254548788070679, -0.034133292734622955, -0.00630281213670969, 0.019778598099946976, 0.05142665654420853, 0.015671178698539734, 0.053179409354925156, -0.03315575793385506, -0.01492307335138321, -0.0476284921169281, 0.035387344658374786, 0.02714272029697895, -0.012423906475305557, -0.028180351480841637, 0.04222806170582771, -0.05054772272706032, 0.013128436170518398, -0.010906117036938667, -0.04237695783376694, 0.03885585814714432, 0.07648207247257233, -0.024077415466308594, -0.018500957638025284, -0.024045197293162346, -0.018640249967575073, 0.006578401662409306, 0.015879863873124123, 0.0010778118157759309, -0.025626005604863167, -0.05227065458893776, -0.017898280173540115, -0.033392284065485, -0.031771883368492126, -0.00011508540046634153, 0.00011244459892623127, 0.03844618797302246, -0.006940745748579502, 0.007847963832318783, 0.015880845487117767, -0.030449790880084038, 0.026867924258112907, -0.010373146273195744, 0.028499776497483253, -0.017293782904744148, -0.02980785258114338, -0.018405048176646233, 0.006769431289285421, 0.00144704501144588, 0.020651184022426605, -0.05118817090988159, -0.01794411614537239, 0.021833080798387527, -0.000637104210909456, 0.05133694037795067, -0.01468881219625473, 0.009161136113107204, -0.050208304077386856, 0.05024008825421333, 0.03044220246374607, 0.05659003555774689, -0.03383719176054001, -0.03963033854961395, -0.007836156524717808, -0.015108195133507252, -0.05374063923954964, -0.010201595723628998, 0.05002933368086815, -0.047881830483675, -0.06881961971521378, -0.013281651772558689, 0.011256533674895763, -0.030311984941363335, -0.04015239700675011, -0.01347449328750372, -0.011582562699913979, -0.03684667497873306, -0.007825356908142567, 0.016412964090704918, -0.01366240531206131, 0.012295952998101711, -0.02938568964600563, 0.05207836255431175, -0.0032069121953099966, -0.05512307584285736, -0.028115345165133476, -0.060836002230644226, 0.04467026889324188, -0.033975567668676376, -0.10323349386453629, -0.04194103553891182, -0.004321242216974497, 0.00203977944329381, -0.008963114582002163, -0.0386011004447937, 0.042308080941438675, 0.02564403787255287, -0.003668329445645213, 0.001324388780631125, 0.002257467480376363, 0.01364789716899395, -0.0005074245273135602, -0.055667128413915634, -0.0005770813440904021, 0.07944783568382263, -0.012616069056093693, -0.03403878211975098, -0.02269020490348339, -0.008171623572707176, -0.01959933340549469, -0.00488327257335186, -0.0005905360449105501, 0.022093160077929497, 0.018788672983646393, -0.038891978561878204, -0.010904254391789436, 0.08457339555025101, 0.03823466598987579, 0.042093388736248016, -0.01458563469350338, 0.023777266964316368, -0.028686901554465294, -0.04745715856552124, -0.02453472837805748, -0.007705256808549166, 0.06696987897157669, -0.02610049583017826, -0.02967020869255066, -0.03309445083141327, -0.08251210302114487, -0.00907428190112114, 0.01565438136458397, -0.0537857785820961, 0.00532419141381979, -0.02130378969013691, 0.029783612117171288, -0.02520792745053768, -0.063023142516613, -0.05073351785540581, -0.05153471976518631, 0.060375865548849106, -0.00012158492609160021, 0.002913782373070717, 0.07420585304498672, -0.017133042216300964, -0.02113049104809761, -0.021524064242839813, 0.05066560581326485, 0.01770283468067646, -0.06356163322925568, 0.05295085906982422, 0.02700343169271946, -0.010788559913635254, -0.020079893991351128, -0.04543859884142876, -0.022291433066129684, -0.015606504864990711, -0.014906469732522964, 0.05185311660170555, 0.007297918666154146, -0.00014256777649279684, -0.020230598747730255, 0.018640222027897835, -0.015967154875397682, -0.024693675339221954, 0.020825089886784554, -0.005604571662843227, 0.07257024198770523, 0.0346200093626976, -0.00927000306546688, 0.02031220868229866, -0.006346100475639105, 0.037164874374866486, 0.005838827695697546, 0.004115039948374033, 0.0017744216602295637, 0.024832312017679214, -0.00987036433070898, -0.06309568136930466, 0.03139737993478775, 0.04495995491743088, -0.022816473618149757, -0.024982333183288574, 0.024137010797858238, 0.05574381351470947, 0.021578805521130562, -0.03373117744922638, 0.020954465493559837, 0.031036971136927605, 0.0021593160927295685, 0.011408223770558834, -0.04047541320323944, 0.04165598750114441, -0.09271809458732605, 0.047673244029283524, 0.0443408228456974, -0.01723352074623108, 0.06658802926540375, -0.028643816709518433, 0.02224525436758995, 0.00038569228490814567, -0.007330289576202631, 0.04851672425866127, 0.03221618011593819, 0.0013107110280543566, 0.06277769058942795, 0.019642028957605362, 0.030068818479776382, -0.01929265260696411, -0.04497028514742851, 0.009174658916890621, -0.006218717433512211, -0.0033835009671747684, 0.039707496762275696, 0.043575137853622437, -0.02797112986445427, -0.047751449048519135, -0.039581622928380966, 0.0328294113278389, -0.012595879845321178, 0.02832046151161194, -0.049420066177845, 0.032476574182510376, 0.02888602204620838, 0.018081624060869217, -0.023791957646608353, -0.01672055944800377, 0.05443858727812767, 0.0669981837272644, 0.02447538636624813, -0.02901245467364788, 0.024575604125857353, 0.006280349567532539, 0.018381468951702118, 0.03959764540195465, 0.026945600286126137, 0.014258911833167076, 0.02755146101117134, -0.03451111912727356, 0.00630968390032649, 0.04348626360297203, 0.031457673758268356, 0.028575854375958443, -0.018144555389881134, 0.03852052986621857, -0.07194875180721283, -0.006793192587792873, 0.040910542011260986, -0.029300279915332794, 0.007010715082287788, 0.03999838978052139, -0.003943820483982563, -0.07829215377569199, -6.205774836668625e-33, 0.00037389781209640205, -0.03341313824057579, 0.01148746907711029, -0.03464724123477936, -0.019108522683382034, -0.01147865317761898, -0.023844100534915924, -0.05786837264895439, 0.020736010745167732, -0.01707121543586254, -0.00435276236385107, 0.03250477835536003, 0.007852685637772083, 0.00880417786538601, 0.05960863083600998, -0.040186963975429535, 0.009705282747745514, -0.005806236527860165, 0.021749673411250114, 0.003133751219138503, 0.07124984264373779, 0.06221267580986023, 0.014482402242720127, -0.03836110606789589, -0.0008383184322156012, 0.029118148609995842, -0.014201643876731396, -0.025155987590551376, -0.01853594183921814, 0.05668478459119797, 0.013622215017676353, 0.01696089096367359, 0.0026902465615421534, -0.10903545469045639, -0.012044395320117474, 0.03379015997052193, -0.014707837253808975, -0.0556141622364521, -0.043259117752313614, 0.0013531171716749668, -0.021260729059576988, 0.007421381771564484, 0.061160627752542496, 0.0018503700848668814, 0.023057961836457253, 0.030044903978705406, 0.035774026066064835, -0.0032185353338718414, 0.000567740120459348, -0.031073855236172676, -0.04726250842213631, -0.02168889343738556, 0.016721228137612343, 0.01790938898921013, 0.022031815722584724, 0.054649706929922104, -0.025655532255768776, -0.002157781971618533, -0.08739195019006729, 0.005961693823337555, -0.0047666882164776325, 0.02639160305261612, -0.024517275393009186, 0.0941389724612236, 0.07247812300920486, -0.009274013340473175, -0.011498019099235535, 0.017901234328746796, 0.004846613388508558, -0.009562933817505836, 0.0030212088022381067, 0.038957007229328156, 0.02665664814412594, -0.07357616722583771, 0.042246706783771515, -0.057696860283613205, -0.03512047976255417, -0.008374323137104511, -0.020195402204990387, 0.06272785365581512, -0.008191179484128952, -0.007660523988306522, -0.03957581892609596, -0.021990681067109108, 0.02642165496945381, 0.008512450382113457, -0.01300125289708376, -0.0006147247040644288, 0.046458519995212555, 0.030039796605706215, 0.022152261808514595, -0.002964107785373926, 0.021954834461212158, -0.017200054600834846, -0.01003999449312687, -0.00846253614872694, 0.06599956005811691, 0.024816054850816727, 0.005562082398682833, -0.020178649574518204, -0.09030228853225708, 0.0001936911285156384, -0.03964568302035332, -0.02336825616657734, -0.03420071303844452, 0.005371154751628637, 0.010328084230422974, 0.02317121811211109, -0.011086090467870235, -0.00934358686208725, 0.010983449406921864, 0.01197265088558197, 0.08062755316495895, 0.027882417663931847, 0.04497143626213074, -0.029197964817285538, -0.026972463354468346, 0.11543361842632294, -0.01355217769742012, -0.0433158315718174, -0.006870643701404333, -0.009329348802566528, -0.007273522671312094, 0.019834717735648155, -0.03213194012641907, 0.026501735672354698, -0.034492120146751404, 0.1118435338139534, -0.06823238730430603, -0.07207436114549637, 0.02510729990899563, 0.06190141290426254, 3.1934803246258525e-07, -0.047646600753068924, 0.002849401207640767, 0.012388736940920353, 0.01286558248102665, 0.06885817646980286, 0.025684766471385956, -0.04485571011900902, 0.01492756325751543, -0.020990733057260513, 0.003103619674220681, 0.028084486722946167, -0.025696638971567154, 0.011681829579174519, -0.04239265248179436, -0.060054536908864975, -0.04850989580154419, -0.009762459434568882, 0.055236801505088806, -0.013210433535277843, -0.006832957733422518, -0.017499081790447235, 0.05734744295477867, 0.017483515664935112, 0.026604605838656425, 0.06300991028547287, 0.038922980427742004, 0.04859969764947891, 0.025128262117505074, 0.03372102975845337, -0.049491047859191895, 0.02991175651550293, 0.0535433255136013, -0.05803554132580757, -0.011825477704405785, -0.02011689729988575, 0.057083334773778915, -0.029328549280762672, 0.013713724911212921, 0.017834700644016266, -0.03948128595948219, 0.02208668738603592, 0.0010519969509914517, 0.031400371342897415, -0.002989760600030422, 0.04276594892144203, -0.10375867038965225, -0.026563771069049835, -0.005554834380745888, 0.001937907887622714, 0.036857884377241135, 0.009324571117758751, 0.03344282507896423, -0.011796263977885246, -0.027767181396484375, -0.014328974299132824, -0.027569258585572243, 0.04351918026804924, -0.04378754645586014, -0.023892221972346306, 0.0332559309899807, -0.026848740875720978, 0.008832409977912903, -0.07275466620922089, 0.03600158914923668, 0.026738006621599197, -0.005813727620989084, -0.034375790506601334, 2.936356878527746e-34, 0.03925449401140213, -0.05647739768028259, -0.04586231708526611, 0.011043626815080643, -0.05888278782367706, -0.014676922000944614, -0.009081598371267319, 0.018729962408542633, 0.057415127754211426, -0.00879617128521204, -0.0821790024638176]

['Emmanuel Dufourq', 'Bruce A. Bassett']

1707.00703v1

Regression or classification? This is perhaps the most basic question faced when tackling a new supervised learning problem. We present an Evolutionary Deep Learning (EDL) algorithm that automatically solves this by identifying the question type with high accuracy, along with a proposed deep architecture. Typically, a significant amount of human insight and preparation is required prior to executing machine learning algorithms. For example, when creating deep neural networks, the number of parameters must be selected in advance and furthermore, a lot of these choices are made based upon pre-existing knowledge of the data such as the use of a categorical cross entropy loss function. Humans are able to study a dataset and decide whether it represents a classification or a regression problem, and consequently make decisions which will be applied to the execution of the neural network. We propose the Automated Problem Identification (API) algorithm, which uses an evolutionary algorithm interface to TensorFlow to manipulate a deep neural network to decide if a dataset represents a classification or a regression problem. We test API on 16 different classification, regression and sentiment analysis datasets with up to 10,000 features and up to 17,000 unique target values. API achieves an average accuracy of $96.3\%$ in identifying the problem type without hardcoding any insights about the general characteristics of regression or classification problems. For example, API successfully identifies classification problems even with 1000 target values. Furthermore, the algorithm recommends which loss function to use and also recommends a neural network architecture. Our work is therefore a step towards fully automated machine learning.

Automated Problem Identification: Regression vs Classification via Evolutionary Deep Networks

http://arxiv.org/pdf/1707.00703v1

Title Automated Problem Identification Regression v Classification via Evolutionary Deep Networks Summary Regression classification perhaps basic question faced tackling new supervised learning problem present Evolutionary Deep Learning EDL algorithm automatically solves identifying question type high accuracy along proposed deep architecture Typically significant amount human insight preparation required prior executing machine learning algorithm example creating deep neural network number parameter must selected advance furthermore lot choice made based upon preexisting knowledge data use categorical cross entropy loss function Humans able study dataset decide whether represents classification regression problem consequently make decision applied execution neural network propose Automated Problem Identification API algorithm us evolutionary algorithm interface TensorFlow manipulate deep neural network decide dataset represents classification regression problem test API 16 different classification regression sentiment analysis datasets 10000 feature 17000 unique target value API achieves average accuracy 963 identifying problem type without hardcoding insight general characteristic regression classification problem example API successfully identifies classification problem even 1000 target value Furthermore algorithm recommends loss function use also recommends neural network architecture work therefore step towards fully automated machine learning Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.017554648220539093, 0.059413518756628036, -0.04749822989106178, 0.021838361397385597, -0.031179143115878105, 0.04083777591586113, 0.023964963853359222, 0.014833181165158749, 0.0026751523837447166, -0.031123120337724686, 0.0407755970954895, 0.03238639608025551, -0.03210805729031563, 0.05949537083506584, 0.019502121955156326, -0.017128219828009605, 0.017432866618037224, 0.047676775604486465, 0.020412132143974304, 0.00018157489830628037, 0.0030116024427115917, -0.007045422215014696, 0.022984812036156654, 0.009032334201037884, -0.02308920957148075, 0.019255487248301506, -0.008058952167630196, -0.029143230989575386, -0.017510147765278816, -0.0088488245382905, 0.0614725798368454, 0.027002740651369095, 0.004019950050860643, 0.05973690375685692, 1.9749863895413e-06, -0.05437176302075386, -0.042484350502491, -0.047156207263469696, -0.025390181690454483, -0.07463996857404709, 0.014389839954674244, -0.019949745386838913, 0.022381067276000977, 0.004284785594791174, -0.043710023164749146, -0.04566897451877594, 0.021501412615180016, 0.06997618824243546, 0.054845038801431656, 0.0564095713198185, -0.005942632909864187, -0.07801543176174164, 0.03158671408891678, 0.015692977234721184, 0.02053661458194256, 0.004209934733808041, 0.02869785949587822, -0.0016451174160465598, -0.040454670786857605, -0.035152871161699295, 0.012246895581483841, 0.022406212985515594, 0.02882249839603901, 0.009721590206027031, 0.015332392416894436, -0.010022724978625774, -0.004000866785645485, -0.025626592338085175, -0.01797911897301674, 0.06129811704158783, -0.06566037982702255, -0.02164185605943203, 0.007652760948985815, 0.010772854089736938, 0.016048388555645943, -0.04543914645910263, 0.0006326563307084143, -0.016713803634047508, -0.02315913513302803, -0.0022169635631144047, 0.021733321249485016, 0.017952842637896538, -0.01058206707239151, 0.011234127916395664, -0.007092738524079323, 0.03827480226755142, -0.03184622526168823, -0.014318211004137993, 0.005743512883782387, -0.020302588120102882, -0.027130426838994026, -0.021485386416316032, 0.028069883584976196, 0.009870877489447594, -0.032625675201416016, -0.021129019558429718, -0.018170511350035667, -0.10264493525028229, 0.010979515500366688, -0.040178585797548294, 0.031176315620541573, -0.0021360989194363356, 0.01886064000427723, -0.009254032745957375, 0.0031407924834638834, 0.08346657454967499, 0.0025598532520234585, -0.011900309473276138, -0.010249851271510124, 0.022243447601795197, -0.06252723187208176, 0.0041295806877315044, -0.012206950224936008, 0.07680929452180862, 0.00868195854127407, -0.0021494622342288494, -0.038266465067863464, -0.0020880764350295067, -0.01747307740151882, -0.017043981701135635, -0.028690418228507042, 0.051753658801317215, 0.0010650655021890998, 0.02527885138988495, -0.03789211064577103, 0.00655394745990634, -0.02099081128835678, 0.042814988642930984, -0.029516153037548065, 0.014352722093462944, 0.05618012696504593, 0.030170420184731483, 0.02826811745762825, 0.04582706466317177, 0.06043963506817818, 0.06002262607216835, 0.037135444581508636, 0.027749357745051384, -0.08130769431591034, -0.030990824103355408, 0.0038031914737075567, -0.018052510917186737, 0.005625604651868343, -0.06984461843967438, -0.0017104289727285504, -0.026013748720288277, -0.06776319444179535, -0.028330156579613686, -0.009891942143440247, -0.017529135569930077, 0.001486567547544837, 0.05269375815987587, -0.030785292387008667, 0.012267245911061764, 0.09415391087532043, -0.020061418414115906, 0.02755690924823284, 0.0584162138402462, -0.00352177070453763, 0.01379804965108633, 0.03399648517370224, -0.01022315863519907, 0.004410320892930031, -0.0029317247681319714, -0.010630377568304539, -0.03820018842816353, 0.001171120791696012, 0.001777398050762713, -0.018263446167111397, 0.0663713589310646, -0.005814167205244303, 0.024219943210482597, 0.019464265555143356, -0.03438862785696983, 0.0424993596971035, 0.027822617441415787, 0.0383925586938858, 0.10865712910890579, 0.009197617881000042, 0.021461758762598038, -0.007834365591406822, -0.0024855583906173706, 0.02881992980837822, 0.013535615988075733, -0.020443281158804893, -0.062436990439891815, -0.04026614502072334, -0.03695246949791908, -0.03416489437222481, -0.06631359457969666, 0.0249400082975626, -0.018373362720012665, -0.007677632384002209, -0.013512751087546349, 0.044650427997112274, 0.002918029436841607, -0.01838373951613903, -0.023955581709742546, 0.020856212824583054, 0.04121966287493706, -0.04749855771660805, -0.08177095651626587, 0.061303768306970596, -0.013755145482718945, -0.019647451117634773, -0.028853094205260277, -0.04523502290248871, -0.038326676934957504, -0.0012286023702472448, -0.013870447874069214, 0.02835012786090374, -0.008285793475806713, -0.03281412273645401, -0.0203004851937294, 0.006643091328442097, 0.009469657205045223, 0.009344851598143578, 0.008778968825936317, -0.015424470417201519, 0.042645346373319626, 0.000906486005987972, 0.03615539148449898, -0.03339945152401924, 0.020730091258883476, -0.018162496387958527, -0.013968496583402157, 0.05503011867403984, 0.031209316104650497, 0.020493842661380768, 0.01785491220653057, 0.012026868760585785, -0.013742293231189251, -0.0009588159155100584, -0.03288906440138817, -0.0921122133731842, -0.02220696210861206, -0.024276552721858025, -0.0176385510712862, 0.026378868147730827, -0.027413060888648033, -0.03184669464826584, 0.06047556921839714, -0.024807123467326164, -0.0035435196477919817, 0.028621407225728035, -0.06294500827789307, 0.013436658307909966, -0.013232163153588772, -0.006814766209572554, -0.04846298694610596, -0.006362017244100571, -0.04959087818861008, 0.0660468265414238, 0.015366283245384693, -0.006419079843908548, -0.043254151940345764, -0.07185222953557968, 0.06021665409207344, -0.0029469795990735292, -0.013516928069293499, -0.012110808864235878, -0.04245688393712044, 0.019689971581101418, 0.0016837792936712503, 0.06144585460424423, -0.03817371279001236, 0.007878418080508709, -0.04130132496356964, 0.0425676666200161, -0.0037598065100610256, 0.002366788452491164, 0.017039630562067032, -0.02034086547791958, 0.0005926270969212055, 0.0009448353666812181, -0.06174897775053978, 0.07457438111305237, 0.02162189595401287, -0.038066569715738297, 0.061684224754571915, 0.020077722147107124, 0.041847165673971176, -0.009737968444824219, -0.011946385726332664, -0.04987004026770592, 0.05034881457686424, 0.03857934847474098, -0.020818935707211494, -0.04604257270693779, -0.007635487709194422, -0.040651626884937286, 0.035383403301239014, 0.03980375453829765, -0.06303456425666809, -0.07412957400083542, -0.013840201310813427, -0.014919399283826351, 0.022102080285549164, 0.015810156241059303, 0.014220178127288818, -0.023241152986884117, 0.07477688789367676, -0.03156840056180954, 0.01405823603272438, -0.04511828348040581, 0.025208916515111923, 0.028036782518029213, 0.019776275381445885, -0.010202516801655293, -0.010239610448479652, 0.02315666899085045, -0.029913106933236122, -0.005828480701893568, 0.09304070472717285, 0.006780702620744705, -0.008495932444930077, -0.03298765420913696, -0.012495213188230991, 0.03258894383907318, 0.01157192513346672, 0.0008974547381512821, -0.042444948107004166, 0.07223787903785706, 0.08398032188415527, 0.01715548150241375, -0.0965556874871254, -0.049419667571783066, -0.018341802060604095, 0.017292702570557594, -0.025117721408605576, 0.017939647659659386, 0.010291650891304016, -0.016728540882468224, -0.033495064824819565, 0.01555860135704279, -0.032276615500450134, -0.021447446197271347, 0.045026421546936035, -0.03576485812664032, -0.016593798995018005, 0.00793578289449215, -0.028488764539361, -0.03881385549902916, -0.026210324838757515, -0.005141751375049353, -0.0020825464744120836, -0.0135756004601717, 0.002432128181681037, 0.007801228202879429, 0.013719093054533005, -0.017585841938853264, 0.018362153321504593, -0.05738837271928787, -0.010557499714195728, -0.002168934093788266, 0.0052268714644014835, 0.04779592156410217, -0.0070548709481954575, 0.0026248584035784006, 0.035443421453237534, 0.07729557156562805, 0.0038818437606096268, -0.03457020968198776, 0.04085122048854828, -0.09683400392532349, 0.04749879613518715, -0.019326647743582726, -0.01909796893596649, -0.020194971933960915, -0.017118914052844048, -0.033557549118995667, -0.05651053786277771, 0.035477399826049805, 0.08353552967309952, 0.01991751603782177, -0.08393880724906921, -0.03863069415092468, -0.012367431074380875, -0.020449593663215637, 0.005314263980835676, 0.045054804533720016, -0.027244552969932556, -0.006694345735013485, -0.016459284350275993, 0.018253840506076813, -0.027289319783449173, -0.043695077300071716, 0.014400067739188671, -0.06325889378786087, -0.0031525150407105684, -0.0454893484711647, -0.03448018804192543, -0.04516158252954483, -0.04095342010259628, -0.015718959271907806, -0.00511447386816144, 0.005020881071686745, -0.027496689930558205, 0.04003698751330376, -0.03028794378042221, 0.047013115137815475, -0.07316512614488602, -0.010953465476632118, 0.04476899281144142, -0.04107800871133804, -0.011995524168014526, 0.07558328658342361, 0.06318581104278564, -0.03946308791637421, -0.007214935030788183, 0.050269026309251785, -0.0033336535561829805, -0.0022859168238937855, -0.028387388214468956, 0.09730133414268494, 0.005632602144032717, 0.0016675181686878204, -0.014181927777826786, 0.07557909190654755, -0.043689798563718796, 0.08896506577730179, 0.02739604189991951, 0.0771271288394928, -0.015337906777858734, -0.04600713774561882, -0.06106988713145256, -0.01607939414680004, 0.04057425260543823, -0.0033265999518334866, 0.003829540219157934, -0.09441442787647247, -0.04084227234125137, 0.009636176750063896, -0.020655343309044838, -0.0341293141245842, -0.012986780144274235, 0.02185262367129326, -0.010861788876354694, -0.0661277323961258, -0.06617754697799683, -0.0030115300323814154, 0.0017763200448825955, 0.02543354593217373, 0.01642266847193241, -0.018853764981031418, 0.007588835433125496, -0.0197953712195158, -0.04733109474182129, -0.034959618002176285, 0.04497160390019417, -0.009731218218803406, -0.03111173026263714, 0.01183146983385086, 0.061294615268707275, -0.02822193317115307, -0.03449079766869545, -0.08946733921766281, -0.029343552887439728, -0.026034746319055557, -0.018529405817389488, 0.04011582210659981, 0.012074948288500309, -0.015197329223155975, -0.0179173331707716, -0.06338236480951309, 0.030249664559960365, 0.03520524874329567, 0.0193518977612257, -0.02416094020009041, -0.003600014140829444, -0.01284222211688757, -0.010936415754258633, 0.025100629776716232, -0.005720953922718763, 0.0568239726126194, 0.025057531893253326, -0.07154981046915054, -0.021604102104902267, -0.003512290073558688, 0.011753365397453308, 0.02069811336696148, 0.03353835642337799, 0.053528424352407455, -0.051150690764188766, -0.007619789335876703, -0.021753940731287003, 0.04654693230986595, -0.04138835892081261, -0.02202690951526165, -0.006880789063870907, 0.0060774944722652435, 0.0402485728263855, 0.003227060893550515, -0.04073936492204666, 0.05844675004482269, -0.04085265472531319, -0.059850942343473434, 0.07211354374885559, 0.02724693901836872, 0.06057317182421684, -0.015682315453886986, 0.03621466085314751, -0.023248685523867607, -0.020048141479492188, 0.04649358615279198, 0.014596402645111084, -0.02505529299378395, 0.02862761914730072, 0.029149753972887993, 0.009600709192454815, -0.038749441504478455, 0.014751085080206394, 0.029263382777571678, -0.03556167706847191, -0.0029916903004050255, 0.023021016269922256, 0.04285547137260437, -0.026735356077551842, -0.03827502205967903, 0.01774182729423046, -0.018188225105404854, -0.02276904135942459, 0.023006856441497803, -0.04139481857419014, 0.015945693477988243, 0.031909387558698654, -0.02081036940217018, -0.021086296066641808, -0.031416237354278564, 0.01038906630128622, 0.0015701648080721498, 0.009516043588519096, 0.007144749164581299, -0.02737719565629959, -0.03174515813589096, 0.06982114911079407, 0.04609198495745659, -0.028902405872941017, 0.015884991735219955, 0.017380408942699432, 0.014649352058768272, -0.03742939233779907, 0.02537941001355648, 0.004764032084494829, 0.0663469210267067, 0.011107442900538445, 0.04439786076545715, 0.057982850819826126, -0.0041090939193964005, 0.015960056334733963, -0.0039493548683822155, 0.003946985118091106, -0.06942038238048553, -0.013319706544280052, -0.03955371677875519, -5.397686755325613e-33, 0.04338756576180458, -0.03838516026735306, -0.014956938102841377, -0.03505687415599823, -0.01825612783432007, 0.01921338215470314, -0.017310230061411858, 0.02147854119539261, -0.02111794799566269, -0.006878553424030542, -0.0033057897817343473, 0.0062466892413794994, -0.01883886381983757, -0.0009106330689974129, 0.06548173725605011, -0.03420299291610718, -0.03933089226484299, -0.04808852821588516, 0.04436216503381729, 0.021832991391420364, 0.016558239236474037, 0.03754967451095581, -0.005706991534680128, -0.04595782235264778, -0.03255351260304451, 0.026460956782102585, 0.036283157765865326, 0.005244042258709669, 0.004849685821682215, 0.039046965539455414, -0.0014946599258109927, 0.07193892449140549, 0.04463518038392067, -0.054124485701322556, -0.006934524979442358, 0.026514869183301926, -0.01094079203903675, -0.054509080946445465, -0.08143586665391922, -0.0025568511337041855, -0.026050178334116936, 0.0015920065343379974, 0.08839680254459381, 0.030398186296224594, -0.02604098618030548, 0.017110737040638924, 0.07826447486877441, -0.004184996243566275, 0.046459585428237915, -0.039486244320869446, -0.013965615071356297, 0.006704034749418497, -0.00862641166895628, 0.014689771458506584, -0.00044397672172635794, 0.06769829243421555, -0.023465121164917946, -0.0018797350348904729, -0.004005229566246271, 0.024467583745718002, -0.02077832818031311, -0.020478475838899612, -0.013959834352135658, -0.005877950228750706, 0.011906692758202553, -0.00032335237483493984, -0.02102004922926426, -0.016993975266814232, -0.035514142364263535, 0.02915172278881073, 0.035282209515571594, 0.03326183184981346, 0.09736452996730804, 0.006867923308163881, 0.03563667833805084, -0.0747436136007309, -0.08072704076766968, 0.04227050393819809, 0.06097804382443428, -0.044003330171108246, 0.002011690055951476, 0.0009097548318095505, -0.022749241441488266, 0.009639158844947815, -0.003253843169659376, -0.0004444543446879834, -0.03741132467985153, -0.032857757061719894, 0.016725804656744003, -0.04976378753781319, -0.0276777446269989, -0.0052973064593970776, 0.004002917092293501, -0.07289092987775803, 0.03747579827904701, -0.014509835280478, -0.021105486899614334, 0.0290995966643095, 0.04351799190044403, 0.030197162181138992, -0.018274860456585884, -0.04045980051159859, -0.05936655402183533, 0.03069969266653061, 0.0536578930914402, 0.01517551951110363, 0.020232783630490303, -0.0016510066343471408, -0.0010792555985972285, 0.005478784907609224, 0.020946374163031578, -0.015127160586416721, 0.009322145022451878, 0.09221825748682022, -0.03495511785149574, -0.011782355606555939, 0.026967613026499748, 0.014260136522352695, 0.04967886582016945, 0.03096894361078739, -0.0490497462451458, 0.031419530510902405, 0.007763104047626257, 0.014926196075975895, -0.05456820875406265, -0.026609325781464577, -0.043455176055431366, 0.012217300944030285, -0.04685269296169281, -0.04777016490697861, -0.0073267556726932526, -0.023043308407068253, 2.628256936532125e-07, 0.014109869487583637, 0.03741377964615822, 0.014491099864244461, 0.00847337581217289, 0.01653122901916504, 0.044779837131500244, 0.03825084865093231, 0.024481449276208878, 0.020248722285032272, -0.0023942862171679735, 0.05611567199230194, -0.037432096898555756, 0.012337574735283852, 0.022888746112585068, -0.0833626464009285, -0.044070638716220856, -0.011495397426187992, 0.07247909903526306, -0.05211630091071129, 0.05384567752480507, 0.07085739076137543, 0.07930505275726318, 0.037898529320955276, -0.02135361358523369, 0.010868123732507229, 0.0324268639087677, -0.029706930741667747, 0.004601932596415281, 0.06316404044628143, 0.025094203650951385, -0.018617581576108932, 0.05160192400217056, -0.02550325356423855, 0.024099774658679962, -0.015410706400871277, 0.033087000250816345, -0.005709315184503794, 0.013471323996782303, 0.005301556084305048, -0.02923140488564968, 0.07916116714477539, 0.037801556289196014, 0.029323287308216095, -0.05885687470436096, 0.06378868967294693, -0.02296985313296318, -0.056799422949552536, -0.05149426683783531, 0.03604669123888016, -0.030386613681912422, 0.02019001543521881, -0.023037709295749664, 0.014663239009678364, -0.0050918711349368095, 0.011635108850896358, -0.06416589021682739, 0.01910318434238434, -0.04952617362141609, 0.04998202621936798, 0.028094099834561348, -0.05034544691443443, 0.014059795066714287, 0.004141489043831825, 0.03459198400378227, 0.09205305576324463, -0.008280433714389801, 0.028597259894013405, 2.4136457647857685e-34, -0.004077840596437454, -0.001018750830553472, 0.013981902971863747, -0.03608166426420212, 0.001899488503113389, 0.012133409269154072, 0.008815303444862366, -0.015484550036489964, 0.02506161294877529, -0.019789312034845352, -0.039891429245471954]

['Nikhil Mishra', 'Mostafa Rohaninejad', 'Xi Chen', 'Pieter Abbeel']

1707.03141v3

Deep neural networks excel in regimes with large amounts of data, but tend to struggle when data is scarce or when they need to adapt quickly to changes in the task. In response, recent work in meta-learning proposes training a meta-learner on a distribution of similar tasks, in the hopes of generalization to novel but related tasks by learning a high-level strategy that captures the essence of the problem it is asked to solve. However, many recent meta-learning approaches are extensively hand-designed, either using architectures specialized to a particular application, or hard-coding algorithmic components that constrain how the meta-learner solves the task. We propose a class of simple and generic meta-learner architectures that use a novel combination of temporal convolutions and soft attention; the former to aggregate information from past experience and the latter to pinpoint specific pieces of information. In the most extensive set of meta-learning experiments to date, we evaluate the resulting Simple Neural AttentIve Learner (or SNAIL) on several heavily-benchmarked tasks. On all tasks, in both supervised and reinforcement learning, SNAIL attains state-of-the-art performance by significant margins.

A Simple Neural Attentive Meta-Learner

http://arxiv.org/pdf/1707.03141v3

Title Simple Neural Attentive MetaLearner Summary Deep neural network excel regime large amount data tend struggle data scarce need adapt quickly change task response recent work metalearning proposes training metalearner distribution similar task hope generalization novel related task learning highlevel strategy capture essence problem asked solve However many recent metalearning approach extensively handdesigned either using architecture specialized particular application hardcoding algorithmic component constrain metalearner solves task propose class simple generic metalearner architecture use novel combination temporal convolution soft attention former aggregate information past experience latter pinpoint specific piece information extensive set metalearning experiment date evaluate resulting Simple Neural AttentIve Learner SNAIL several heavilybenchmarked task task supervised reinforcement learning SNAIL attains stateoftheart performance significant margin Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.004009567201137543, 0.03183344751596451, -0.025987913832068443, -0.008682005107402802, 0.004264588467776775, -0.02678695321083069, 0.03491746261715889, -0.0019520559580996633, -0.0837555080652237, 0.006071198731660843, -0.02262096107006073, 0.020031025633215904, -0.023839369416236877, 0.03718545287847519, 0.04783983156085014, -0.02815944328904152, 0.02943655103445053, 0.03465279936790466, 0.005194991361349821, 0.010797625407576561, -0.010609161108732224, -0.030375540256500244, 0.017939116805791855, 0.05283297970890999, 0.016472943127155304, 0.016481822356581688, -0.020769057795405388, -0.009766009636223316, 0.003116851206868887, -0.0769743099808693, 0.05350591987371445, 0.006794745568186045, 0.0227862186729908, 0.07218752056360245, 2.3923078060761327e-06, -0.02693624049425125, -0.005846054758876562, -0.026858145371079445, -0.0020115755032747984, -0.023482754826545715, 0.01020404975861311, -0.051458798348903656, 0.004343206062912941, 0.007587488740682602, -0.041597630828619, -0.013893507421016693, 0.037740856409072876, 0.06553850322961807, 0.029167726635932922, 0.04622137174010277, -0.0063997977413237095, 0.017620477825403214, 0.009413416497409344, -0.025965798646211624, 0.0543331652879715, -0.04657531529664993, -0.015118197537958622, -0.04403609037399292, 0.017161201685667038, 0.009712566621601582, -0.02687990851700306, 0.06008250266313553, 0.02865838073194027, -0.0009360130643472075, 0.0952635183930397, 0.06422840803861618, 0.02088669128715992, -0.006771680433303118, -0.032454151660203934, 0.040687043219804764, -0.07217045873403549, 0.024045301601290703, -0.01846987195312977, 0.0019963181111961603, -0.020470907911658287, -0.029951609671115875, -0.03968201205134392, 0.004044927656650543, -0.043303072452545166, -0.0038397680036723614, -0.02355673350393772, 0.052564214915037155, -0.017298530787229538, 0.016840364784002304, -0.02575301006436348, 0.023147379979491234, -0.0774293839931488, -0.035337936133146286, 0.03423279523849487, -0.020294254645705223, 0.08697868138551712, -0.05117342993617058, 0.03607400506734848, 0.05654788017272949, -0.02912474051117897, -0.01951609179377556, 0.02133893221616745, -0.07788542658090591, 0.037707455456256866, -0.031140819191932678, 0.12269098311662674, -0.006462925113737583, -0.05626742169260979, 0.021098701283335686, -0.033076994121074677, 0.03173309937119484, -0.04834489896893501, 0.006526265759021044, -0.0012101392494514585, 0.04459458589553833, -0.048474229872226715, 0.013503491878509521, -0.03488028421998024, 0.02827398292720318, 0.020455574616789818, -0.03975383937358856, -0.027711061760783195, -0.017417343333363533, -0.0023601504508405924, 0.019418859854340553, 0.006472339387983084, 0.03136437013745308, -0.048689041286706924, 0.024763846769928932, -0.01906125247478485, 0.025472354143857956, -0.07243359088897705, 0.044018980115652084, 0.01795775070786476, 0.0030794201884418726, -0.008496686816215515, 0.011988276615738869, -0.0023808167316019535, -0.02497846633195877, 0.013901053927838802, 0.09096965193748474, -0.015095347538590431, 0.007123296614736319, -0.0446927584707737, 0.002628402318805456, 0.018726801499724388, -0.03883029520511627, 0.0007715062238276005, -0.026608403772115707, 0.02610236592590809, -0.05294748395681381, -0.03415277600288391, 0.004005552269518375, 0.0035525162238627672, -0.011400321498513222, 0.007985197938978672, 0.07309886068105698, 0.0173038337379694, -0.018414627760648727, 0.05897874757647514, -0.004033742938190699, -0.01154937781393528, 0.032023631036281586, 0.003179283579811454, 0.058395806699991226, -0.021070091053843498, -0.011300523765385151, 0.020585276186466217, -0.04730701446533203, -0.006238510832190514, -0.02108261175453663, 0.030158232897520065, -0.003487048903480172, -0.06192254647612572, 0.05411280319094658, 0.021086348220705986, 0.006517513655126095, 0.020801717415452003, 0.025431305170059204, 0.06800130754709244, 0.020800359547138214, 0.04901786148548126, 0.028937308117747307, 0.0055426643230021, -0.0002627217036206275, -0.003958073444664478, -0.051327887922525406, -0.04108961299061775, 0.08275073021650314, -0.040959060192108154, 0.005347567144781351, -0.05270780995488167, 0.01627328060567379, -0.05211225524544716, -0.0639800876379013, 0.030354702845215797, 0.01171189360320568, -0.039571020752191544, 0.0019460378680378199, 0.05402092635631561, 0.01191062480211258, -0.03857078030705452, -0.05845596641302109, -0.011396684683859348, 0.020623408257961273, -0.037433017045259476, -0.056845374405384064, 0.03698686882853508, -0.006055544596165419, -0.041857630014419556, -0.07893887162208557, -0.06074107065796852, -0.08242060989141464, 0.016476918011903763, 0.023325592279434204, 0.00960762333124876, 0.011509086936712265, 0.006365499459207058, -0.039836857467889786, -0.025317037478089333, 0.004179475829005241, -0.0077369180507957935, 0.03032023087143898, -0.03137429431080818, 0.024918122217059135, -0.0056661879643797874, 0.02172180637717247, -0.00031225517159327865, 0.057676564902067184, 0.01845780946314335, -0.02526669204235077, 0.009894611313939095, 0.027584660798311234, 0.03402410075068474, -0.0024240801576524973, 0.04831705614924431, -0.0010393550619482994, 0.022438719868659973, -0.04120638966560364, -0.022194754332304, -0.025195863097906113, -0.00679355300962925, 0.02753976173698902, -0.007788726128637791, -0.015659043565392494, -0.0010198361705988646, 0.02895897440612316, -0.008698299527168274, -0.036839358508586884, -0.0020791657734662294, -0.021358802914619446, 0.011419546790421009, 0.020164616405963898, 0.022880643606185913, 0.002012083539739251, 0.015690824016928673, -0.03726695477962494, 0.03635210543870926, -0.006414130330085754, -0.003937238827347755, -0.021354803815484047, -0.06553501635789871, 0.013515190221369267, -0.11089450865983963, -0.01614980772137642, -0.005936991423368454, -0.04066851735115051, 0.025138497352600098, -0.020882833749055862, 0.06358019262552261, -0.016031742095947266, 0.016542088240385056, 0.004402657505124807, 0.010543172247707844, -0.01356158871203661, -0.013951423577964306, -0.013916458934545517, -0.007349098566919565, 0.007079819682985544, -0.05237589031457901, -0.043909601867198944, 0.04127996787428856, -0.005169502459466457, -0.021056722849607468, 0.04703376814723015, 0.04326222091913223, 0.03880912438035011, -0.06747886538505554, -0.02997312694787979, -0.0009210193529725075, 0.020772993564605713, 0.073166124522686, -0.04220682010054588, -0.048083774745464325, 0.003385170828551054, -0.015488645993173122, 0.015471850521862507, -0.00021627718524541706, -0.04290124401450157, -0.008606011047959328, -0.033607643097639084, -0.03233752027153969, 0.11495965719223022, 0.014451294206082821, 0.06587915867567062, 0.016208035871386528, 0.07462847232818604, -0.04162567853927612, 0.03793254867196083, -0.034355636686086655, 0.009746627882122993, 0.016795283183455467, 0.026402171701192856, 0.004118200391530991, 0.0328979566693306, 0.004573928192257881, 0.025630831718444824, -0.01993965171277523, 0.06278400868177414, 0.013197829946875572, -0.010966872796416283, -0.042296428233385086, 0.005656085442751646, 0.0071060750633478165, 0.038231197744607925, -0.005458655767142773, -0.041177090257406235, 0.06442881375551224, 0.06420346349477768, 0.0057348706759512424, -0.01587020792067051, -0.06263350695371628, -0.00561015959829092, 0.010682987980544567, -0.01214271504431963, 0.010968214832246304, 0.01024749968200922, -0.03953109681606293, -0.042627643793821335, 0.016084441915154457, 0.0027371631003916264, -0.008359134197235107, 0.06453534215688705, 0.004590006545186043, -0.015281208790838718, -0.002296436345204711, -0.058196570724248886, -0.04623863101005554, 0.014966458082199097, -0.021490810438990593, 0.03600841760635376, -0.026085417717695236, 0.009876556694507599, -0.09637750685214996, 0.007886524312198162, 0.03391147777438164, 0.03292619436979294, -0.03481796383857727, -0.04528895765542984, -0.023952769115567207, 0.0060392748564481735, 0.006657681427896023, 0.0085733188316226, -0.012269293889403343, -0.018288610503077507, 0.02996988408267498, 0.020911484956741333, 0.019317682832479477, -0.012972163036465645, -0.08643999695777893, 0.015306013636291027, -0.0006606138194911182, -0.05120179057121277, -0.006536743137985468, 0.0009797647362574935, -4.428606553119607e-05, -0.07760314643383026, 0.00042716338066384196, 0.0153365358710289, -0.00260841753333807, -0.07145410031080246, -0.0009430525824427605, 0.01989678665995598, -0.006608529016375542, 0.018291762098670006, 0.04091969504952431, -0.0037473381962627172, 0.023917051032185555, -0.010723338462412357, 0.02987564727663994, 0.015534627251327038, -0.03946152329444885, 0.00397186866030097, -0.0672975704073906, 0.031187687069177628, -0.037701621651649475, -0.11902692168951035, -0.023667311295866966, -0.030250309035182, 0.005277817603200674, -0.05450325086712837, -0.0194206815212965, 0.055466774851083755, 0.019713466987013817, -0.02340090647339821, 0.04462933540344238, -0.013847466558218002, -0.031911179423332214, 0.024986175820231438, -0.044466283172369, 0.01724371500313282, 0.05870315805077553, 0.04342743754386902, -0.05992456525564194, 0.017279455438256264, 0.04979614540934563, 0.021468108519911766, 0.03005186654627323, -0.022031862288713455, 0.0914754867553711, -0.02445187419652939, 0.0006791313062421978, 0.003593207336962223, 0.03991571441292763, -0.024575652554631233, 0.050456903874874115, 0.051439348608255386, 0.06972704082727432, -0.01578618958592415, 0.02078893780708313, -0.06241501495242119, -0.0019774320535361767, 0.05443853139877319, -0.02286810800433159, 0.006832970306277275, -0.020925283432006836, -0.04799912869930267, -0.0012200347846373916, 0.019254906103014946, -0.040519829839468, -0.019200308248400688, 0.03320002555847168, -0.02513081021606922, -0.023223115131258965, -0.07129087299108505, -0.04275578632950783, 0.013191933743655682, 0.06282351911067963, 0.029359892010688782, -0.01706337369978428, 0.0020477487705647945, 0.0028748009353876114, -0.03037048503756523, 0.004542293027043343, 0.05114925280213356, 0.029067134484648705, -0.049368374049663544, -0.013437203131616116, 0.016646670177578926, -0.03314533084630966, -0.012423457577824593, -0.06826599687337875, -0.049062058329582214, 0.008780677802860737, -0.008621628396213055, 0.07212555408477783, 0.034214142709970474, 0.004896781872957945, -0.0511813722550869, -0.03370072320103645, 0.01713462360203266, -0.03431807830929756, -0.03534988686442375, -0.037212394177913666, 0.05516757443547249, -0.031107857823371887, -0.016103630885481834, -0.005642393603920937, -0.0271407850086689, 0.08313651382923126, 0.029692064970731735, -0.014350070618093014, -0.007005348801612854, -0.009166979230940342, 0.0020422074012458324, -0.023352663964033127, 0.0677347332239151, 0.009596390649676323, -0.04312838613986969, -0.027012133970856667, 0.013916566967964172, 0.04031882435083389, 0.005502253770828247, -0.03035721182823181, -0.006490581203252077, 0.018742207437753677, 0.023988772183656693, 0.016957318410277367, -0.041590720415115356, 0.058410778641700745, 0.012574920430779457, -0.07820532470941544, 0.08861733227968216, -0.018540581688284874, 0.013618950732052326, -0.026831071823835373, 0.05926220864057541, -0.009478864260017872, 0.014439237304031849, 0.03622222691774368, 0.04278110712766647, 0.021923895925283432, 0.031842686235904694, 0.015067284926772118, 0.004739615134894848, -0.0467914454638958, 0.027642592787742615, -0.08176898956298828, -0.03384758532047272, -0.027722248807549477, 0.0068914759904146194, 0.02382870391011238, -0.06416576355695724, -0.017864054068922997, 0.023855149745941162, 0.014691362157464027, 0.0008105969172902405, 0.0678248479962349, -0.035061486065387726, 0.03160471469163895, 0.009905887767672539, 0.035522639751434326, 0.02309664525091648, -0.042298391461372375, 0.037911366671323776, -0.01646086946129799, -0.02421879768371582, -0.024306437000632286, -0.008214999921619892, -0.043450627475976944, 0.0522732138633728, 0.02491864189505577, 0.06214265152812004, 0.015437189489603043, -0.017307018861174583, -0.030047157779335976, -0.01234364788979292, 0.031603168696165085, 0.028761152178049088, 0.02978152222931385, -0.017345834523439407, 0.042952023446559906, 0.01692681573331356, 0.02450728975236416, 0.0038679009303450584, -0.0028910848777741194, 0.0005434837657958269, 0.0039974418468773365, 0.01170774269849062, -0.055632539093494415, -6.236295078119787e-33, 0.006653596181422472, -0.01931668445467949, -0.0024371277540922165, -0.0059930868446826935, -0.05987756699323654, 0.01643308624625206, -0.04359488561749458, -0.05095469951629639, -0.02501894347369671, -0.019092170521616936, -0.03667872026562691, 0.01500032376497984, 0.02054797299206257, 0.010755290277302265, 0.06747926026582718, -0.005579699762165546, 0.0160011388361454, 0.007386872544884682, 0.01976451836526394, -0.009254400618374348, -0.023235509172081947, 0.07131309062242508, 0.028350159525871277, -0.07777789980173111, -0.012820771895349026, 0.0541665256023407, 0.005781080108135939, -0.014270136132836342, -0.04145059734582901, 0.06148013472557068, 0.01022490207105875, 0.024917909875512123, 0.0073371282778680325, -0.06727629154920578, -0.021377041935920715, 0.003902176860719919, -0.10013610869646072, -0.05201335623860359, -0.08562681823968887, -0.0055447230115532875, -0.020787833258509636, 0.018023326992988586, 0.0582672655582428, -0.016118867322802544, 0.008179607801139355, -0.026958279311656952, 0.08066491782665253, -0.035758230835199356, -0.04363500326871872, -0.05781391263008118, -0.0714126005768776, 0.019546495750546455, -0.007624799385666847, -0.0010848568053916097, 0.05331733822822571, 0.022421732544898987, -0.014199077151715755, 0.02119627594947815, -0.03752783313393593, 0.022464901208877563, 0.011947130784392357, 0.017721286043524742, 0.006177428178489208, 0.07258210331201553, 0.006410003639757633, 0.017908798530697823, 0.042949628084897995, 0.05535827577114105, -0.023960618302226067, -0.03835073485970497, -0.0005341516807675362, 0.04404029622673988, 0.07346003502607346, -0.04647127911448479, 0.04483705386519432, -0.014133819378912449, -0.04520190507173538, 0.03459426388144493, 0.02928254008293152, 0.04715200886130333, 0.0031442255713045597, 0.028593584895133972, -0.03784877061843872, 0.0011553893564268947, 0.029892943799495697, -0.014187985099852085, -0.02068985439836979, -0.02534434199333191, 0.021525446325540543, 0.009444951079785824, 0.02693362347781658, 0.014257638715207577, -0.0014414727920666337, -0.018627390265464783, 0.06406200677156448, -0.02304953895509243, 0.03743896633386612, 0.02418595738708973, 0.02395678125321865, -0.04915802925825119, -0.057378869503736496, 0.01710251346230507, -0.0448337197303772, 0.05436490476131439, 0.04041951894760132, 0.01644774340093136, 0.0449858158826828, 0.0191356111317873, -0.0538359098136425, -0.02573300339281559, -0.010091166011989117, -0.03150210157036781, 0.025695227086544037, 0.031781911849975586, 0.0008938670507632196, -0.05743695795536041, 0.004539674147963524, 0.0478682667016983, 0.033884111791849136, -0.037735484540462494, -0.053280241787433624, 0.039551153779029846, -0.015255147591233253, 0.018639473244547844, -0.04893893748521805, 0.0068797823041677475, -0.038711585104465485, 0.052391666918992996, -0.0012608180986717343, -0.06834673136472702, -0.009043515659868717, 0.008098687045276165, 3.0382508953152865e-07, -0.00820970255881548, 0.007745315786451101, 0.007998569868505001, -0.014179768972098827, -0.01770653948187828, -0.0072999680414795876, -0.02546750381588936, -0.01007151696830988, -0.021016720682382584, 0.007063986733555794, 0.07821956276893616, -0.005982584785670042, 0.01542828418314457, 0.015572145581245422, -0.0692368596792221, -0.062023282051086426, -0.04205428436398506, 0.022182971239089966, -0.042961038649082184, -0.0012630288256332278, 0.04459333047270775, 0.10656629502773285, 0.043594781309366226, -0.029679613187909126, 0.010940992273390293, -0.007588772568851709, -0.01555855292826891, -0.006959632039070129, 0.07127026468515396, -0.01588902436196804, 0.0379067100584507, 0.010982423089444637, -0.05734987184405327, 0.04295853152871132, -0.004356559365987778, 0.007115485612303019, 0.016768144443631172, 0.03288743272423744, -0.028446119278669357, 0.003344281343743205, 0.034030333161354065, 0.02816695347428322, 0.04555073007941246, -0.05669354647397995, 0.0017262364272028208, -0.04845764487981796, -0.016386959701776505, 0.016146838665008545, -0.010953214950859547, 0.014225345104932785, 0.04484464228153229, -0.007648959755897522, -0.0051514036022126675, -0.024672701954841614, -0.012046492658555508, -0.007976808585226536, -0.009028324857354164, -0.053193435072898865, 0.007177031133323908, 0.04983697086572647, -0.024897977709770203, -0.017050528898835182, -0.016979090869426727, -0.010541463270783424, 0.04588334634900093, -0.028065143153071404, -0.0627540722489357, 2.670319548062623e-34, 0.0012435723328962922, 0.011639151722192764, 0.0010123573010787368, 0.019484106451272964, -0.04072128236293793, -0.010705782100558281, 0.0237190630286932, 0.019222769886255264, 0.05095614865422249, -0.03247265890240669, -0.05537085607647896]

['Simone Scardapane', 'Steven Van Vaerenbergh', 'Simone Totaro', 'Aurelio Uncini']

1707.04035v2

Neural networks are generally built by interleaving (adaptable) linear layers with (fixed) nonlinear activation functions. To increase their flexibility, several authors have proposed methods for adapting the activation functions themselves, endowing them with varying degrees of flexibility. None of these approaches, however, have gained wide acceptance in practice, and research in this topic remains open. In this paper, we introduce a novel family of flexible activation functions that are based on an inexpensive kernel expansion at every neuron. Leveraging over several properties of kernel-based models, we propose multiple variations for designing and initializing these kernel activation functions (KAFs), including a multidimensional scheme allowing to nonlinearly combine information from different paths in the network. The resulting KAFs can approximate any mapping defined over a subset of the real line, either convex or nonconvex. Furthermore, they are smooth over their entire domain, linear in their parameters, and they can be regularized using any known scheme, including the use of $\ell_1$ penalties to enforce sparseness. To the best of our knowledge, no other known model satisfies all these properties simultaneously. In addition, we provide a relatively complete overview on alternative techniques for adapting the activation functions, which is currently lacking in the literature. A large set of experiments validates our proposal.

Kafnets: kernel-based non-parametric activation functions for neural networks

http://arxiv.org/pdf/1707.04035v2

Title Kafnets kernelbased nonparametric activation function neural network Summary Neural network generally built interleaving adaptable linear layer fixed nonlinear activation function increase flexibility several author proposed method adapting activation function endowing varying degree flexibility None approach however gained wide acceptance practice research topic remains open paper introduce novel family flexible activation function based inexpensive kernel expansion every neuron Leveraging several property kernelbased model propose multiple variation designing initializing kernel activation function KAFs including multidimensional scheme allowing nonlinearly combine information different path network resulting KAFs approximate mapping defined subset real line either convex nonconvex Furthermore smooth entire domain linear parameter regularized using known scheme including use ell1 penalty enforce sparseness best knowledge known model satisfies property simultaneously addition provide relatively complete overview alternative technique adapting activation function currently lacking literature large set experiment validates proposal Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.022498300299048424, 0.017312129959464073, -0.030839217826724052, 0.00999076571315527, 0.004893321078270674, -0.04123031347990036, 0.03281127288937569, -0.023878756910562515, -0.062344033271074295, 0.02721944823861122, -0.052044257521629333, 0.06830356270074844, -0.0011952181812375784, 0.08157125115394592, 0.045075297355651855, -0.0026651162188500166, -0.019749809056520462, 0.026160527020692825, -0.05530055984854698, -0.01539780106395483, 0.031772758811712265, -0.028401847928762436, -0.0021879461128264666, 0.041307784616947174, -0.05610556900501251, 0.004272946156561375, -0.03216740861535072, -0.007869884371757507, 0.05852483958005905, -0.003922670613974333, 0.07646450400352478, -0.009155447594821453, -0.02094874158501625, 0.02525230497121811, 2.3863776732468978e-06, 0.008595723658800125, 0.025991717353463173, -0.030292797833681107, 0.03357146307826042, -0.001923315110616386, -0.00013656815281137824, -0.016996871680021286, -0.015625564381480217, -0.029288142919540405, -0.019138246774673462, -0.009334364905953407, 0.08101313561201096, 0.08394019305706024, 0.03342397138476372, 0.04330838844180107, -0.00574476970359683, -0.08128079771995544, 0.020035918802022934, -0.024173615500330925, -0.01036188006401062, -0.01667044498026371, -0.0028361142612993717, 0.002313012955710292, -0.03861816227436066, -0.03501790761947632, -0.015545795671641827, 0.0781426727771759, 0.06741013377904892, -0.04828844219446182, 0.08116121590137482, 0.012912723235785961, -0.04977569356560707, 0.0170710738748312, 0.00022088128025643528, 0.032191623002290726, -0.08779142796993256, 0.014446922577917576, 0.007414608728140593, -0.036929357796907425, -0.024345355108380318, -0.015121840871870518, -0.015250004827976227, -0.043926361948251724, -0.005810292903333902, -0.010277866385877132, -0.0892811194062233, 0.038254451006650925, 0.030565978959202766, 0.030981523916125298, 0.0024430053308606148, 0.0511944442987442, -0.024070411920547485, 0.0325339138507843, 0.024943873286247253, -0.05107187107205391, -0.06188402324914932, 0.028912290930747986, 0.011400874704122543, 0.007612839341163635, 0.01819821260869503, -0.014387198723852634, -0.027653003111481667, -0.045028652995824814, 0.025013800710439682, -0.08221335709095001, 0.07875508069992065, 0.014911066740751266, -0.0015143111813813448, -0.04026680067181587, -0.0888497456908226, 0.03014313243329525, -0.06192880496382713, 0.037868283689022064, -0.03804117068648338, 0.010442188009619713, -0.06757280230522156, -0.005890534725040197, 0.008847714401781559, 0.04790275916457176, 0.013753334991633892, 0.003722795285284519, -0.0560748316347599, 0.04245924577116966, -0.042183734476566315, -0.04332670941948891, 0.005858286749571562, 0.05858003348112106, 0.022072123363614082, 0.0013476628810167313, -0.013201703317463398, 0.030314626172184944, -0.018472909927368164, 0.0543031208217144, -0.018886201083660126, 0.025245191529393196, 0.014870875515043736, 0.018638871610164642, 0.020170390605926514, 0.04172434285283089, 0.002992585999891162, 0.002690449357032776, -0.011362343095242977, 0.02365056984126568, -0.06842038035392761, -0.012203955091536045, -0.006840829737484455, -0.013305804692208767, -0.020904822275042534, -0.06531637907028198, 0.0245103370398283, -0.03934229537844658, -0.055322956293821335, 0.01216962281614542, -0.0076978071592748165, -0.02028564177453518, -0.03898501396179199, 0.020459381863474846, 0.01554399449378252, -0.018966786563396454, 0.07573873549699783, -0.03134934976696968, -0.02987244352698326, 0.05802183598279953, 0.007577176205813885, -0.00017539426335133612, -0.024071283638477325, 0.009395656175911427, -0.06329699605703354, -0.002666478743776679, 0.01724916510283947, -0.039224591106176376, -0.04118836298584938, -0.08812689036130905, -0.04624951258301735, 0.01643882878124714, 0.022603731602430344, -0.0004660731938201934, -0.020039860159158707, -0.032920531928539276, 0.014722741208970547, 0.025711266323924065, 0.01565820351243019, 0.06554779410362244, -0.011719479225575924, 0.0014189948560670018, 0.004453990142792463, -0.042433664202690125, 0.02595629170536995, 0.052367694675922394, -0.03865384683012962, -0.05528932437300682, -0.05818762630224228, -0.00758258206769824, -0.055147916078567505, -0.05249674245715141, 0.04085446521639824, -0.03611641377210617, 0.016323503106832504, -0.03776674345135689, 0.05332750454545021, 0.006394113879650831, -0.006869341246783733, -0.005844337400048971, -0.004753931891173124, -0.0013531188014894724, -0.029481474310159683, -0.0030576209537684917, -0.02962607704102993, -0.027383863925933838, 0.005409505218267441, -0.02097802609205246, -0.05165047198534012, -0.013993986882269382, -0.04441395401954651, -0.0075349360704422, -0.016509654000401497, 0.00591264246031642, 0.0050925202667713165, -0.04891134798526764, -0.005744414869695902, 0.002850235439836979, 0.008479068987071514, 0.020536771044135094, -0.03252909332513809, 0.04260783642530441, 0.04804893583059311, 0.017214374616742134, 0.014543881639838219, -0.018554288893938065, -0.014086504466831684, 0.049275558441877365, 0.042078081518411636, 0.017916787415742874, 0.00011301635822746903, 0.009687175042927265, 0.030797462910413742, -0.00885789655148983, 0.0012427986366674304, -0.04824496805667877, -0.05244698002934456, -0.005329150706529617, -7.158424705266953e-05, -0.002636315766721964, 0.018941765651106834, 0.0072702388279139996, 0.06765490025281906, 0.02494465373456478, 0.007522861938923597, -0.06296538561582565, 0.026044435799121857, 0.03170064836740494, -0.015132864005863667, -0.02432037703692913, -0.012909602373838425, 0.02937253937125206, 0.004228244535624981, -0.00930922944098711, -0.010316796600818634, 0.009160077199339867, 0.013081472367048264, -0.04244661331176758, 0.04335319250822067, 0.004617455415427685, -0.0063533661887049675, -0.039860330522060394, 0.00641520693898201, -0.05511531978845596, 0.008450528606772423, -0.008707192726433277, -0.035359688103199005, 0.059912290424108505, 0.00028894157730974257, -0.02732779271900654, -0.010526581667363644, -0.005911519750952721, -0.02557404898107052, 0.003011181019246578, 0.02259901911020279, 0.05589998885989189, -0.00469641387462616, -0.04870592802762985, 0.15015201270580292, 0.01057911291718483, -0.05999800190329552, 0.0020349943079054356, 0.012598077766597271, 0.032895684242248535, -0.011487816460430622, -0.042324695736169815, 0.006107339635491371, 0.051215965300798416, -0.0008927348535507917, -0.058436762541532516, -0.004572225268930197, 0.0008832797757349908, -0.02860322780907154, 0.032214753329753876, -0.03089459240436554, -0.049448009580373764, -0.040126003324985504, -0.008876940235495567, -0.0528031662106514, 0.03273266926407814, 0.01084099616855383, -0.060289036482572556, -0.033352382481098175, 0.07341498881578445, -0.03140636906027794, 0.052253879606723785, -0.02829291857779026, -0.012747935950756073, -0.008325684815645218, 0.0637897402048111, -0.04386845603585243, 0.004899842664599419, 0.02975235879421234, -0.0190639179199934, -0.04066716879606247, -0.016821984201669693, 0.036743879318237305, -0.057625673711299896, -0.08946949988603592, -0.0010323302121832967, 0.02771466039121151, -0.02585129253566265, -0.013155837543308735, 0.001978910295292735, -0.018442317843437195, 0.04752339795231819, 0.009236278012394905, 0.030540313571691513, -0.02547575905919075, 0.02163708582520485, 0.0030327681452035904, 0.052681777626276016, 0.0265966784209013, 0.0217776857316494, 0.04271667078137398, -0.0018414236837998033, -0.032255303114652634, -0.024377873167395592, -0.00863216444849968, 0.06518241763114929, 0.030375201255083084, 0.00847600307315588, 0.005438039544969797, 0.005367652513086796, -0.05995842069387436, 0.019927022978663445, 0.03488028049468994, -0.002117890166118741, -0.026077954098582268, -0.022895576432347298, 0.022119970992207527, 0.02172301709651947, -0.0038786567747592926, 0.0664648786187172, -0.03397885337471962, 0.007963405922055244, -0.012138365767896175, 0.011697471141815186, 0.015627523884177208, 0.022046338766813278, -0.030423635616898537, 0.0628252774477005, 0.042132485657930374, 0.023859918117523193, -0.029493538662791252, -0.00500186812132597, -0.05800193175673485, 0.009156855754554272, -0.05708542838692665, 0.013996785506606102, -0.03100193291902542, -0.07499862462282181, 0.0009705955744720995, -0.03470557555556297, 0.0565914511680603, 0.023859571665525436, 0.00027793424669653177, -0.06950556486845016, 0.004156958311796188, -0.008627383038401604, 0.012156344018876553, -0.007053136359900236, 0.024004308506846428, -0.0008725976222194731, 0.017378810793161392, -0.009609581902623177, 0.012778184376657009, -0.04229166731238365, -0.018661580979824066, 0.024831704795360565, -0.040104977786540985, 0.023511167615652084, 0.04718509688973427, -0.06026837229728699, -0.020541086792945862, -0.018727300688624382, 0.015122462064027786, 0.003979989793151617, -0.03787652775645256, 0.01407502219080925, 0.036725547164678574, -0.04735586419701576, 0.031058458611369133, 0.003374750493094325, -0.02383342944085598, -0.047183193266391754, -0.0569194070994854, 0.01830175518989563, -0.00880947895348072, -0.014567436650395393, -0.035268399864435196, -0.020793674513697624, -0.007299354765564203, 0.012171623297035694, 0.016806479543447495, 0.00012877192057203501, 0.008477955125272274, 0.05814843252301216, -0.025044718757271767, 0.024193231016397476, 0.05723239481449127, -0.025913678109645844, 0.04362691566348076, -0.03133787587285042, 0.029901918023824692, -0.018466437235474586, 0.0316992923617363, -0.03199676424264908, -0.033415187150239944, -0.0037852060049772263, -0.026499928906559944, -0.035488229244947433, -0.018312154337763786, -0.008089771494269371, 0.020595867186784744, -0.028565989807248116, -0.025360241532325745, -0.04166778177022934, 0.03093487024307251, -0.0054787700064480305, -0.09313197433948517, -0.05952470749616623, -0.009227413684129715, -0.058974675834178925, 0.051603857427835464, 0.021471109241247177, 0.004670073743909597, 0.08005600422620773, 0.02810755930840969, -0.053374625742435455, -0.004256676882505417, 0.05887802317738533, 0.009752066805958748, 0.00600409833714366, 0.028223685920238495, 0.06401071697473526, -0.0311611108481884, 0.005873025394976139, -0.03521503135561943, -0.02795204147696495, -0.02467452362179756, -0.011394034139811993, 0.008307632058858871, -0.011158749461174011, -0.006674995180219412, -0.04190457984805107, -0.019462602213025093, 0.1005028560757637, 0.010101886466145515, 0.06675976514816284, 0.0271307285875082, 0.06158773601055145, -0.010263134725391865, -0.0035890189465135336, 0.03933287784457207, -0.03533490002155304, 0.08115696161985397, -0.011094353161752224, -0.007866072468459606, -0.006341984961181879, -0.03928287699818611, -0.025750963017344475, -0.01188307162374258, 0.013456277549266815, 0.06582016497850418, -0.004773138556629419, -0.04167194664478302, 0.013899857178330421, 0.0373077392578125, 0.036167800426483154, -0.03442777693271637, -0.006440436001867056, 0.02766362950205803, 0.04926467314362526, 0.004574508406221867, -0.07491809129714966, 0.1175844594836235, -0.020326606929302216, 0.03287568315863609, 0.0012086037313565612, -0.012471857480704784, 0.011820964515209198, -0.05681108310818672, 0.030699511989951134, -0.03067348152399063, -0.014174059964716434, 0.017692746594548225, -0.019282257184386253, -0.02069641649723053, 0.039014920592308044, 0.0024870752822607756, -0.002259850036352873, -0.0468733049929142, 0.017022710293531418, -0.015432804822921753, 0.00543011911213398, -0.04005640745162964, -0.0011863134568557143, 0.03447593376040459, -0.0011692754924297333, 0.016371360048651695, -0.013381484895944595, 0.011550713330507278, -0.04554558917880058, -0.003037366783246398, 0.016481973230838776, 0.030277935788035393, 0.06281168013811111, 0.0010192157933488488, 0.01788509078323841, -0.02404549904167652, -0.02700812555849552, 0.019701356068253517, 0.026758192107081413, -0.06441201269626617, 0.04702393710613251, 0.006097071338444948, 0.03882033750414848, -0.0025680928956717253, 0.03463088721036911, -0.009961324743926525, 0.011225917376577854, 0.034729041159152985, -0.017570260912179947, 0.06691306084394455, -0.016378281638026237, 0.017041072249412537, -0.017076080664992332, 0.036240119487047195, -0.033030662685632706, -0.001961465459316969, -0.00437071081250906, -0.04538034275174141, -0.04689326882362366, -0.021828068420290947, 0.0024183851201087236, -0.01656249724328518, -5.998937789433812e-33, 0.029870906844735146, 0.03160744160413742, -0.061417900025844574, 0.010103601962327957, -0.05311759188771248, 0.019984683021903038, -0.004462257027626038, 0.023638669401407242, -0.02603502757847309, -0.04533207416534424, -0.03783596679568291, -0.010088011622428894, 0.0031371936202049255, 0.05412427335977554, -0.004049378447234631, -0.006563014816492796, 0.008574597537517548, -0.013196881860494614, 0.06467437744140625, 0.01809384860098362, 0.04384030029177666, 0.02954660914838314, 0.005824157502502203, -0.05653446912765503, -0.03736355900764465, 0.0212190393358469, -0.014196360483765602, 0.0010246941819787025, -0.020084310322999954, 0.01145358756184578, -0.005506278481334448, 0.049443285912275314, 0.0014596726978197694, 0.0019193810876458883, -0.008975370787084103, -0.03848056122660637, -0.022919239476323128, -0.014322865754365921, -0.03466453775763512, 0.036444224417209625, -0.044928282499313354, -0.014289856888353825, 0.12881945073604584, -0.032704126089811325, -0.024580953642725945, 0.03393656760454178, 0.040802229195833206, -0.007338962983340025, 0.002265293151140213, 0.017028210684657097, -0.0015000520506873727, 0.01755187101662159, -0.0036084470339119434, 0.006370050832629204, 0.02913583628833294, 0.033157896250486374, -0.04186141490936279, -0.04599718376994133, -0.08729568868875504, -0.0201962161809206, -0.0432329960167408, 0.04265781119465828, 0.012807776220142841, 0.08232342451810837, 0.05807529389858246, 0.03160233050584793, 0.029949266463518143, -0.014106551185250282, -0.032980456948280334, -0.021407023072242737, 0.012708081863820553, 0.032807689160108566, 0.06868036836385727, 0.01108916662633419, 0.05068729817867279, -0.12473448365926743, -0.016143279150128365, 0.002982384990900755, 0.008198034018278122, -0.017319215461611748, 0.015380138531327248, 0.024550005793571472, -0.03644325211644173, 0.018518252298235893, 0.005131521727889776, -0.04588223993778229, -0.001466403715312481, -0.041600827127695084, 0.02473689243197441, -0.01730346493422985, -0.005253918934613466, 0.01110219769179821, -0.011058342643082142, -0.020392416045069695, 0.11368575692176819, 0.018545974045991898, 0.053903136402368546, 0.08166904747486115, 0.02796039916574955, -0.010705293156206608, -0.0515979640185833, -0.010400348342955112, -0.03106764703989029, 0.013234044425189495, 0.01292402669787407, 0.0035500682424753904, -0.014126269146800041, 0.06395212560892105, 0.016011571511626244, -0.02124251239001751, -0.025085145607590675, 0.002146901097148657, 0.039499107748270035, 0.054196350276470184, 0.038323454558849335, -0.04932001605629921, -0.0029619557317346334, 0.033639661967754364, -0.01980791613459587, -0.015118416398763657, 0.014731470495462418, -0.033078987151384354, 0.03280935809016228, 0.011078125797212124, -0.04011658951640129, -0.010346705093979836, -0.018047843128442764, 0.018215034157037735, -0.05745933577418327, -0.07251782715320587, 0.03244210034608841, 0.0323643758893013, 3.146729454783781e-07, -0.028879860416054726, -0.036480143666267395, -0.0248651634901762, -0.028322523459792137, 0.04655619338154793, -0.016401223838329315, 0.012521765194833279, 0.02463587000966072, -0.06242179498076439, -0.004429884720593691, 0.016467265784740448, -0.015155067667365074, 0.012888312339782715, -0.01862599514424801, -0.0653659775853157, -0.029829539358615875, 0.01094844751060009, 0.042359016835689545, 0.03326107934117317, 0.028265880420804024, 0.07598816603422165, 0.08498263359069824, 0.03759443387389183, -0.003495651762932539, 0.07188306748867035, -0.012755152769386768, 0.0021254881285130978, 0.0594259612262249, 0.05328876152634621, -0.00525668216869235, 0.023644760251045227, 0.007261635735630989, -0.011633777059614658, 0.035425134003162384, 0.021111587062478065, 0.06558173894882202, 0.03075532615184784, 0.03804650902748108, -0.03171660006046295, -0.06413938105106354, 0.03857811912894249, 0.033495206385850906, 0.06273286789655685, -0.05175711214542389, 0.05726107954978943, 0.012206786312162876, -0.0029983557760715485, 0.03594326972961426, 0.025615215301513672, 0.02930833213031292, 0.04038800299167633, -0.019332926720380783, -0.019559424370527267, -0.025253750383853912, 0.017079582437872887, -0.052075233310461044, -0.010300991125404835, -0.05693140625953674, 0.009203335270285606, 0.04517026245594025, -0.033062972128391266, -0.00431037275120616, -0.05736665055155754, -0.014743579551577568, 0.08167843520641327, 0.032331906259059906, -0.029258178547024727, 2.390501153455291e-34, -0.012626010924577713, -0.014124980196356773, -0.0036118049174547195, -0.0018515242263674736, -0.0577511340379715, 0.014426250010728836, -0.006587988696992397, 0.01821155659854412, -0.0185849592089653, -0.041756052523851395, -0.056373026221990585]

['Razvan Pascanu', 'Yujia Li', 'Oriol Vinyals', 'Nicolas Heess', 'Lars Buesing', 'Sebastien Racanière', 'David Reichert', 'Théophane Weber', 'Daan Wierstra', 'Peter Battaglia']

1707.06170v1

Conventional wisdom holds that model-based planning is a powerful approach to sequential decision-making. It is often very challenging in practice, however, because while a model can be used to evaluate a plan, it does not prescribe how to construct a plan. Here we introduce the "Imagination-based Planner", the first model-based, sequential decision-making agent that can learn to construct, evaluate, and execute plans. Before any action, it can perform a variable number of imagination steps, which involve proposing an imagined action and evaluating it with its model-based imagination. All imagined actions and outcomes are aggregated, iteratively, into a "plan context" which conditions future real and imagined actions. The agent can even decide how to imagine: testing out alternative imagined actions, chaining sequences of actions together, or building a more complex "imagination tree" by navigating flexibly among the previously imagined states using a learned policy. And our agent can learn to plan economically, jointly optimizing for external rewards and computational costs associated with using its imagination. We show that our architecture can learn to solve a challenging continuous control problem, and also learn elaborate planning strategies in a discrete maze-solving task. Our work opens a new direction toward learning the components of a model-based planning system and how to use them.

Learning model-based planning from scratch

http://arxiv.org/pdf/1707.06170v1

Title Learning modelbased planning scratch Summary Conventional wisdom hold modelbased planning powerful approach sequential decisionmaking often challenging practice however model used evaluate plan prescribe construct plan introduce Imaginationbased Planner first modelbased sequential decisionmaking agent learn construct evaluate execute plan action perform variable number imagination step involve proposing imagined action evaluating modelbased imagination imagined action outcome aggregated iteratively plan context condition future real imagined action agent even decide imagine testing alternative imagined action chaining sequence action together building complex imagination tree navigating flexibly among previously imagined state using learned policy agent learn plan economically jointly optimizing external reward computational cost associated using imagination show architecture learn solve challenging continuous control problem also learn elaborate planning strategy discrete mazesolving task work open new direction toward learning component modelbased planning system use Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.006597284693270922, 0.017582206055521965, -0.01829913817346096, -0.030757684260606766, -0.02217869460582733, -0.004649126436561346, -0.02426075004041195, -0.014787039719522, -0.0075731598772108555, 0.007130926474928856, 0.03597297519445419, 0.03913571685552597, -0.04022463038563728, 0.1198381632566452, -0.01350487768650055, -0.0658540353178978, 0.01179099828004837, -0.018232308328151703, -0.01738600991666317, 0.026156548410654068, -0.007085570599883795, -0.010748081840574741, -0.04452912509441376, 0.051875628530979156, -0.024181311950087547, -0.0049977293238043785, -0.08737381547689438, -0.0048643131740391254, 0.01798548921942711, -0.11916615813970566, 0.03250722959637642, -0.0014377353945747018, 0.04527813568711281, 0.031899772584438324, 2.318889755770215e-06, -0.043969426304101944, -0.07478326559066772, -0.058148447424173355, -0.0010815649293363094, -0.08763713389635086, 0.013978194445371628, -0.00884812232106924, 0.002069148700684309, 0.009885123930871487, -0.03798086196184158, 0.0158900897949934, 0.005429427605122328, 0.06808692961931229, 0.04011101648211479, 0.00341759598813951, -0.003979087341576815, -0.06817325204610825, -0.004704579710960388, 0.019700422883033752, -0.02768176794052124, -0.012908818200230598, 0.0031679519452154636, 0.04667941480875015, 0.05653461441397667, -0.010783622972667217, 0.0021489320788532495, -0.01934020221233368, 0.017937740311026573, -0.01839793659746647, 0.019449079409241676, 0.02380499430000782, 0.08205971121788025, -0.0314737893640995, -0.01526738703250885, 0.035573966801166534, -0.020258178934454918, -0.0023254239931702614, 0.04431239143013954, -0.01654198206961155, -0.028991760686039925, 0.017222940921783447, -0.017191875725984573, 0.021876992657780647, -0.03009149432182312, -0.013256172649562359, -0.022763516753911972, 0.028594570234417915, -0.028848284855484962, 0.004454948473721743, -0.000801106623839587, 0.06636153161525726, -0.04751015827059746, -0.023896150290966034, 0.03158703073859215, -0.0027715791948139668, 0.02987423725426197, -0.04861238971352577, 0.014341778121888638, 0.05016153305768967, -0.05423862114548683, -0.013710581697523594, 0.02868550270795822, 0.02108454704284668, -0.0019938305485993624, -0.015161814168095589, 0.09445243328809738, 0.03714636713266373, 0.04411082714796066, 0.028823046013712883, 0.015317852608859539, 0.037589095532894135, -0.059271641075611115, 0.011133135296404362, -0.051042795181274414, 0.10300453007221222, -0.08238428086042404, 0.03560110181570053, -0.06932531297206879, 0.0613873153924942, -0.043613631278276443, -0.02389923855662346, -0.013945626094937325, 0.04725959897041321, -0.01793697103857994, 0.03839607909321785, 0.0011006647255271673, 0.05506181716918945, 0.018572406843304634, -0.0017313399584963918, -0.08885150402784348, -0.028408706188201904, -0.06652513146400452, 0.018644655123353004, -0.03126828372478485, 0.05812739580869675, 0.028742412105202675, -0.0089256064966321, -0.029617702588438988, 0.028886020183563232, -0.023900890722870827, 0.06631284207105637, 0.007543800864368677, 0.05236073583364487, -0.06312242895364761, -0.0645974650979042, 0.07156535983085632, -0.040183328092098236, 0.028074463829398155, -0.052833788096904755, -0.04784011095762253, -0.07034412771463394, -0.02501128986477852, 0.024930385872721672, 0.014218444935977459, -0.022835474461317062, 0.013417116366326809, 0.029003670439124107, 0.01734629087150097, -0.0012250799918547273, 0.022263476625084877, 0.030357742682099342, -0.006378615275025368, 0.07143425941467285, 0.016132406890392303, 0.05675334483385086, -0.03573983535170555, 0.04890067130327225, 0.04849429801106453, -0.007327292114496231, 0.00237265438772738, -0.00974013190716505, 0.04757506027817726, -0.009008374065160751, 0.0014118592953309417, 0.04490134119987488, -0.06935501098632812, -0.04659590497612953, -0.03850291669368744, 0.078069768846035, 0.020777149125933647, 0.014707988128066063, 0.035259880125522614, 0.004436915274709463, 0.04463314265012741, 0.0138906454667449, -0.024169765412807465, -0.029766926541924477, -0.0038285371847450733, 0.05565665662288666, -0.040574099868535995, -0.0008117114193737507, -0.11643149703741074, 0.006885808892548084, -0.011170050129294395, -0.05527684837579727, 0.03807424381375313, -0.004898636136204004, 0.019511064514517784, -0.02746886946260929, 0.007704285439103842, 0.013286366127431393, -0.04771413281559944, -0.02546069398522377, -0.03525315597653389, 0.03965378552675247, -0.041414808481931686, -0.04393832013010979, 0.001525465864688158, 0.029431046918034554, 0.019629310816526413, -0.07315941154956818, -0.060869477689266205, -0.016631269827485085, -0.016071097925305367, -0.029052989557385445, -0.017951663583517075, -0.050644516944885254, 0.011668636463582516, 0.006304488051682711, -0.036800891160964966, 0.00027211132692173123, 0.03202375769615173, 0.012860434129834175, -0.03339975327253342, -0.02974170446395874, -0.03867802023887634, 0.0749952644109726, 0.02527516521513462, 0.027318397536873817, -0.0728827565908432, -0.018764672800898552, -0.0018199934856966138, -0.013427581638097763, 0.0346342958509922, -0.003066972829401493, -0.0013893600553274155, 0.021547453477978706, 0.06394077092409134, 0.0035758623853325844, -0.04190051183104515, 0.009009342640638351, -0.047012679278850555, 0.0001544973492855206, 0.01963028311729431, 0.0016561737284064293, 0.040475208312273026, -0.016117524355649948, -0.003344804747030139, -0.04004833847284317, 0.009090734645724297, -0.009461131878197193, 0.011907601729035378, 0.022959494963288307, 0.04385114088654518, -0.0050064981915056705, -0.08035740256309509, -0.030477844178676605, 0.031845204532146454, -0.004503600765019655, -0.014276723377406597, 0.01752181351184845, -0.010509942658245564, 0.028442583978176117, -0.027989674359560013, 0.029355475679039955, 0.02990291640162468, 0.004147942177951336, -0.024774640798568726, 0.00041504018008708954, 0.0451069250702858, -0.03910955414175987, 0.029593631625175476, -0.06431892514228821, -0.0379861555993557, -0.014498294331133366, -0.02147408202290535, 0.030536605045199394, -0.02082347497344017, 0.007243145257234573, -0.03837933391332626, 0.007097488734871149, 0.03238103538751602, -0.0034017832949757576, -0.039643555879592896, -0.025801317766308784, 0.04990362375974655, -0.014103333465754986, -0.009438679553568363, 0.020464442670345306, -0.04072868078947067, -0.007563592400401831, 0.041879795491695404, -0.05120133236050606, -0.028071418404579163, -0.00848440919071436, -0.006744819693267345, 0.03002239763736725, -0.00522717647254467, -0.012965789996087551, 0.007802196312695742, -0.022384194657206535, -0.005583696532994509, 0.008624978363513947, -0.03462313488125801, 0.027571123093366623, 0.03958176076412201, 0.002639930695295334, -0.05399187281727791, 0.04154323413968086, -0.046111300587654114, 0.023018725216388702, -0.004681397695094347, 0.016596099361777306, 0.011873846873641014, 0.04902022331953049, -0.014840696938335896, 0.04037140682339668, -0.024637261405587196, 0.049861788749694824, 0.025361226871609688, -0.04128639027476311, -0.016440436244010925, -0.027008123695850372, -0.0008824468241073191, 0.09726545214653015, -0.04349036514759064, -0.0225626640021801, 0.04752643406391144, 0.047713279724121094, -0.026063445955514908, -0.024773232638835907, -0.005978889763355255, -0.01961483247578144, 0.03962813690304756, -0.0013049169210717082, 0.023098427802324295, -0.003745023161172867, 0.0044661941938102245, -0.03457615152001381, -0.019622543826699257, 0.004803770687431097, -0.002962148515507579, -0.002152512315660715, -0.07428032159805298, -0.022176070138812065, 0.020915577188134193, -0.044833604246377945, -0.06498070806264877, 0.03277880325913429, -0.00362801575101912, 0.03494824841618538, 0.014270705170929432, -0.01455407589673996, -0.015298749320209026, -0.04347581788897514, 0.03534495830535889, 0.06100035831332207, -0.016375163570046425, -0.020574312657117844, 0.006201926153153181, -0.004224154632538557, 0.04089958593249321, -0.0032635729294270277, 0.01912681758403778, -0.006663140840828419, 0.09611890465021133, 0.0434139147400856, -0.017641788348555565, -0.043319009244441986, -0.04236334189772606, 0.05111127346754074, 0.006737023126333952, -0.022518005222082138, -0.016678184270858765, 0.048483025282621384, 0.026454532518982887, -0.02508377470076084, -0.033478185534477234, 0.025097129866480827, 0.03571046516299248, -0.024776211008429527, 0.0028888583183288574, -0.06814072281122208, 0.044330522418022156, 0.026019129902124405, 0.06175187975168228, -0.007966713048517704, 0.039641767740249634, 0.0007709536585025489, 0.011174479499459267, -0.055709242820739746, -0.05879172310233116, -0.009354660287499428, -0.08217234909534454, 0.04505326598882675, 0.0005726441158913076, -0.05019198730587959, 0.03990147262811661, -0.01354038156569004, -0.025821994990110397, -0.017890464514493942, -0.10667215287685394, 0.011948976665735245, -0.0011341122444719076, -0.007851107977330685, 0.02252069301903248, -0.04124591872096062, 0.028133459389209747, -0.023566795513033867, -0.011825410649180412, -0.005853658076375723, 0.06779918074607849, 0.0016538422787562013, 0.014078943058848381, 0.005559135228395462, 0.02159527875483036, 0.0632406622171402, 0.03216656297445297, -0.0735265389084816, -0.0011790941935032606, 0.030870474874973297, 0.03866494074463844, 0.021106142550706863, 0.024776456877589226, -0.001968440366908908, -0.04520696774125099, 0.04724797233939171, 0.10872440040111542, -0.04881945624947548, 0.057921022176742554, -0.05368112027645111, 0.04087741672992706, 0.060090694576501846, -0.05742174759507179, -0.05433313548564911, 0.014570855535566807, -0.0394812673330307, -0.0033023131545633078, 0.025242384523153305, -0.04295019060373306, -0.04575163871049881, -0.020607128739356995, 0.005681280512362719, 0.04275377467274666, -0.06857601553201675, -0.009456952102482319, 0.024680374190211296, 0.07873358577489853, 0.029767438769340515, -0.04724934697151184, 0.004729223903268576, 0.0378800705075264, -0.012668348848819733, -0.048328697681427, 0.050595223903656006, 0.007817846722900867, -0.022331420332193375, -0.0264457818120718, 0.005036485847085714, -0.039917733520269394, 0.011375753208994865, -0.04727345332503319, -0.03348864987492561, -0.03450712561607361, 0.018399469554424286, 0.09880823642015457, 0.022503305226564407, -3.9566577470395714e-05, 0.01539115235209465, 0.0209468025714159, 0.04138437286019325, -0.0878407210111618, -0.017799122259020805, -0.03388988971710205, 0.03222530335187912, 0.05570853874087334, 0.00806418526917696, -0.0057442025281488895, -0.009465543553233147, 0.05980301275849342, 0.01893668808043003, -0.0009507826762273908, -0.041695475578308105, 0.019388899207115173, 0.015334655530750751, -0.01017030980437994, 0.00198569823987782, 0.00844130851328373, -0.015492048114538193, -0.024098675698041916, 0.029415378347039223, -0.01692650094628334, -0.020998544991016388, -0.06484992802143097, 0.024902883917093277, 0.027467478066682816, 0.008475029841065407, 0.05607827752828598, -0.016185613349080086, 0.0310448557138443, -0.03196258842945099, 0.02962234988808632, 0.028897536918520927, 0.04002297669649124, 0.013850770890712738, -0.011383128352463245, 0.028950726613402367, -0.0019137918716296554, -0.009172252379357815, 0.011358862742781639, 0.06130977347493172, 0.03978106752038002, 0.05835508555173874, -0.004136296454817057, 0.00687050586566329, -0.06714047491550446, -0.009758679196238518, -0.012129955925047398, -0.11003249138593674, 0.010152523405849934, 0.03976855054497719, 0.03723687678575516, -0.00039847844163887203, -0.008992372080683708, -0.0479431115090847, 0.032791003584861755, 0.017520062625408173, 0.0044506611302495, -0.03668772056698799, -0.003973029088228941, 0.0061936830170452595, 0.03523875027894974, 0.004040106665343046, -0.04257503151893616, 0.01081711146980524, 0.016278769820928574, 0.043649833649396896, -0.03505929931998253, -0.027870366349816322, -0.02615228109061718, 0.01612892933189869, 0.03779597580432892, 0.06425030529499054, 0.00308815436437726, -0.0022288127802312374, -0.07446198910474777, 0.012571852654218674, 0.03641512244939804, 0.06045425310730934, 0.02706310898065567, -0.007586566731333733, 0.06368265300989151, -0.05217486247420311, 0.0070708878338336945, -0.044163502752780914, -0.02778070792555809, -0.06004146486520767, 0.010187553241848946, -0.010429628193378448, -0.06478532403707504, -5.481084038754623e-33, 0.0033620351459831, -0.04740603640675545, 0.04654812067747116, -0.10025439411401749, -0.03032156638801098, -0.05373893305659294, -0.0038287390489131212, 0.024609260261058807, 0.012333426624536514, 0.002863267669454217, -0.02680109068751335, -0.03752008080482483, 0.004929214715957642, -0.014895734377205372, 0.04107419028878212, 0.012304791249334812, 0.019455596804618835, -0.009633178822696209, -0.016750356182456017, -0.03010016307234764, 0.013619762845337391, 0.03367667272686958, -0.014606731943786144, -0.042629048228263855, -0.03892720490694046, 0.03221941739320755, -0.01275115180760622, 0.03277396038174629, -0.04122672975063324, 0.01787348836660385, 0.0036835719365626574, -0.04829636588692665, 0.016829105094075203, -0.03850352391600609, -0.04205679893493652, -0.004437214694917202, -0.024460015818476677, -0.053988873958587646, -0.02322482503950596, -0.0023316373117268085, -0.05505341291427612, 0.014151064679026604, 0.012377402745187283, -0.0008842308889143169, -0.0061139934696257114, 0.0010836072033271194, 0.025718722492456436, -0.0015546828508377075, 0.022509798407554626, 0.03597932308912277, -0.06052621454000473, 0.008845074102282524, -0.01951564848423004, 0.01720951311290264, 0.0670117735862732, 0.031080003827810287, -0.0020561320707201958, -0.0354730598628521, 0.023230837658047676, 0.03455643355846405, -0.010426771827042103, -0.001207701163366437, 0.002887158887460828, 0.03147602826356888, 0.027307966724038124, 0.04402667656540871, 0.028753023594617844, 0.015361867845058441, -0.05833868682384491, 0.008874241262674332, -0.02488437481224537, 0.09205688536167145, 0.006068550981581211, -0.007873515598475933, -0.0002716774761211127, 0.029971566051244736, -0.015827113762497902, 0.024659333750605583, -0.01270062755793333, 0.07367171347141266, -0.014836444519460201, 0.01501554250717163, -0.009518817067146301, -0.014142831787467003, 0.011569306254386902, 0.01445543672889471, 0.02170945517718792, -0.01823555864393711, 0.013554125092923641, 0.003830874804407358, 0.010773122310638428, 0.02385052852332592, 0.008998630568385124, -0.010583573020994663, 0.0281405970454216, 0.01489296555519104, 0.015643388032913208, 0.025293344631791115, -0.009148003533482552, 0.013303553685545921, -0.0750967264175415, -0.05536077171564102, -0.031273938715457916, -0.009470726363360882, 0.005490489769726992, 0.01450345665216446, -0.03987979143857956, 0.030677558854222298, -0.008435013704001904, 0.014162630774080753, -0.01654639095067978, -0.0017758889589458704, 0.054587896913290024, -0.008266374468803406, 0.030421659350395203, -0.059763453900814056, -0.016011139377951622, 0.02268669568002224, 0.02064949832856655, -0.10265415161848068, -0.03780217468738556, -0.019081592559814453, -0.02823249064385891, 0.02799111232161522, -0.016954220831394196, -0.02545982412993908, -0.037373561412096024, 0.00375728914514184, -0.006883725523948669, -0.04443817213177681, 0.010017229244112968, 0.03217476233839989, 2.9140664992155507e-07, -0.06715337187051773, 0.021636387333273888, -0.008046609349548817, -0.0069416118785738945, 0.02377266436815262, 0.01239953376352787, -0.01485714502632618, -0.007631340995430946, -0.0509224571287632, -0.006240645423531532, 0.08357436954975128, -0.011113970540463924, 0.010375484824180603, 0.020073555409908295, -0.05272364988923073, -0.03864102065563202, 0.022571628913283348, 0.04803250730037689, -0.03687877580523491, -0.028245069086551666, 0.0744347870349884, 0.03912508860230446, 0.03839351609349251, 0.020852694287896156, 0.046175517141819, 0.02449910156428814, -0.008249706588685513, -0.0068229492753744125, 0.04719620570540428, -0.018861398100852966, -0.026006901636719704, 0.008734348230063915, -0.01515829749405384, -0.019497251138091087, -0.01971776969730854, 0.018249299377202988, -0.05681934207677841, 0.044412896037101746, 0.012652351520955563, -0.0055517032742500305, 0.024096406996250153, -0.011467553675174713, 0.029775165021419525, 0.0030516835395246744, 0.028381727635860443, -0.039752520620822906, 0.011377865448594093, 0.035341568291187286, 0.018065663054585457, -0.02370108664035797, -0.005771800875663757, 0.035731155425310135, -0.01253483071923256, 0.02003663219511509, -0.023025544360280037, 0.009513740427792072, 0.023362917825579643, -0.008865219540894032, 0.03590984269976616, 0.02051808312535286, -0.04006323963403702, -0.0066407849080860615, -0.014868825674057007, 0.03659549728035927, -0.04769540950655937, -0.04496427997946739, -0.03363791108131409, 3.0708244783009403e-34, -0.038174912333488464, -0.013104511424899101, -0.0024448344483971596, 0.04896557703614235, 0.004931854549795389, 0.00833773985505104, 0.08284710347652435, 0.008635729551315308, 0.04982074722647667, 0.004022783599793911, -0.04869455099105835]

['Isabeau Prémont-Schwarz', 'Alexander Ilin', 'Tele Hotloo Hao', 'Antti Rasmus', 'Rinu Boney', 'Harri Valpola']

1707.09219v4

We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The architecture shows close-to-optimal results on temporal modeling of video data, competitive results on music modeling, and improved perceptual grouping based on higher order abstractions, such as stochastic textures and motion cues. We present results for fully supervised, semi-supervised, and unsupervised tasks. The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions, learning iterative inference and handling temporal information.

Recurrent Ladder Networks

http://arxiv.org/pdf/1707.09219v4

Title Recurrent Ladder Networks Summary propose recurrent extension Ladder network whose structure motivated inference required hierarchical latent variable model demonstrate recurrent Ladder able handle wide variety complex learning task benefit iterative inference temporal modeling architecture show closetooptimal result temporal modeling video data competitive result music modeling improved perceptual grouping based higher order abstraction stochastic texture motion cue present result fully supervised semisupervised unsupervised task result suggest proposed architecture principle powerful tool learning hierarchy abstraction learning iterative inference handling temporal information Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.008140220306813717, 0.0573250949382782, 0.0059646740555763245, 0.04990041255950928, 0.00830447394400835, 0.0008088753093034029, 0.01290297694504261, -0.02803797833621502, -0.05059698969125748, 0.03342720493674278, -0.022068766877055168, -0.007347153499722481, -0.00231430702842772, 0.031997282058000565, 0.045655060559511185, -0.11156047880649567, -0.010095798410475254, -0.018481047824025154, 0.016749553382396698, 0.009534686803817749, -0.011174355633556843, -0.03871750086545944, -0.012545432895421982, 0.02058189921081066, -0.038135070353746414, 0.011402027681469917, -0.046238820999860764, -0.0033267377875745296, -0.013242621906101704, -0.03854592144489288, 0.015617676079273224, 0.022624125704169273, 0.06548057496547699, 0.033601343631744385, 2.5240067316190107e-06, 0.02388770505785942, 0.008367419242858887, -0.03909364715218544, 0.0407772921025753, -0.04215339198708534, -0.015549352392554283, 0.005558791570365429, -0.031112533062696457, 0.014254611916840076, -0.0027958450373262167, -0.041019123047590256, 0.046433281153440475, 0.02208772674202919, 0.01690538413822651, 0.04375861957669258, -0.02037416398525238, -0.07466862350702286, -0.0012482519960030913, -0.07251992076635361, 0.02995285764336586, -0.03679134324193001, 0.030138250440359116, 0.02530919946730137, 0.02159905806183815, 0.02351829968392849, -0.05016991123557091, 0.026027187705039978, 0.04799734801054001, 0.01279713399708271, 0.054579805582761765, 0.030525879934430122, 0.07037965208292007, -0.00198049983009696, -0.009146656841039658, 0.021603649482131004, -0.05635654181241989, -0.0029568150639533997, 0.007857671007514, 0.011746124364435673, 0.015652300789952278, -0.023916132748126984, -0.03825385868549347, 0.0049277315847575665, 0.00782005488872528, -0.018397409468889236, -0.02641686610877514, 0.0410088412463665, 0.006796654313802719, -0.0068131303414702415, 0.02501521073281765, 0.02609136328101158, -0.001723198452964425, -0.005331238266080618, -0.040047090500593185, -0.05065833032131195, 0.05123914033174515, -0.068992480635643, 0.013188321143388748, 0.03413994237780571, 0.013346468098461628, -0.02100231498479843, 0.011210470460355282, -0.03634610027074814, -0.03780011832714081, -0.0411221869289875, 0.04786856472492218, 0.001096400897949934, 0.0033896206878125668, 0.03801945596933365, 0.017198823392391205, 0.0445232018828392, -0.07820737361907959, -0.0181418489664793, -0.03234710544347763, 0.017726877704262733, -0.027155408635735512, -0.018131639808416367, -0.002680355915799737, 0.044688425958156586, -0.009137756191194057, -0.037454161792993546, -0.03824552893638611, -0.009804390370845795, -0.018492748960852623, -0.011981473304331303, -0.03848527744412422, 0.05929138511419296, -3.0480582609015983e-06, -0.014117345213890076, -0.005995802115648985, 0.035534560680389404, -0.04615069925785065, 0.06383860111236572, 0.008557711727917194, 0.03738490864634514, 0.01086929626762867, 0.01650966890156269, 0.014452430419623852, 0.05495753884315491, 0.02437777817249298, 0.061553798615932465, -0.0014639334985986352, 0.053326379507780075, -0.045591603964567184, 0.0020393156446516514, -0.011764644645154476, -0.033128198236227036, 0.030132636427879333, -0.10147865116596222, 0.0035369552206248045, -0.04696521908044815, -0.023773193359375, 0.013794736005365849, -0.00284592411480844, -0.01624280773103237, -0.03375234082341194, 0.03586336970329285, -0.0016437264857813716, 0.023802440613508224, 0.049390166997909546, -0.005112471524626017, -0.013395991176366806, 0.015329377725720406, 0.05969950556755066, 0.07627429068088531, -0.018644070252776146, 0.004894911777228117, 0.04618940129876137, 0.05577436089515686, -0.043737899512052536, -0.061331938952207565, -0.04866014048457146, -0.11335194110870361, -0.06803523749113083, 0.03323766589164734, 0.020311878994107246, -0.015463273040950298, 0.014718112535774708, -0.020302390679717064, 0.018558969721198082, 0.012309310957789421, 0.038460083305835724, 0.025634221732616425, 0.05824775621294975, -0.030184345319867134, 0.005169461015611887, 0.04610582813620567, -0.003342395182698965, 0.08565399795770645, 0.034415170550346375, -0.016951939091086388, -0.04884333536028862, -0.01873714104294777, -0.05748603865504265, -0.05294042453169823, 0.0300492774695158, 0.015754150226712227, -0.001123170368373394, -0.01875208131968975, 0.06291001290082932, 0.040424395352602005, -0.03621993213891983, -0.04364793747663498, -0.004798934329301119, -0.004594561643898487, -0.019504522904753685, -0.009286775253713131, 0.020420676097273827, 0.044837575405836105, 0.012890649959445, -0.04496057331562042, 0.00043292733607813716, -0.0038816689047962427, 0.005809924099594355, -0.0036840317770838737, -0.056239400058984756, -0.032467834651470184, 0.028271717950701714, -0.03558899462223053, -0.05550574138760567, 0.002200373914092779, 0.02897479198873043, 0.03494798392057419, -0.045833878219127655, -0.0201259795576334, 0.0007160056266002357, 0.02358386479318142, -0.009597739204764366, 0.015318050049245358, -0.009301435202360153, 0.012532656081020832, 0.024381762370467186, 0.025436419993638992, 0.049062687903642654, -0.002243740949779749, 0.029383176937699318, 0.011139892041683197, 0.017452821135520935, -0.05628271773457527, -0.020120395347476006, -0.030565941706299782, -0.05403531715273857, -0.04579249024391174, 0.0005485448054969311, -0.006459794007241726, 0.04396456852555275, 0.017321914434432983, -0.041283220052719116, -0.04270123317837715, 0.07575087249279022, 0.008781404234468937, 0.015521666966378689, 0.008991912938654423, 0.02411435917019844, 0.031104594469070435, -0.011200069449841976, 0.022756638005375862, 0.054243020713329315, -0.04578167200088501, -0.008372846990823746, -0.0069645908661186695, 0.040313638746738434, -0.0016945230308920145, -0.015972333028912544, -0.002426374005153775, 0.026330240070819855, -0.02351539395749569, -0.04585283249616623, -0.0018576422007754445, -0.006608122028410435, -0.025151049718260765, -0.015353863127529621, -0.03267856314778328, -0.0012365223374217749, -0.023407846689224243, -0.020398994907736778, -0.029463469982147217, -0.024682465940713882, 0.00525805214419961, -0.051736705005168915, -0.026829104870557785, 0.05860495939850807, -0.008626890368759632, -0.03196830302476883, 0.006350588519126177, -0.0161809753626585, -0.04074165225028992, -0.014186217449605465, -0.017952661961317062, -0.003386041149497032, 0.03512074053287506, -0.005633319728076458, -0.10560336709022522, 0.047164689749479294, -0.03587452694773674, -0.029827971011400223, 0.0420055128633976, -0.007125680800527334, -0.03704024478793144, -0.025820503011345863, -0.03104572929441929, 0.07818710803985596, 0.05118251591920853, 0.019500654190778732, 0.0291686300188303, -0.024845605716109276, -0.006634732708334923, 0.012689505703747272, 0.010150408372282982, -0.012117140926420689, -0.010113437660038471, 0.05031031370162964, 0.003504237625747919, -0.019139934331178665, 0.04395149648189545, 0.05548480898141861, 0.027231523767113686, -0.02550012245774269, 0.002273679245263338, 0.0028296252712607384, -0.009781002067029476, -0.02641134336590767, -0.031429558992385864, 0.01599147729575634, 0.0032162710558623075, -0.04596647620201111, -0.02515503577888012, 0.02159019373357296, 0.01622910238802433, -0.032661814242601395, 0.04058695212006569, -0.028719164431095123, -0.03300759568810463, 0.045953378081321716, 0.06767188012599945, -0.008438180200755596, -0.018042512238025665, -0.05973124876618385, -0.060652390122413635, -0.0018248892156407237, 0.045433901250362396, -0.01693364605307579, -0.030805258080363274, -0.05546225607395172, -0.005114453379064798, 0.004284524824470282, -0.003417378757148981, -0.051793172955513, 0.024013841524720192, 0.033249326050281525, -0.007112396880984306, -0.08753625303506851, 0.03182552754878998, 0.004596630576997995, 0.00956378411501646, 0.0019215908832848072, 0.05859280005097389, -0.023664850741624832, 0.013534302823245525, -0.009004381485283375, 0.09106569737195969, 0.027707073837518692, -0.011178453452885151, -0.037388235330581665, -0.03701798617839813, 0.058504920452833176, 0.02678949013352394, 0.021266860887408257, -0.01187834795564413, -0.0948750227689743, 0.05202176794409752, -0.018110502511262894, 0.018694112077355385, -0.01726832054555416, 0.03192499279975891, -0.017651181668043137, -0.08569718152284622, 0.05651646852493286, 0.037851765751838684, -0.025388602167367935, -0.03386518359184265, 0.004213797859847546, 0.026187893003225327, -0.021365785971283913, 0.011282947845757008, -0.017127415165305138, -0.019078217446804047, 0.017312662675976753, 0.012616433203220367, -0.0065482184290885925, 0.0349724218249321, -0.01638028398156166, 0.0074058291502296925, -0.045906420797109604, 0.1032903715968132, 0.01670476235449314, -0.06164482980966568, -0.028152264654636383, 0.02368217147886753, 0.00895618461072445, 0.017432712018489838, -0.047915924340486526, 0.036025263369083405, 0.005733341444283724, -0.01747767999768257, 0.044644810259342194, -0.07163199037313461, 0.0016175454948097467, 0.01432008482515812, -0.06915760040283203, -0.009790834970772266, 0.037377770990133286, 0.03233817219734192, -0.03584825620055199, -0.014358633197844028, 0.007725316099822521, -0.02314108796417713, 0.006487241014838219, -0.011544455774128437, 0.04227006435394287, 0.038330238312482834, -0.0008329010452143848, 0.006897664628922939, 0.09282383322715759, 0.012415898963809013, 0.028139270842075348, 0.021910158917307854, 0.023413706570863724, 0.0032577896490693092, -0.029978498816490173, -0.06023772060871124, 0.027841903269290924, 0.0026227557100355625, -0.0001869533589342609, 0.02255692519247532, -0.013908703811466694, -0.006140878424048424, 0.01910410448908806, 0.0025875424034893513, 0.010074801743030548, -0.007524402346462011, -0.0008408268913626671, 0.014189561828970909, -0.08086792379617691, -0.06747269630432129, 0.006675454322248697, -0.015625324100255966, 0.056432660669088364, -0.004244446288794279, 0.02959156036376953, -0.0017087218584492803, -0.0306765828281641, -0.04824948310852051, 0.025523385033011436, 0.04475872963666916, -0.008654318749904633, -0.012401832267642021, -0.03212982043623924, 0.03257934749126434, -0.021654943004250526, -0.01462569646537304, -0.06895198673009872, -0.051754429936409, -0.01460850890725851, -0.042366109788417816, 0.058092162013053894, 0.0046695745550096035, 0.06546156853437424, -0.01313753891736269, -0.006906535010784864, 0.049043335020542145, -0.04673101380467415, 0.005989257246255875, 0.003453571116551757, 0.023290878161787987, -0.03010203130543232, -0.01626916602253914, 0.007009430788457394, -0.043228939175605774, 0.09944989532232285, 0.010172403417527676, -0.015430400148034096, 0.008616188541054726, -0.016075503081083298, -0.0017771209822967649, -0.08129887282848358, 0.03894469514489174, 0.01095342542976141, -0.04875548183917999, -0.06239929795265198, 0.005918008740991354, -0.011853259988129139, 0.008604028262197971, -0.05349703133106232, 0.030736081302165985, 0.036805737763643265, 0.06593110412359238, -0.03639250993728638, -0.06984486430883408, 0.0899781808257103, -0.052955932915210724, -0.014781265519559383, 0.010906045325100422, -0.042609356343746185, -0.0024489029310643673, -0.04351501539349556, 0.022328229621052742, 0.014645890332758427, 0.020002584904432297, -0.004097931087017059, 0.02369985543191433, 0.020343584939837456, 0.05972874537110329, 0.019919589161872864, 0.029110925272107124, -0.03446287661790848, 0.037900082767009735, -0.0054465364664793015, -0.033064018934965134, -0.05083385482430458, 0.03504563868045807, 0.08570247143507004, -0.03772988170385361, -0.007470443844795227, 0.012642460875213146, 0.026100261136889458, -0.025069957599043846, 0.044138047844171524, -0.02086949720978737, -0.05665707588195801, 0.023352352902293205, 0.004374271724373102, -0.02379726804792881, 0.0016103537054732442, 0.043493520468473434, 0.06554318964481354, -0.03978047892451286, -0.008798732422292233, 0.03970259800553322, -0.0005984582239761949, 0.023505445569753647, 0.00099930539727211, 0.0003019680443685502, -0.00502652395516634, 0.04822533577680588, -0.003630184568464756, -0.06305748224258423, -0.025850554928183556, 0.019076714292168617, 0.030479922890663147, 0.004140777047723532, 0.03582021966576576, 0.0354735292494297, 0.0035421729553490877, -0.01991552673280239, -0.007272874005138874, -0.06644843518733978, 0.00866416934877634, -0.024428101256489754, -0.04952574521303177, -6.525869295237226e-33, -0.04829049110412598, -0.03115122951567173, 0.000767088495194912, 0.049131568521261215, -0.034114520996809006, 0.017305273562669754, -0.05778864398598671, -0.01897471398115158, 0.013552861288189888, 0.009469839744269848, -0.008427099324762821, 0.020926903933286667, 0.005792572163045406, 0.018297288566827774, 0.08505721390247345, -0.0016895198496058583, 0.03818172961473465, -0.009758209809660912, 0.02863532491028309, 0.007377161178737879, 0.046903274953365326, 0.030082598328590393, 0.05431543290615082, -0.0760919526219368, -0.0950738862156868, 0.022962279617786407, -0.005317644216120243, 0.005938135087490082, 0.008852778933942318, 0.0024595041759312153, -0.021485768258571625, -0.05540398880839348, 0.03247837722301483, -0.04510817304253578, -0.008103677071630955, -0.007426420226693153, -0.11838917434215546, -0.024441983550786972, -0.05769472196698189, 0.01607053168118, -0.0709441527724266, -0.004912520293146372, 0.06983909755945206, -0.011534132063388824, -0.009431160986423492, -0.00720176612958312, 0.0622577928006649, -0.04545086622238159, 0.015339142642915249, -0.07290120422840118, -0.04904419928789139, 0.018965551629662514, -0.02214602753520012, -0.033259350806474686, 0.025214362889528275, 0.017099561169743538, -0.012214293703436852, 0.01048207376152277, -0.059067774564027786, 0.027051666751503944, -0.021203579381108284, 0.03547364100813866, 0.04136720672249794, 0.04346304014325142, 0.032889846712350845, 0.00923238880932331, 0.003908953163772821, -0.04390067234635353, -0.05230444669723511, 0.006985352840274572, -0.005093114450573921, 0.07353374361991882, 0.07460424304008484, -0.0828385204076767, 0.08502310514450073, -0.013923682272434235, -0.04863647744059563, 0.0371340773999691, 0.00016385014168918133, 0.06314200162887573, -0.04529789462685585, 0.05480282008647919, -0.0009389835176989436, 0.012693793512880802, 0.024420984089374542, -0.008422011509537697, -0.017645539715886116, -0.07378171384334564, 0.019082650542259216, 0.0016680924454703927, 0.06250578910112381, -0.047257810831069946, 0.014384324662387371, -0.013582231476902962, 0.022866934537887573, -0.00849699042737484, 0.0028489266987890005, 0.04778684675693512, 0.035474132746458054, 0.01606988161802292, -0.03884102404117584, 0.019730806350708008, 0.034826863557100296, 0.0074107954278588295, -0.011911354027688503, 0.032968487590551376, 0.004624988418072462, 0.05351245403289795, 0.00096392777049914, -0.02560047246515751, 0.016401484608650208, -0.016795070841908455, 0.017084090039134026, 0.05706380307674408, 0.04119007661938667, -0.022824499756097794, -0.017729202285408974, 0.086029551923275, -0.018809430301189423, 0.03564092144370079, -0.014890043064951897, 0.02965979278087616, 0.0005661636241711676, 0.051929593086242676, -0.03458636626601219, -0.006275510415434837, -0.08296569436788559, -0.060262519866228104, 0.0015493963146582246, -0.03628110885620117, -0.01858176477253437, 0.029668567702174187, 3.2685343853700033e-07, -0.04839355871081352, -0.027969587594270706, 0.055875521153211594, -0.00793433841317892, 0.06214115023612976, 0.0038822083733975887, -0.03453630581498146, -0.0012230676366016269, 0.01449433621019125, -0.005019441246986389, 0.05059506371617317, -0.005428086966276169, 0.04403619468212128, -0.004697923082858324, -0.05755315721035004, -0.0309072844684124, -0.030612217262387276, -0.013807586394250393, -0.026609843596816063, -0.02693507820367813, 0.03296101838350296, 0.097767174243927, 0.0489216074347496, 0.003950327634811401, 0.025489408522844315, 0.001341052702628076, 0.01985604129731655, 0.04757613688707352, -0.005942902527749538, -0.022311365231871605, 0.02475408837199211, 0.02130368910729885, -0.0450793132185936, 0.005170933436602354, -0.026340370997786522, 0.047221120446920395, 0.023203514516353607, 0.000619941798504442, -0.027616653591394424, -0.010878930799663067, 0.015148513950407505, 0.05171196907758713, 0.027762610465288162, -0.009435995481908321, 0.04708581045269966, -0.044718850404024124, -0.03541781008243561, -0.0059007564559578896, -0.006959132384508848, 0.06566553562879562, -0.009651568718254566, 0.00984924379736185, -0.021980980411171913, -0.03483196347951889, 0.04207722097635269, -0.04250207170844078, -0.0024579435121268034, -0.060371655970811844, 0.04395010322332382, 0.04440750554203987, -0.033353328704833984, 0.013350415974855423, -0.0019047546666115522, 0.0024871735367923975, 0.0041388580575585365, 0.009375210851430893, -0.06871525943279266, 2.945482112603485e-34, 0.009642143733799458, -0.04598795622587204, -0.022128988057374954, 0.0031325919553637505, -0.014134086668491364, -0.007841468788683414, -0.05026250332593918, 0.038955818861722946, 0.004651352297514677, -0.01391072478145361, -0.039301346987485886]

['Kenji Kawaguchi', 'Leslie Pack Kaelbling', 'Yoshua Bengio']

1710.05468v3

With a direct analysis of neural networks, this paper presents a mathematically tight generalization theory to partially address an open problem regarding the generalization of deep learning. Unlike previous bound-based theory, our main theory is quantitatively as tight as possible for every dataset individually, while producing qualitative insights competitively. Our results give insight into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, answering to an open question in the literature. We also discuss limitations of our results and propose additional open problems.

Generalization in Deep Learning

http://arxiv.org/pdf/1710.05468v3

Title Generalization Deep Learning Summary direct analysis neural network paper present mathematically tight generalization theory partially address open problem regarding generalization deep learning Unlike previous boundbased theory main theory quantitatively tight possible every dataset individually producing qualitative insight competitively result give insight deep learning generalize well despite large capacity complexity possible algorithmic instability nonrobustness sharp minimum answering open question literature also discus limitation result propose additional open problem Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.012876843102276325, 0.04441167414188385, -0.01813766546547413, 0.03599070385098457, 0.007772340439260006, -0.008717292919754982, 0.000206919910851866, -0.012016835622489452, -0.043246444314718246, 0.04879344627261162, 0.012480729259550571, -0.02803785540163517, -0.015330921858549118, 0.05843678116798401, 0.013379241339862347, -0.062310703098773956, -0.007134734652936459, 0.01489038486033678, 0.0016824579797685146, -0.05787450075149536, 0.02079741470515728, -0.04564163461327553, 0.018651770427823067, 0.03511654958128929, -0.0466933436691761, 0.024894459173083305, -0.006646694615483284, -0.016545426100492477, 0.008777433075010777, 0.011953301727771759, 0.037351369857788086, -0.017746882513165474, 0.02818211354315281, 0.01722269132733345, 2.357874109293334e-06, -0.04938988387584686, -0.01875377632677555, -0.03289981186389923, 0.005388742312788963, 0.011782707646489143, -0.02171989716589451, -0.023157864809036255, 0.013788782060146332, -0.018007803708314896, -0.027428654953837395, -0.038178447633981705, 0.04356417432427406, 0.05712052062153816, 0.02102072536945343, 0.04881548509001732, -0.019309690222144127, -0.04502565786242485, 0.03194424510002136, -0.027468625456094742, -0.011822142638266087, -0.04004918783903122, 0.009333238005638123, 0.01993095688521862, -0.04982326924800873, -0.05734098330140114, -0.0009666848345659673, 0.045969776809215546, 0.06802704185247421, 0.036644864827394485, 0.019335448741912842, 0.03130844607949257, -0.04466353729367256, -0.01769316755235195, 0.012181209400296211, 0.06720679998397827, -0.030033988878130913, 0.031040703877806664, -0.03406188264489174, -0.015474864281713963, -0.008631554432213306, -0.02103365585207939, -0.03719613701105118, 0.01574806682765484, 0.011514945887029171, 0.012984644621610641, -0.051189400255680084, 0.05491222068667412, 0.04746008664369583, 0.015349209308624268, -0.04659814015030861, 0.0426076203584671, -0.006014922633767128, 0.0077883172780275345, 0.009389887563884258, -0.023692425340414047, -0.06521350145339966, 0.01779961958527565, 0.0006468997453339398, 0.040292564779520035, -0.010538296774029732, -0.037463411688804626, -0.021335888653993607, -0.043786145746707916, 0.02129921317100525, -0.0635245144367218, 0.04696403071284294, -0.027440568432211876, -0.01019503828138113, 0.005934945307672024, 0.004744399338960648, 0.049538347870111465, -0.06559309363365173, 0.02689509280025959, 0.008663710206747055, -0.010114485397934914, -0.025041935965418816, -0.004613508004695177, -0.014568738639354706, 0.10307934135198593, 0.009173023514449596, -0.020289305597543716, -0.06587427854537964, -0.0012002709554508328, -0.0509917251765728, -0.0014058565720915794, -0.009935865178704262, 0.07043854892253876, -0.0005898072267882526, -0.001527248416095972, 0.002442436758428812, -0.022172508761286736, -0.0507507249712944, 0.050640713423490524, -0.007196665741503239, -0.03432703763246536, 0.035164929926395416, -0.0012903959723189473, 0.033316995948553085, 0.02508951723575592, 0.028512198477983475, 0.08692789077758789, -0.0074402280151844025, 0.015622302889823914, -0.045928969979286194, -0.010154030285775661, -0.019753554835915565, -0.014356318861246109, -0.05055157467722893, -0.06545458734035492, 0.0005436186329461634, -0.03943679854273796, 0.012905195355415344, 0.001089510158635676, -0.028422409668564796, -0.03426149860024452, -0.02394806407392025, 0.03368690609931946, -0.05162281170487404, -0.012135017663240433, 0.09777530282735825, 0.017329560592770576, 0.0048466091975569725, 0.02674846164882183, 0.022832583636045456, 0.021106669679284096, 0.025678277015686035, -0.03368695452809334, 0.020548200234770775, 0.03328344225883484, 0.015189391560852528, -0.053658049553632736, -0.02264019288122654, -0.04205566272139549, -0.0028292371425777674, 0.013623612001538277, -0.029459698125720024, 0.044201381504535675, -0.02443581447005272, -0.0638248398900032, 0.03339201956987381, 0.05643511191010475, 0.04375525563955307, 0.07785044610500336, 0.023214105516672134, -0.011355689726769924, 0.03519849106669426, 0.03596087917685509, 0.01862543821334839, 0.005057964473962784, 0.0014995072269812226, -0.046646490693092346, -0.02732500620186329, -0.05387691408395767, -0.06825386732816696, -0.04324125871062279, 0.03285104036331177, -0.01912085898220539, 0.0022775293327867985, -0.023801634088158607, 0.08230653405189514, -0.01660907082259655, 8.258083107648417e-05, 0.02494964376091957, 0.019663000479340553, 0.00981966219842434, -0.003999867010861635, -0.0259300097823143, 0.01261278335005045, -0.06732021272182465, -0.014980030246078968, -0.03780659660696983, -0.04512176290154457, 0.001698939478956163, -0.009122367016971111, -0.056513361632823944, 0.03324396535754204, 0.001343758194707334, 0.07124122232198715, -0.02911965735256672, 0.01928541250526905, 0.014479078352451324, -0.005583684891462326, -0.012591073289513588, -0.02832948975265026, 0.001009393366985023, 0.03986053168773651, 0.022570190951228142, -0.03328392282128334, 0.014482582919299603, 0.0003645741962827742, -0.026273585855960846, 0.04783083498477936, 0.06691430509090424, 0.041347697377204895, 0.029621047899127007, 0.0024844598956406116, -0.047089919447898865, 0.021463865414261818, -0.05768076702952385, -0.03705717995762825, -0.02766287513077259, -0.03968704864382744, 0.04867001995444298, 0.018448689952492714, -0.05468311905860901, 0.026444049552083015, 0.07129355520009995, -0.028311287984251976, -0.07607871294021606, 0.02794736437499523, 0.01375154685229063, -0.00018706271657720208, -0.014586363919079304, 0.0012076223501935601, -0.0426589734852314, 0.06606270372867584, 0.004910503048449755, 0.024635732173919678, 0.0068191466853022575, 0.030491888523101807, -0.002761844778433442, 0.0027300419751554728, 0.0583011768758297, -0.03632890060544014, -0.06646741926670074, -0.010960404761135578, -0.06847088038921356, 0.01017336081713438, 0.04526912048459053, 0.009232406504452229, 0.022637711837887764, 0.03549560159444809, -0.023270592093467712, -0.01053518895059824, -0.01560455746948719, -0.026004334911704063, -0.010737758129835129, 0.015033473260700703, 0.030493592843413353, 0.0028871886897832155, -0.039250269532203674, 0.06638100743293762, 0.02877206541597843, -0.042983826249837875, 0.06352221220731735, 0.027663318440318108, -0.007822596468031406, -0.010726395063102245, -0.05204097926616669, 0.0005562377627938986, 0.035867515951395035, 0.04476549103856087, -0.03285672515630722, 0.018020024523139, 0.028648529201745987, -0.030897649005055428, 0.035244133323431015, -0.02035045064985752, -0.05901487171649933, 0.006140165496617556, -0.05623941868543625, -0.06046818941831589, 0.05580427497625351, -0.010713516734540462, -0.028827641159296036, -0.00976110901683569, 0.08136876672506332, -0.04657837003469467, 0.016587447375059128, -0.022260364145040512, -0.0077398186549544334, 0.00783092062920332, 0.012854191474616528, -0.002217109315097332, 0.053050797432661057, 0.009589135646820068, -0.0064411167986691, -0.009025360457599163, 0.016018975526094437, 0.0008378924103453755, -0.015924304723739624, -0.06405876576900482, 0.01873915083706379, 0.017649322748184204, 0.012849695980548859, -0.03690142557024956, -0.06639756262302399, 0.029974916949868202, 0.046075690537691116, 0.018529746681451797, 0.05237949267029762, -0.07310517877340317, -0.005930441897362471, 0.03036004677414894, 0.0137253412976861, 0.013384547084569931, -0.03886468708515167, -0.07321402430534363, -0.046990618109703064, -0.010732898488640785, -0.022460775449872017, -0.0226446446031332, 0.06957344710826874, 0.006278745364397764, -0.018072428181767464, -0.03759535029530525, -0.015537534840404987, -0.03583351895213127, 0.010275425389409065, 0.024777326732873917, 0.030441243201494217, 0.01247571874409914, -0.01394905149936676, -0.002339213853701949, -0.0030563788022845984, -0.011279321275651455, 0.04181923344731331, -0.018476521596312523, -0.009569155983626842, -0.031339604407548904, 0.03808789327740669, -0.0017030664021149278, -0.0328790619969368, -0.04130927473306656, 0.014422573149204254, 0.026116618886590004, 0.002622186904773116, -0.02490042708814144, 0.07442321628332138, -0.11665990203619003, -0.0005064260330982506, -0.009620100259780884, -0.009402723982930183, -0.029228633269667625, 0.0031458772718906403, 0.023435816168785095, -0.03346554562449455, 0.027932656928896904, 0.0529816634953022, -0.040755048394203186, -0.06818103790283203, 0.0021060039289295673, 0.029498636722564697, -0.03685044124722481, 0.01615612581372261, 0.01399518083781004, -0.021893778815865517, 0.007609910797327757, 0.0033266067039221525, -0.02237565815448761, 0.007289351895451546, -0.04681815952062607, 0.011691552586853504, -0.059472568333148956, -0.02209562435746193, 0.0014729282120242715, -0.05563701316714287, -0.056788600981235504, 0.02841281145811081, 0.026691963896155357, -0.03419338911771774, 0.01024014875292778, -0.010759902186691761, 0.04252937063574791, -0.05482051894068718, 0.053061459213495255, -0.057181380689144135, -0.011425526812672615, 0.027913812547922134, -0.10770231485366821, -0.0074737477116286755, 0.0213987547904253, 0.030072879046201706, -0.05284508690237999, -0.029547253623604774, 0.028684813529253006, 0.02674570307135582, -0.00740422448143363, -0.012567386962473392, 0.05615236982703209, 0.06127023696899414, -0.04427803307771683, 0.02769411914050579, 0.06458797305822372, -0.024994848296046257, 0.06924545764923096, 0.0070436312817037106, 0.058390796184539795, 0.006637022364884615, -0.020307792350649834, -0.04111970216035843, -0.021137721836566925, -0.014085263013839722, -0.014656168408691883, 0.006052213255316019, -0.04237210005521774, -0.019580015912652016, -0.006396177224814892, 0.048184867948293686, -0.03556545078754425, -0.012154761701822281, 0.029749535024166107, 0.03203786909580231, -0.01985696703195572, -0.057769063860177994, 0.007220402825623751, -0.03575746715068817, 0.08281721919775009, 0.020828094333410263, -0.02123183198273182, 0.011697781272232533, 0.024074498564004898, -0.026014400646090508, 0.01011631079018116, 0.045992881059646606, 0.010824385099112988, -0.0060934522189199924, 0.01664077863097191, -7.120678492356092e-05, -0.016735658049583435, -0.009543671272695065, -0.015723928809165955, -0.01677907258272171, -0.033159174025058746, -0.03274528309702873, 0.031701017171144485, 0.014599473215639591, -0.016814246773719788, -0.02677142061293125, -0.1018218919634819, 0.04037041217088699, 0.027697023004293442, 0.04271756485104561, -0.0033065418247133493, 0.07657935470342636, -0.013473454862833023, -0.0002496294036973268, 0.03762276470661163, -0.019492242485284805, 0.07238561660051346, 0.022385263815522194, -0.042785149067640305, -0.027895180508494377, 0.0011405980912968516, 0.022021068260073662, 0.020509658381342888, 0.07402245700359344, 0.07980280369520187, 0.012568462640047073, -0.037029948085546494, 0.00238188193179667, 0.07064152508974075, 0.002495786175131798, -0.06018779054284096, 0.01603115163743496, 0.052565205842256546, 0.034854456782341, -0.004971619695425034, -0.05559002608060837, 0.060926105827093124, -0.025973254814743996, -0.042841825634241104, -0.0009948277147486806, 0.020259486511349678, 0.060128871351480484, -0.005908907391130924, 0.036759234964847565, -0.04617463797330856, 0.013043832033872604, 0.0011436898494139314, -0.030833503231406212, 0.0018016077810898423, 0.00820024311542511, -0.0008261673501692712, 0.0729079470038414, -0.055549636483192444, -0.03547849878668785, -0.005785444285720587, -0.05155942216515541, -0.022552886977791786, 0.02547105774283409, 0.0200568325817585, 0.003477181075140834, -0.0746203362941742, 0.012330805882811546, 0.032586440443992615, -0.04188276827335358, 0.014407596550881863, -0.026086388155817986, 0.004061799496412277, 0.03350070118904114, -0.0179290808737278, -0.008355483412742615, 0.023740055039525032, 0.06459838896989822, 0.00536000169813633, -0.011095241643488407, -0.0465814545750618, 0.0090569369494915, -0.018912410363554955, 0.014741850085556507, 0.06666183471679688, 0.029906025156378746, -0.004936412442475557, 0.024093497544527054, 0.023532556369900703, -0.04852648451924324, 0.017316747456789017, 0.002888571238145232, 0.07141880691051483, 0.01015805546194315, -0.007943426258862019, 0.05602138116955757, 0.004825317766517401, -0.01881389319896698, 0.0046509732492268085, -0.0169654693454504, -0.0026648566126823425, 0.011664126999676228, -0.04674125835299492, -6.353645413846345e-33, 0.03221622854471207, 0.025943228974938393, -0.050408367067575455, -0.01451144553720951, -0.012709332630038261, 0.05228671059012413, 0.010586962103843689, -0.035124361515045166, -0.042220063507556915, -0.01999950036406517, -0.03866369649767876, 0.02580246515572071, -0.010685911402106285, 0.033463314175605774, 0.031351618468761444, -0.027167854830622673, 7.695060776313767e-05, -0.004875056445598602, 0.038199856877326965, 0.014178730547428131, 0.05132962018251419, 0.051463160663843155, 0.05543893575668335, -0.05607719346880913, -0.014881307259202003, -0.0042369370348751545, -0.03451612591743469, 0.008635944686830044, -0.015699660405516624, 0.0026391674764454365, -0.02131291665136814, 0.042640846222639084, 0.03414102643728256, -0.033736102283000946, 0.0002984523307532072, -0.012259638868272305, -0.039251867681741714, -0.041565924882888794, -0.05884888768196106, 0.019712261855602264, -0.05700182542204857, 0.017834991216659546, 0.11968445777893066, -0.022644435986876488, -0.030093198642134666, -0.004901394713670015, 0.06212468445301056, 0.0017529549077153206, -0.03496754169464111, -0.04925674572587013, -0.006332058925181627, 0.011278078891336918, -0.015470179729163647, 0.03185475245118141, -0.027951564639806747, 0.029125014320015907, -0.03149469196796417, 0.005256586242467165, -0.06885167956352234, 0.007073530927300453, 0.014785779640078545, 0.03487126901745796, -0.019629208371043205, 0.0018260459182783961, 0.042637914419174194, 0.04313305765390396, 0.054199088364839554, -0.02092762477695942, -0.027095582336187363, -0.012164472602307796, -0.0027130546513944864, 0.051160939037799835, 0.025311879813671112, 0.0199288222938776, 0.10480991750955582, -0.09012820571660995, -0.09670521318912506, -0.004027026239782572, 0.0017331278650090098, 0.011811062693595886, -0.016103524714708328, 0.004575546830892563, -0.02681048959493637, -0.008122183382511139, 0.011567661538720131, -0.0376555360853672, -0.026093777269124985, -0.011381320655345917, 0.008278684690594673, 0.004448470193892717, -0.007005201652646065, 0.01934772916138172, -0.04200064390897751, -0.06334647536277771, 0.0640743300318718, -0.0044471160508692265, 0.012081232853233814, 0.04247333109378815, 0.03239438682794571, -0.02428898774087429, -0.023894814774394035, -0.06948860734701157, -0.06870143860578537, 6.570939876837656e-05, 0.03562645614147186, 0.03128770366311073, 0.03329605609178543, 0.0521082729101181, 0.028278905898332596, -0.058741141110658646, -0.02201429381966591, -0.05325943976640701, 0.015444621443748474, 0.06078512966632843, 0.03926504775881767, -0.056421950459480286, 0.015995126217603683, 0.08112477511167526, 0.004003419075161219, 0.03757975250482559, -0.009929261170327663, 0.007497054990381002, 0.02717341110110283, 0.014847604557871819, -0.021930426359176636, -0.031052736565470695, -0.01791241765022278, -0.03158250451087952, 0.03195752948522568, -0.06641122698783875, -0.004147805273532867, -0.0017075228970497847, 2.951690589725331e-07, -0.03340211510658264, -0.029703684151172638, -0.0008058078237809241, 0.0035801345948129892, 0.010407756082713604, 0.01695035584270954, 0.008509354665875435, 0.04510379210114479, -0.08033088594675064, 0.008866789750754833, 0.051498785614967346, -0.02578696794807911, 0.014242293313145638, -0.004863569047302008, -0.056970465928316116, -0.014823532663285732, -0.05944964289665222, 0.05699244141578674, 0.0022101853974163532, 0.0352291502058506, 0.008522886782884598, 0.09148971736431122, 0.03714679554104805, -0.03179777413606644, 0.039799463003873825, -0.0414087288081646, -0.006266109179705381, -0.016829900443553925, 0.05196917802095413, 0.024356210604310036, 0.05707008019089699, 0.024194685742259026, -0.004717276431620121, 0.0027889225166291, 0.006414100062102079, 0.09232374280691147, 0.03629273176193237, 0.009015750139951706, 0.0017302108462899923, 0.0066339243203401566, 0.015542488545179367, -0.03710998594760895, 0.030765756964683533, -0.01429780013859272, 0.06427226215600967, -0.04234824702143669, -0.045839618891477585, -0.029225021600723267, 0.017000021412968636, 0.023106373846530914, 0.03803165256977081, -0.015019338577985764, 0.05557343736290932, -0.010221467353403568, -0.016538528725504875, -0.06633967906236649, 0.0011021457612514496, -0.07386147975921631, 0.052603889256715775, 0.029946744441986084, -0.03619058057665825, -0.0021727958228439093, -0.004178750328719616, -0.015462164767086506, 0.07412061095237732, 0.02861119620501995, 0.010071173310279846, 2.5545473594197916e-34, -0.023227771744132042, -0.009450927376747131, 0.02566887065768242, -0.02264309860765934, -0.010829263366758823, -0.030883068218827248, -0.030289379879832268, -0.01682121306657791, 0.023131024092435837, -0.021952329203486443, -0.027951989322900772]

['Yannic Kilcher', 'Gary Becigneul', 'Thomas Hofmann']

1710.11386v1

It is commonly agreed that the use of relevant invariances as a good statistical bias is important in machine-learning. However, most approaches that explicitly incorporate invariances into a model architecture only make use of very simple transformations, such as translations and rotations. Hence, there is a need for methods to model and extract richer transformations that capture much higher-level invariances. To that end, we introduce a tool allowing to parametrize the set of filters of a trained convolutional neural network with the latent space of a generative adversarial network. We then show that the method can capture highly non-linear invariances of the data by visualizing their effect in the data space.

Parametrizing filters of a CNN with a GAN

http://arxiv.org/pdf/1710.11386v1

Title Parametrizing filter CNN GAN Summary commonly agreed use relevant invariance good statistical bias important machinelearning However approach explicitly incorporate invariance model architecture make use simple transformation translation rotation Hence need method model extract richer transformation capture much higherlevel invariance end introduce tool allowing parametrize set filter trained convolutional neural network latent space generative adversarial network show method capture highly nonlinear invariance data visualizing effect data space Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.018514923751354218, 0.07642007619142532, -0.01028684712946415, 0.010576027445495129, 0.019531575962901115, -0.013879798352718353, 0.008748224005103111, 0.00696737552061677, -0.10806851089000702, -0.002081956248730421, -0.0034765591844916344, 0.07079602032899857, -0.026015527546405792, 0.02715121954679489, 0.06811004877090454, -0.08368003368377686, -0.00954139232635498, 0.0197456032037735, -0.06309007108211517, -0.03484651818871498, -0.018855800852179527, 0.011743429116904736, 0.0038924720138311386, 0.06289327889680862, -3.4639615478226915e-05, -0.017552746459841728, -0.009163931012153625, 0.05841860547661781, 0.040136586874723434, 0.023877054452896118, 0.003582186298444867, -0.008921097964048386, -0.018371455371379852, 0.03608561307191849, 2.7080679956270615e-06, 0.011784488335251808, -0.02095933072268963, -0.02364237979054451, 0.0323096327483654, 0.04564787074923515, 0.05358494818210602, -0.0025966260582208633, -0.04172835126519203, -0.010794812813401222, -0.03926844894886017, -0.07832726091146469, 0.01861402578651905, 0.006928083952516317, -0.011256189085543156, 0.040733035653829575, -0.019124748185276985, -0.02977127954363823, 0.0032146573066711426, -0.043751947581768036, -0.024231458082795143, -0.06429698318243027, -0.0159545186907053, -0.012726418673992157, -0.04628421366214752, -0.01092662662267685, -0.046261753886938095, 0.05445009469985962, 0.03334546834230423, -0.00034416007110849023, 0.030962828546762466, 0.024439364671707153, -0.010128497146070004, 0.0009844154119491577, 0.005886609200388193, 0.026077644899487495, -0.111628957092762, -0.035647761076688766, -0.020672449842095375, -0.012732146307826042, 0.03224707022309303, 0.04203944280743599, -0.04761379584670067, 0.0012923753820359707, -0.0058943117037415504, -0.001029942650347948, -0.10218838602304459, 0.02825508452951908, 0.00022514144075103104, -0.01849406771361828, -0.06612062454223633, -0.014504906721413136, 0.047744158655405045, 0.04986671358346939, -0.07559384405612946, -0.051894523203372955, -0.07774566859006882, -0.0064842794090509415, 0.02899825945496559, -0.0020444891415536404, -0.014012668281793594, -0.04733333736658096, -0.018012937158346176, -0.03813957795500755, 0.01159471645951271, 0.009242124855518341, 0.059223420917987823, -0.02091473899781704, 0.010200157761573792, 0.014340721070766449, -0.020370425656437874, 0.016307294368743896, -0.09620202332735062, 0.07064603269100189, -0.040387850254774094, -0.03844933956861496, 0.0065347859635949135, -0.009315211325883865, -0.00161762535572052, -0.010175252333283424, 0.02641887217760086, 0.005654595326632261, -0.030669474974274635, 0.007627118844538927, 0.012872730381786823, 0.011205111630260944, 0.01397989597171545, 0.08048278093338013, -0.018290972337126732, -0.03368910402059555, 0.034332260489463806, 0.033544667065143585, -0.04229896888136864, 0.02155553363263607, 0.016000209376215935, -0.007470515090972185, -0.0006659599603153765, 0.02414124831557274, 0.016109976917505264, -0.002039907034486532, 0.016411637887358665, 0.07006122171878815, 0.005533192306756973, 0.024992037564516068, -0.02846258133649826, 0.007137727458029985, -0.014823978766798973, -0.012808064930140972, 0.021376481279730797, -0.009394703432917595, 0.003096797736361623, -0.029538176953792572, -0.01223332155495882, -0.02264411933720112, -0.011668894439935684, 0.003719589440152049, 0.005262295715510845, 0.04288267344236374, 0.07515430450439453, -0.052444279193878174, 0.06182778626680374, -0.0018117488361895084, 0.020518332719802856, -0.0112809082493186, 0.03482143580913544, 0.061747852712869644, -0.012657742016017437, -0.06879261136054993, -0.021995779126882553, 0.015982357785105705, 0.009647620841860771, -0.01767793297767639, -0.09995247423648834, -0.05584746599197388, 0.016307266429066658, -0.016460241749882698, 0.02427414059638977, -0.025352198630571365, -0.0018313699401915073, -0.058238450437784195, 0.06463682651519775, 0.028586359694600105, 0.03164287284016609, 0.04055124893784523, -0.008146283216774464, -0.023549361154437065, -0.03217104822397232, -0.02231190912425518, -0.016552960500121117, 0.08736411482095718, -0.05176891013979912, -0.04975754767656326, -0.0731230303645134, 0.07514317333698273, -0.04925614222884178, -0.05404859036207199, 0.04758910462260246, 0.003615916706621647, -0.02488463930785656, -0.005406683776527643, 0.03279547765851021, 0.04253995046019554, -0.030272915959358215, -0.058209698647260666, -0.03227477893233299, -0.04152193292975426, -0.006224633194506168, 0.016611190512776375, 0.01551957055926323, -0.06183665618300438, 0.032481394708156586, -0.00287227937951684, -0.01723880134522915, -0.021815434098243713, 0.02951863780617714, -0.018409639596939087, -0.022772235795855522, 0.019310040399432182, 0.009880295023322105, -0.039013396948575974, -0.022530600428581238, 0.006533097475767136, 0.01045430637896061, 0.026391884312033653, 0.006469004787504673, -0.006580905057489872, 0.018603267148137093, -0.017199257388710976, -0.0009555945871397853, 0.013235798105597496, 0.003558350959792733, -0.03605283424258232, 0.04792877659201622, 0.013309977948665619, 0.03992566093802452, 3.143590583931655e-05, 0.04489872232079506, -0.02070547826588154, 0.05080169439315796, -0.030930299311876297, -0.022882914170622826, 0.028328552842140198, 0.021014651283621788, -0.004645503591746092, -0.03032110072672367, -0.10767437517642975, 0.026707155629992485, 0.02828528918325901, -0.020863676443696022, -0.03837836906313896, 0.03671707212924957, 0.01839330419898033, -0.020706525072455406, 0.0038171724881976843, 0.016682451590895653, 0.008353039622306824, 0.06754337251186371, -0.039764728397130966, -0.0144118657335639, -0.002763679949566722, -0.034944623708724976, -0.0023293751291930676, 0.06692807376384735, -0.00031025087810121477, 0.0024433147627860308, 0.006477678194642067, 0.03769988194108009, -0.0016700791893526912, -0.03939012810587883, 0.020183498039841652, -9.940838208422065e-05, 0.018899984657764435, -0.018444547429680824, 0.037663161754608154, 0.005412229336798191, 0.02628660574555397, -0.0442042201757431, 0.03437383845448494, 0.007615693379193544, 0.00355562474578619, -0.014138487167656422, -0.01229240745306015, 0.0793570876121521, -0.01731087639927864, -0.07437458634376526, 0.02808876894414425, -0.01889217644929886, -0.025107158347964287, -0.024010326713323593, -0.0008321548812091351, -0.013623697683215141, 0.07382617890834808, 0.036678869277238846, 0.003836228745058179, 0.0005741606582887471, -0.033478956669569016, 0.017118047922849655, 0.03801660239696503, -0.007720585912466049, -0.10465820878744125, -0.04601098224520683, 0.0027148898225277662, 0.021768048405647278, 0.13596923649311066, 0.031241269782185555, -0.022269058972597122, -0.006549215875566006, 0.04456562548875809, -0.010059269145131111, -0.00569396885111928, -0.053523238748311996, -0.025293542072176933, 0.05667407438158989, -0.004729492589831352, -0.0030712252482771873, -0.015583368949592113, 0.042980507016181946, 0.015109065920114517, -0.018175708130002022, 0.045552972704172134, -0.023754296824336052, -0.00042651762487366796, -0.02938605658710003, 0.052854448556900024, -0.003775421530008316, -0.017891010269522667, -0.0189057569950819, -0.027489010244607925, -0.008319346234202385, 0.00955908466130495, -0.04374221712350845, 0.024512959644198418, -0.008240027353167534, 0.020049888640642166, -0.01007736474275589, 0.031404972076416016, 0.01377103477716446, 0.014532789587974548, 0.012030556797981262, -0.045056793838739395, 0.035646822303533554, 0.029117798432707787, -0.009294035844504833, 0.003953527193516493, -0.010225352831184864, -0.034079909324645996, -0.004327456001192331, 0.0020972327329218388, -0.055079586803913116, 0.0030392571352422237, 0.10181768238544464, 0.002043099608272314, 0.028431963175535202, -0.0508749894797802, -0.0066119288094341755, -0.0062784492038190365, -0.009397059679031372, 0.024755962193012238, -0.05588093027472496, 0.01205477025359869, -0.018021587282419205, 0.0057983724400401115, 0.003712613368406892, -0.03459541127085686, -0.027351249009370804, 0.04866926744580269, 0.0664258524775505, 0.05645114555954933, -0.04743080586194992, 0.007115317042917013, -0.08609305322170258, 0.016087638214230537, -0.05329209193587303, 0.03874789923429489, 0.01868567243218422, 0.0013702716678380966, 0.022112898528575897, -0.025584731251001358, 0.027404308319091797, -0.026126369833946228, -0.03568055480718613, -0.07483101636171341, 0.0349784679710865, 0.023947274312376976, -0.012624228373169899, 0.031791601330041885, 0.02431465871632099, 0.016797184944152832, 0.0067271338775753975, -0.01020327489823103, -0.011529558338224888, 0.043456848710775375, -0.0009684879332780838, 0.041285086423158646, -0.00968078337609768, 0.074126236140728, 0.04145443066954613, -0.018210379406809807, -0.032646920531988144, 0.029151400551199913, 0.017826151102781296, -0.036935675889253616, 0.015470639802515507, 0.00021131764515303075, 0.003186999587342143, -0.011930154636502266, 0.03715436905622482, 0.048914115875959396, -0.02355833537876606, 0.0008278772002086043, -0.040377382189035416, -0.055704254657030106, -0.018171772360801697, 0.027914468199014664, -0.022094212472438812, -0.07288912683725357, 0.03665691241621971, 0.015427443198859692, -0.001296853180974722, 0.005331774707883596, 0.050512541085481644, 0.04015587270259857, -0.006443549878895283, 0.029861140996217728, 0.07963317632675171, -0.06358778476715088, 0.03585245832800865, 0.015593362040817738, 0.0004805917269550264, -0.032433055341243744, 0.06193454936146736, -0.022840222343802452, -0.008409176953136921, -0.02313566952943802, -0.00041409488767385483, 0.02357291430234909, 0.000670257315505296, -0.005488385912030935, -0.026404134929180145, 0.030164051800966263, -0.0430426225066185, -0.027481544762849808, -0.0031976669561117887, 0.07321272045373917, -0.07202497124671936, -0.06162714958190918, 0.016588279977440834, -0.022463496774435043, 0.02393019199371338, 0.021153796464204788, -0.04239215329289436, 0.0035138954408466816, -0.009901244193315506, -0.01658446714282036, 0.006893819198012352, 0.029084857553243637, 0.029866976663470268, 0.0004019354819320142, -0.003502091858536005, 0.034842461347579956, -0.019740423187613487, -0.014783205464482307, 0.045617230236530304, -0.05029330030083656, -0.0154414726421237, 0.020416175946593285, 0.04388239234685898, -0.001216492964886129, 0.05512112379074097, -0.021516509354114532, 0.015587212517857552, 0.00828320998698473, -0.030134810134768486, 0.06109084561467171, -0.006459272466599941, 0.03810518607497215, 0.031608209013938904, -0.0007391180261038244, -0.003232889110222459, 0.0009739974047988653, 0.05072351545095444, 0.0016308515332639217, -0.06548426300287247, -0.037889063358306885, -0.007213552948087454, 0.04995992034673691, -0.08585884422063828, 0.04995666444301605, 0.010382888838648796, 0.007148366887122393, -0.04771311953663826, 0.038751356303691864, -0.03068801388144493, 0.01009006891399622, -0.03587266802787781, -0.03369699418544769, 0.07398340851068497, 0.0029510855674743652, 0.009505735710263252, 0.01516326516866684, 0.04177713021636009, 0.02735743671655655, -0.04241150617599487, -8.491376502206549e-05, -0.030942082405090332, 0.07241690158843994, -0.04859011247754097, 0.026546934619545937, 0.035356465727090836, 0.026439175009727478, 0.0012111272662878036, 0.01676466502249241, -0.024640284478664398, 0.02086665853857994, 0.03232835233211517, 0.028126880526542664, -0.062411729246377945, 0.02626604586839676, -0.044582169502973557, 0.005166057031601667, -0.05351177230477333, 0.016131939366459846, 0.09121021628379822, -0.035290591418743134, 0.018601132556796074, -0.010445534251630306, 0.017269110307097435, 0.014624330215156078, 0.03707268461585045, 0.011659310199320316, 0.03071850910782814, 0.060461580753326416, -0.034098051488399506, 0.02054722048342228, -0.0714922547340393, 0.038525838404893875, 0.0721646398305893, 0.033571042120456696, -0.05916866660118103, 0.01045281533151865, -0.015928512439131737, 0.017940280959010124, 0.024797294288873672, -0.032725121825933456, -0.008268559351563454, 0.012194949202239513, 0.00723512377589941, -0.0017083571292459965, -0.07764682173728943, -0.026925737038254738, 0.044737204909324646, -0.00544413598254323, 0.024625107645988464, 0.02609729766845703, -0.05104580149054527, -0.07445147633552551, -0.0156622976064682, -0.028018655255436897, 0.03972965478897095, 0.015115690417587757, -0.03662236034870148, -7.373361049245756e-33, -0.02376932092010975, -0.010135025717318058, -0.03581634536385536, -0.029100326821208, 0.01114672888070345, -0.053542185574769974, -0.0009505664347670972, -0.030118893831968307, -0.012939373962581158, 0.006169478874653578, -0.022468529641628265, 0.035155199468135834, -0.008309194818139076, 0.013886393047869205, 0.018620330840349197, 0.024382706731557846, 0.02808232046663761, -0.03628019616007805, 0.02870088443160057, 0.04216741770505905, 0.01841788925230503, 0.04940478876233101, 0.053845878690481186, -0.04109440743923187, -0.08416000008583069, -0.005099588073790073, -0.046759311109781265, -0.04622509703040123, -0.05705847218632698, -0.01661836914718151, 0.035431187599897385, -0.044027380645275116, -0.01336891669780016, -0.0069395434111356735, 0.013097441755235195, -0.07047294825315475, -0.01708296127617359, 0.006500309333205223, -0.0372484065592289, 0.050533946603536606, -0.0505235381424427, -0.028067966923117638, 0.040368616580963135, -0.05739074945449829, -0.01572011597454548, -0.011949101462960243, 0.035132527351379395, -0.01935056410729885, -0.0019211586331948638, 0.023959020152688026, -0.026368379592895508, 0.002143444027751684, -0.06320708245038986, -0.02504655160009861, -0.024542920291423798, 0.014833117835223675, -0.028203414753079414, 0.0636388435959816, -0.020460082218050957, 0.008998513221740723, -0.008073789067566395, 0.07309383153915405, 0.01900371164083481, 0.043384846299886703, 0.04487792029976845, -0.012664024718105793, 0.001622439594939351, -0.02082110196352005, -0.04702833667397499, -0.0015515144914388657, 0.012785554863512516, 0.0375492125749588, 0.0374283641576767, -0.004127311985939741, 0.05432984232902527, -0.052391499280929565, -0.03553963825106621, 0.03693762794137001, -0.04715033993124962, 0.10754889249801636, -0.045495565980672836, 0.04453154653310776, 0.03441215679049492, 0.0010026179952546954, 0.035253386944532394, -0.15664272010326385, 0.009962096810340881, 0.004558106884360313, 0.05060935020446777, -0.007031919434666634, -0.06079934537410736, -0.016570068895816803, 0.005159587599337101, -0.020320439711213112, 0.029551222920417786, 0.012584910728037357, -0.01727195829153061, 0.0031208116561174393, 0.018009712919592857, -0.021393295377492905, 0.026927171275019646, -0.0057783713564276695, 0.06048353388905525, 0.03600919246673584, 0.017541944980621338, 0.003238064469769597, 0.028261857107281685, 0.04239509254693985, 0.035905275493860245, -0.011595223098993301, -0.03816203027963638, -0.001981820212677121, 0.012814844958484173, 0.037620287388563156, 0.0023078175727277994, -0.008868727833032608, 0.01747426949441433, 0.0018633573781698942, 0.031691186130046844, 0.011036044918000698, -0.018110567703843117, -0.03565353527665138, 0.015343371778726578, 0.042531128972768784, -0.05570397153496742, 0.0047129071317613125, -0.02424275316298008, -0.05499719828367233, 0.09047254920005798, -0.07056941092014313, -0.031901758164167404, -0.0061156367883086205, 3.3629905260568194e-07, 0.020923348143696785, 0.02684694714844227, 0.023830533027648926, -0.0028183595277369022, 0.007929235696792603, -0.040270060300827026, -0.029328087344765663, 0.020673491060733795, -0.018919991329312325, -0.0126496572047472, 0.03029579669237137, -0.0012237506452947855, 0.03761127218604088, 0.015511129051446915, -0.015005342662334442, 0.027357429265975952, -0.04589523375034332, 0.03729903697967529, -0.0006857651751488447, -0.0034930852707475424, 0.019901297986507416, 0.07322447001934052, 0.011461107060313225, -0.024054136127233505, 0.06201891601085663, 0.020059766247868538, 0.015962306410074234, -0.002469763159751892, 0.038246724754571915, -0.010675545781850815, -0.009501868858933449, -0.016993505880236626, -0.026314152404665947, -0.003588315099477768, -0.022545089945197105, 0.020234672352671623, 0.04686558246612549, 0.018464257940649986, -0.04331193491816521, 0.015381396748125553, -0.02757115848362446, 0.03031863085925579, 0.019763130694627762, -0.1035362184047699, 0.04370718076825142, -0.012599170207977295, -0.010282907634973526, -0.005048470571637154, -0.029752308502793312, 0.04680826514959335, 0.058412179350852966, -0.017474550753831863, -0.021197959780693054, -0.00717865489423275, 0.02448374778032303, 0.004435216076672077, -0.003835662268102169, -0.015850620344281197, 0.010128247551620007, -0.02409766986966133, -0.04026377573609352, 0.0053701382130384445, -0.011014333926141262, -0.0333794504404068, 0.05714773014187813, 0.052662599831819534, -0.07952477782964706, 3.7168564288811955e-34, -0.03670112043619156, -0.004639027640223503, 0.007633273024111986, -0.033296771347522736, -0.008447851985692978, -0.004034132231026888, -0.01002167072147131, 0.015953265130519867, 0.005778932943940163, -0.013046946376562119, -0.05587136000394821]

['Zhen He', 'Shaobing Gao', 'Liang Xiao', 'Daxue Liu', 'Hangen He', 'David Barber']

1711.01577v3

Long Short-Term Memory (LSTM) is a popular approach to boosting the ability of Recurrent Neural Networks to store longer term temporal information. The capacity of an LSTM network can be increased by widening and adding layers. However, usually the former introduces additional parameters, while the latter increases the runtime. As an alternative we propose the Tensorized LSTM in which the hidden states are represented by tensors and updated via a cross-layer convolution. By increasing the tensor size, the network can be widened efficiently without additional parameters since the parameters are shared across different locations in the tensor; by delaying the output, the network can be deepened implicitly with little additional runtime since deep computations for each timestep are merged into temporal computations of the sequence. Experiments conducted on five challenging sequence learning tasks show the potential of the proposed model.

Wider and Deeper, Cheaper and Faster: Tensorized LSTMs for Sequence Learning

http://arxiv.org/pdf/1711.01577v3

Title Wider Deeper Cheaper Faster Tensorized LSTMs Sequence Learning Summary Long ShortTerm Memory LSTM popular approach boosting ability Recurrent Neural Networks store longer term temporal information capacity LSTM network increased widening adding layer However usually former introduces additional parameter latter increase runtime alternative propose Tensorized LSTM hidden state represented tensor updated via crosslayer convolution increasing tensor size network widened efficiently without additional parameter since parameter shared across different location tensor delaying output network deepened implicitly little additional runtime since deep computation timestep merged temporal computation sequence Experiments conducted five challenging sequence learning task show potential proposed model Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.00562323397025466, 0.033965133130550385, -0.014653699472546577, 0.014243245124816895, -0.020695164799690247, 0.005932270083576441, 0.042821645736694336, 0.03192581981420517, 0.0015997419832274318, -0.037798233330249786, -0.031120603904128075, -0.05774397403001785, 0.03605860844254494, 0.02911956235766411, 0.003458281746134162, -0.07518915086984634, 0.016285736113786697, -0.020470667630434036, 0.014630099758505821, 0.005328299943357706, 0.0005688549135811627, -0.02950344793498516, -0.010622736066579819, -0.004168704152107239, 0.0035977240186184645, 0.03718218579888344, -0.05570322647690773, -0.050125062465667725, -0.0005053397035226226, -0.06359773874282837, 0.03251026198267937, 0.042868077754974365, 0.07331134378910065, 0.04503777623176575, 2.2744923171558185e-06, 0.023968365043401718, -0.021207185462117195, -0.045600418001413345, 0.03498394787311554, 0.008192963898181915, -0.038697611540555954, -0.028969092294573784, 0.0005564080202020705, 0.013667123392224312, -0.054700639098882675, -0.025412240996956825, 0.03377462550997734, 0.045839305967092514, 0.013934939168393612, 0.0908202975988388, -0.0003530817339196801, -0.026164837181568146, 0.052123211324214935, -0.056801699101924896, 0.03479578346014023, -0.038312677294015884, 0.0026758858002722263, -0.05636202171444893, 0.006654837634414434, 0.0033087474294006824, -0.028981752693653107, 0.047036878764629364, 0.041778407990932465, -0.0068885707296431065, 0.006564781069755554, 0.049758583307266235, 0.018431562930345535, 0.006628583651036024, -0.0015784148126840591, 0.06066050007939339, -0.06692136079072952, 0.01683126576244831, 0.017020365223288536, -0.00819226261228323, -0.03184575214982033, -0.07288059592247009, -0.025432268157601357, 0.011829100549221039, 0.015484645031392574, 0.019314775243401527, -0.015003843232989311, 0.02028772607445717, 0.03494229540228844, 0.013520481996238232, -0.0056568169966340065, -0.03190332278609276, 0.004767198581248522, -0.0179651640355587, -0.06224178895354271, -0.043201643973588943, 0.01607883907854557, -0.04405833035707474, 0.01799381896853447, 0.04847037419676781, -0.01909935288131237, -0.02063726633787155, -0.001889859326183796, -0.11425434052944183, 0.022583045065402985, -0.036714501678943634, 0.08869261294603348, 0.03193414583802223, -0.02523213066160679, 0.009929238818585873, -0.07904426753520966, 0.05270320549607277, -0.039930760860443115, -0.028649933636188507, -0.02031787484884262, 0.038563359528779984, -0.026201041415333748, 0.0028601246885955334, 0.003322905395179987, 0.042758509516716, -0.022584574297070503, -0.033202435821294785, -0.1019182875752449, -0.027274291962385178, 0.0032584047876298428, -0.0019541133660823107, 0.021678728982806206, 0.014164004474878311, -0.007079115137457848, -0.003255763091146946, -0.04366406053304672, 0.041173748672008514, -0.004562714137136936, 0.018535884097218513, -0.019629880785942078, -0.007904880680143833, -0.0005244556814432144, 0.03031964972615242, 0.043436210602521896, 0.015793422237038612, 0.02231326326727867, 0.06650590896606445, 0.0007337278220802546, -0.07323025166988373, -0.04118159040808678, 0.011621159501373768, 0.005362759344279766, -0.04135601967573166, 0.040462758392095566, -0.04747682437300682, 0.015995383262634277, -0.03661617636680603, -0.04304441437125206, 0.019812433049082756, 0.02960076928138733, 0.016783136874437332, 0.0006925741326995194, 0.03914286196231842, 0.0008713328279554844, -0.048090897500514984, 0.034496765583753586, 0.030297301709651947, 0.06932427734136581, 0.008768231607973576, 0.06102611869573593, 0.05074978619813919, -0.008594621904194355, -0.04257167875766754, -0.006921262480318546, -0.00806182436645031, 0.03321268782019615, -0.02174636907875538, -0.03668026998639107, -0.021168377250432968, 0.0008839243091642857, 0.07147235423326492, -0.00011003631516359746, 0.041929759085178375, -0.015740571543574333, -0.01647215709090233, 0.03986593708395958, 0.03944537416100502, 0.06993059068918228, 0.021212000399827957, 0.024362822994589806, -0.017066268250346184, -0.029743339866399765, -0.021603187546133995, -0.03446812927722931, 0.08576411753892899, 0.012731977738440037, 0.0017501101829111576, 0.022474737837910652, 0.005460137967020273, -0.036255110055208206, -0.019612982869148254, 0.016239134594798088, -0.06489331275224686, 0.061596475541591644, -0.022893456742167473, 0.029422396793961525, -0.007817432284355164, -0.08560384064912796, 0.037930648773908615, 0.004193715285509825, -0.00854911282658577, -0.01746099255979061, 0.015579578466713428, 0.040497247129678726, 0.02991664595901966, -0.01589885912835598, -0.020808737725019455, -0.060819465667009354, -0.02070683054625988, -0.05685700848698616, 0.01935536414384842, -0.017872633412480354, 0.016318896785378456, 0.013707417994737625, -0.0872177705168724, -0.00412216130644083, 0.010512148961424828, -0.023603808134794235, 0.05843557417392731, -0.024380264803767204, 0.044612616300582886, 0.052770014852285385, 0.06443491578102112, 0.014250640757381916, 0.001560498378239572, -0.06541968882083893, -0.04684603959321976, 0.03570394217967987, 0.04255909472703934, 0.030481748282909393, 0.007071475498378277, 0.046566542237997055, 0.009077317081391811, 0.032067690044641495, -0.06139468774199486, -0.04736132174730301, -0.03584273159503937, -0.08580221980810165, -0.023277636617422104, 0.021376242861151695, 0.046332500874996185, 0.008174767717719078, 0.02347203716635704, -0.033649854362010956, -0.08291756361722946, 0.06317828595638275, -0.05816889926791191, -0.01276438683271408, -0.009287344291806221, 0.03534610569477081, 0.0499347522854805, -0.0019721516873687506, -0.0021752642933279276, -0.003506747540086508, -0.04628409817814827, 0.02108343131840229, 0.005438833963125944, -0.00262421160005033, 0.024862494319677353, -0.028098369017243385, 0.006479938980191946, 0.054688625037670135, 0.013379248790442944, -0.03929011523723602, 0.022839082404971123, -0.012852419167757034, -0.015358702279627323, -0.022401394322514534, -0.06242542341351509, -0.017167309299111366, 0.004055422730743885, 0.01671995036303997, -0.013315471820533276, 0.008812868036329746, 0.017560293897986412, -0.014425494708120823, -0.07659077644348145, 0.024909967556595802, 0.0059827109798789024, -0.018101753666996956, 0.05124611034989357, 0.04656558856368065, -0.030166029930114746, -0.038737427443265915, -0.010114147327840328, 0.0021439846605062485, 0.04100971296429634, -0.03453441709280014, -0.039517708122730255, -0.01681818999350071, -0.09135668724775314, -0.018794987350702286, 0.06369829922914505, -0.013177108950912952, -0.03414332494139671, -0.024607839062809944, -0.031939730048179626, 0.06050797551870346, 0.015960978344082832, 0.06637860834598541, -0.03505132347345352, 0.009463720954954624, 0.004603447858244181, 0.023955509066581726, 0.03734584525227547, -0.02924307994544506, 0.04698827490210533, -0.02795466035604477, 0.008136325515806675, -0.049233898520469666, 0.07019389420747757, -0.0008433768525719643, 0.029864149168133736, -0.06167420744895935, -0.03602581098675728, 0.026491733267903328, 0.0060897041112184525, -0.0046119773760437965, -0.03913040831685066, -0.0252176895737648, 0.016189446672797203, 0.020641928538680077, -0.030510101467370987, 0.02375631406903267, 0.005671835970133543, -0.015640882775187492, -0.02880682982504368, -0.0441502146422863, -0.05664471909403801, 0.0643240436911583, 0.02623947523534298, 0.021413572132587433, -0.03228844702243805, -0.03977173566818237, -0.011712765321135521, 0.0008917773375287652, 0.013168500736355782, -0.04421009123325348, 0.020615335553884506, -0.010276781395077705, -0.010208063758909702, -0.05947405472397804, -0.013193324208259583, -0.028065452352166176, 0.031060243025422096, 0.002640585182234645, -0.005317565053701401, 0.003949579317122698, -0.03490100055932999, 0.004862989764660597, 0.005524774547666311, -0.015504846349358559, 0.07207231223583221, -0.023691538721323013, 0.03051530383527279, -0.0038780015893280506, 0.07795006781816483, 0.01008549239486456, -0.020414061844348907, -0.02034672163426876, 0.02800135500729084, 0.037476297467947006, 0.03979974985122681, 0.01697630248963833, 0.008756888099014759, -0.09794774651527405, -0.004082828294485807, 0.010106762871146202, -0.074246846139431, -0.03227178007364273, -0.0008312644786201417, -0.012224645353853703, -0.10525041073560715, 0.022450612857937813, 0.07452083379030228, -0.015613107942044735, -0.05456550791859627, -0.0031708632595837116, 0.05003800615668297, -0.02747223898768425, -0.007639359217137098, -0.02646314725279808, -0.03898176923394203, 0.014059984125196934, -0.013503187336027622, -0.007690084632486105, -0.024205295369029045, -0.05687669292092323, -0.03170536831021309, -0.0722113847732544, 0.006695711053907871, 0.001367011689580977, -0.01829051785171032, -0.025189043954014778, -0.06389220058917999, -0.024381496012210846, 0.05417735129594803, 0.036757659167051315, 0.04055698961019516, 0.02028377540409565, -0.03610498085618019, 0.044084157794713974, -0.036711663007736206, -0.011656312271952629, 0.00683297123759985, -0.04062473401427269, -0.012139556929469109, -0.0021548354998230934, 0.03032616898417473, -0.0069292341358959675, -0.07164710015058517, 0.01996583491563797, 0.012390547432005405, 0.03258688002824783, -0.0015076781855896115, 0.016349706798791885, 0.0053390697576105595, -0.022047344595193863, -0.0011240909807384014, 0.051743827760219574, -0.007574327755719423, 0.03124186210334301, -0.04270636662840843, 0.05791905149817467, 0.011908084154129028, -0.02696814015507698, -0.03366205841302872, -0.001703574787825346, 0.005924701225012541, -0.0011290159309282899, 0.009803269058465958, -0.013988787308335304, -0.009178376756608486, 0.05392280966043472, -0.024529941380023956, -0.05899462848901749, -0.032898567616939545, -0.016177790239453316, 0.008206991478800774, -0.03418285772204399, -0.07839859277009964, -0.03360595554113388, -0.04450104758143425, 0.048789892345666885, -0.002108521992340684, 0.06710901111364365, 0.015279593877494335, 0.0030169750098139048, -0.04551983252167702, -0.0046045514754951, 0.03871260583400726, 0.033208396285772324, -0.03714119270443916, 0.03017675131559372, 0.010173415765166283, 0.025332573801279068, 0.01879558525979519, -0.044361621141433716, -0.11503847688436508, -0.054010797291994095, -0.036553509533405304, 0.030362196266651154, -0.0063224174082279205, 0.010739942081272602, 0.02350393868982792, 0.00447873305529356, 0.10879391431808472, -0.005395615939050913, -0.02483622170984745, -0.0004353320400696248, 0.04623967781662941, -0.013352440670132637, -0.018461156636476517, 0.012704617343842983, -0.009632732719182968, 0.036461230367422104, -0.0025628807488828897, -0.004257296212017536, -0.02679777517914772, 0.004725322127342224, -0.0013122106902301311, -0.014823191799223423, 0.07018586248159409, -0.012314262799918652, 0.045343026518821716, -0.02711213007569313, 0.04658420383930206, -0.025937136262655258, 0.026583746075630188, -0.030885901302099228, 0.0009857721161097288, 0.020331114530563354, 0.006622695829719305, -0.017286602407693863, -0.031525686383247375, 0.06100789085030556, -0.07380139082670212, -0.009494763799011707, 0.0802520364522934, -0.004754858091473579, 0.04898109287023544, -0.024055931717157364, 0.019127553328871727, -0.024567145854234695, -0.006564476992934942, -0.026681743562221527, 0.03779714182019234, -0.015461048111319542, 0.02634979784488678, 0.01587587781250477, 0.016561780124902725, -0.01592736318707466, 0.03504069149494171, 0.004769840743392706, -0.04634540155529976, -0.01866738684475422, -0.0023655174300074577, 0.07362311333417892, -0.04611752927303314, -0.01900840364396572, -0.0034091027919203043, 0.02692801132798195, 0.005190479103475809, 0.054626189172267914, -0.050309039652347565, 0.004141577053815126, 0.026416828855872154, 0.00887646246701479, -0.006825684569776058, 0.01075733732432127, 0.07554417103528976, 0.02631545066833496, 0.018788112327456474, 0.05482178181409836, 0.007548414636403322, -0.006311693228781223, -0.013041004538536072, 0.002263483125716448, 0.026037391275167465, -0.012747677974402905, 0.02080691233277321, 0.021672410890460014, -0.04682162404060364, 0.028537936508655548, -0.03325900062918663, 0.06740562617778778, -0.02979225479066372, 0.055159732699394226, -0.013721859082579613, 0.0135826226323843, 0.02648351900279522, -0.01646680198609829, 0.0243185106664896, 0.031459491699934006, -0.0543714314699173, -0.052931323647499084, -6.483556641395409e-33, 0.012074884958565235, 0.012335537001490593, 0.024525629356503487, -0.028974119573831558, -0.05731275677680969, 0.04631611332297325, -0.03359907120466232, -0.0034504218492656946, 0.03636793792247772, -0.01557081937789917, -0.005137827713042498, -0.0013828389346599579, -0.007402205839753151, 0.010344048961997032, 0.061316367238759995, 0.006014626007527113, 0.029340969398617744, -0.004546779673546553, 0.03194419667124748, 0.027276640757918358, 0.05677279457449913, 0.040208593010902405, 0.09048052877187729, -0.05718670040369034, -0.019353549927473068, 0.02746749296784401, 0.022533610463142395, 0.010899091139435768, 0.04082810506224632, 0.013238819316029549, -0.0045254104770720005, -0.022281773388385773, 0.02936013787984848, -0.0800451710820198, -0.00215220358222723, -0.006960464641451836, -0.05395875871181488, -0.008072759956121445, -0.03795328363776207, 0.00269910367205739, -0.08043578267097473, -0.022405371069908142, 0.007878023199737072, -0.007231459487229586, 0.011515194550156593, 0.009627033956348896, 0.0034875262062996626, -0.010409368202090263, -0.03089947998523712, -0.04753169044852257, -0.014788982458412647, 0.047064702957868576, -0.016547318547964096, -0.009054506197571754, 0.03722640499472618, -0.000966748979408294, 0.009344244375824928, 0.010251765139400959, -0.06938372552394867, 0.005979015491902828, 0.0009515008423477411, 0.05106735602021217, -0.00034067497472278774, 0.017822472378611565, 0.017522212117910385, 0.021779945120215416, 0.0029152892529964447, -0.009519169107079506, -0.00847572647035122, 0.023371152579784393, -0.03618047386407852, 0.018939794972538948, 0.07655786722898483, -0.031259242445230484, 0.08852700144052505, -0.02979835495352745, -0.06344760954380035, -0.00935540720820427, 0.020768335089087486, 0.04863809049129486, 0.01999441161751747, 0.04568146541714668, -0.019545838236808777, 0.012571660801768303, 0.004022522363811731, 0.02272600121796131, -0.010608376003801823, -0.04789290949702263, 0.00015792157500982285, 0.05591254308819771, 0.013229306787252426, -0.013495951890945435, 0.016395756974816322, 0.010157803073525429, 0.042928725481033325, 0.011189163662493229, 0.02905823476612568, -0.009915350936353207, 0.023980075493454933, -0.00911833718419075, -0.05187581107020378, -0.023927200585603714, 0.013418631628155708, -0.04699726402759552, -0.00539484852924943, -0.0021304970141500235, 0.03433648869395256, 0.03154301270842552, -0.04592272639274597, -0.028331339359283447, -0.002159339841455221, 0.01659071072936058, 0.006520198192447424, 0.012561837211251259, 0.03219524770975113, -0.0357784740626812, -0.012095487676560879, 0.10211745649576187, -0.0002501819690223783, 0.026916205883026123, -0.027411311864852905, -0.016540123149752617, 0.03885849192738533, 0.04436140134930611, -0.008134238421916962, -0.021054869517683983, -0.07332997769117355, 0.02452251687645912, 0.02159247361123562, -0.07200708240270615, -0.011157821863889694, 0.021866410970687866, 3.0223154112718476e-07, -0.05550338327884674, -0.009418215602636337, 0.03358836844563484, -0.0007889867410995066, 0.041960034519433975, -0.004377107601612806, 0.011601237580180168, 0.03775545954704285, -0.012386691756546497, 0.05538991838693619, 0.049143169075250626, -0.002735959831625223, -0.008732630871236324, 0.0032511341851204634, -0.054928358644247055, -0.05921938270330429, -0.074131540954113, 0.038124002516269684, -0.02738657407462597, 0.015059348195791245, 0.01425432600080967, 0.1114155575633049, 0.048870768398046494, -0.026936708018183708, 0.054452937096357346, -0.00524882460013032, 0.024712035432457924, 0.01243702881038189, 0.02573409117758274, -0.017157044261693954, 0.021820705384016037, 0.01855522021651268, -0.01740088127553463, -0.007155511993914843, -0.04634445533156395, 0.03324969485402107, -0.034860558807849884, 0.004744736477732658, 0.017121607437729836, -0.03335314244031906, 0.04640955477952957, 0.04457351192831993, 0.004336609970778227, -0.01463808212429285, 0.033759213984012604, -0.011530008167028427, -0.04305671900510788, -0.02185296081006527, -0.02106449194252491, -0.012281743809580803, 0.022991010919213295, 0.029634028673171997, -0.016648903489112854, 0.030542075634002686, 0.02565005049109459, -0.015378528274595737, 0.03770056739449501, -0.110150046646595, 0.01353716291487217, 0.029026780277490616, -0.02172849513590336, -0.006333759054541588, -0.07499060034751892, -0.00312456744723022, 0.03935612365603447, -0.011394087225198746, -0.05616751313209534, 2.7177865609618038e-34, 0.005000378470867872, -0.04980933293700218, -0.011669743806123734, 0.052498459815979004, 0.009332068264484406, -0.01595759205520153, -0.027971116825938225, 0.016877539455890656, 0.060559239238500595, -0.0607791543006897, -0.07271106541156769]

['Shruti R. Kulkarni', 'John M. Alexiades', 'Bipin Rajendran']

1711.03637v1

We describe a novel spiking neural network (SNN) for automated, real-time handwritten digit classification and its implementation on a GP-GPU platform. Information processing within the network, from feature extraction to classification is implemented by mimicking the basic aspects of neuronal spike initiation and propagation in the brain. The feature extraction layer of the SNN uses fixed synaptic weight maps to extract the key features of the image and the classifier layer uses the recently developed NormAD approximate gradient descent based supervised learning algorithm for spiking neural networks to adjust the synaptic weights. On the standard MNIST database images of handwritten digits, our network achieves an accuracy of 99.80% on the training set and 98.06% on the test set, with nearly 7x fewer parameters compared to the state-of-the-art spiking networks. We further use this network in a GPU based user-interface system demonstrating real-time SNN simulation to infer digits written by different users. On a test set of 500 such images, this real-time platform achieves an accuracy exceeding 97% while making a prediction within an SNN emulation time of less than 100ms.

Learning and Real-time Classification of Hand-written Digits With Spiking Neural Networks

http://arxiv.org/pdf/1711.03637v1

Title Learning Realtime Classification Handwritten Digits Spiking Neural Networks Summary describe novel spiking neural network SNN automated realtime handwritten digit classification implementation GPGPU platform Information processing within network feature extraction classification implemented mimicking basic aspect neuronal spike initiation propagation brain feature extraction layer SNN us fixed synaptic weight map extract key feature image classifier layer us recently developed NormAD approximate gradient descent based supervised learning algorithm spiking neural network adjust synaptic weight standard MNIST database image handwritten digit network achieves accuracy 9980 training set 9806 test set nearly 7x fewer parameter compared stateoftheart spiking network use network GPU based userinterface system demonstrating realtime SNN simulation infer digit written different user test set 500 image realtime platform achieves accuracy exceeding 97 making prediction within SNN emulation time le 100ms Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.029836155474185944, -0.004212182946503162, -0.005331828258931637, 0.062443844974040985, 0.03699972480535507, 0.010561011731624603, 0.06665130704641342, 0.006106346379965544, 0.006240308750420809, -0.013324867002665997, -0.020448651164770126, 0.02570227161049843, 0.025979647412896156, 0.09828615933656693, 0.012058358639478683, -0.02138534188270569, 0.0044233729131519794, 0.017325015738606453, -0.013076914474368095, -0.025059502571821213, 0.05208823084831238, -0.03348461911082268, -0.024997608736157417, 0.020913295447826385, -0.03414669260382652, 0.012606578879058361, -0.015795614570379257, -0.02373712882399559, 0.03441346809267998, -0.0226771030575037, 0.004487792029976845, -0.00787435658276081, 0.012308481149375439, 0.07508203387260437, 2.059427743006381e-06, -0.01716018095612526, 0.017355773597955704, -0.010158626362681389, 0.000621364510152489, -0.028017140924930573, 0.0271379966288805, -0.00680758198723197, -0.02684742398560047, 0.002118151867762208, -0.032809022814035416, -0.034547071903944016, 0.07292507588863373, 0.0941447839140892, -0.00466472003608942, 0.0012395750964060426, -0.014797063544392586, 0.0029558681417256594, 0.046291619539260864, -0.011853823438286781, 0.052738577127456665, 0.04398791864514351, 0.023337678983807564, -0.005949025042355061, -0.009660815820097923, -0.04082071781158447, -0.010364124551415443, 0.02697259560227394, 0.018718285486102104, -0.0284423865377903, 0.023066774010658264, 0.052420780062675476, -0.04550289362668991, 0.0017134288791567087, -0.020009825006127357, 0.04767467826604843, -0.0651407390832901, 0.011087493970990181, 0.03434242680668831, -0.018628817051649094, -0.048976458609104156, -0.045254528522491455, -0.00595216965302825, 0.004643049091100693, -0.04699571803212166, 0.009022394195199013, -0.03289192169904709, -0.0006370450719259679, 0.04735815152525902, -0.0037617390044033527, 0.05265681818127632, 0.004946484230458736, -0.025094415992498398, 0.016894884407520294, 0.020662516355514526, -0.018748974427580833, -0.0066285403445363045, -0.006037789862602949, 0.04588940739631653, -0.005162064451724291, -0.0114656463265419, -0.0128637058660388, -0.0543651320040226, -0.08861273527145386, -0.007460794877260923, -0.07716988027095795, 0.06108934432268143, 0.027106303721666336, 0.02294684201478958, 0.002658433746546507, -0.05332190915942192, 0.007868345826864243, -0.05315635725855827, 0.04731170833110809, 0.004388798493891954, 0.04135571047663689, -0.05483084172010422, -0.02136852964758873, -0.018091898411512375, 0.06153608858585358, 0.00314830313436687, -0.008645073510706425, -0.0994613766670227, 0.018755866214632988, -0.013966752216219902, -0.008958607912063599, 0.007049625273793936, 0.06158314272761345, 0.0024851919151842594, 0.018281789496541023, -0.01667720451951027, -0.019062625244259834, -0.00023774264263920486, 0.014360526576638222, -0.022585198283195496, -0.011339780874550343, 0.028711069375276566, 0.02404797449707985, 0.032026685774326324, 0.026052147150039673, 0.030440829694271088, 0.029668722301721573, -0.005711067467927933, 0.018502146005630493, -0.05478412285447121, 0.06805002689361572, 0.015842029824852943, 0.049375761300325394, -0.0007214226061478257, -0.04970145598053932, 0.008012323640286922, -0.013772197999060154, -0.03309422358870506, 0.006391151808202267, 0.02832101844251156, -0.012622375041246414, 0.044269852340221405, 0.05534765496850014, -0.08952859044075012, -0.050513628870248795, 0.09518785774707794, -0.036967646330595016, -0.03758887201547623, -0.014967910014092922, 0.06810132414102554, 0.039696212857961655, 0.0038901048246771097, -0.045912403613328934, 0.0294665340334177, 0.0023815385065972805, -0.00036981995799578726, -0.0642203614115715, -0.032648246735334396, -0.05473417043685913, 0.03237070143222809, 0.03894200921058655, 0.03634108603000641, 0.04333409294486046, -0.0037939511239528656, -0.031890869140625, 0.029264356940984726, 0.06380195170640945, -0.0244622603058815, 0.04123007506132126, -0.012475152499973774, -0.021788058802485466, -0.008123681880533695, -0.034105028957128525, -0.03680090978741646, 0.06306260824203491, 0.003630538936704397, -0.0044497475028038025, -0.04977846145629883, -0.019533758983016014, -0.012586496770381927, -0.06250742077827454, 0.020591408014297485, -0.06411102414131165, 0.011575082316994667, 0.028072703629732132, 0.05704498663544655, -0.01859089732170105, -0.010014900006353855, -0.0024908322375267744, -0.010992434807121754, 0.03524737432599068, -0.032015588134527206, -0.06449586153030396, 0.026416998356580734, 0.021394599229097366, -0.007923244498670101, -0.04206012189388275, 0.002492255996912718, -0.029779590666294098, -0.0349372960627079, -0.0002451664477121085, -0.0953424870967865, 0.003194202668964863, 0.059768036007881165, -0.07904912531375885, 0.011179845780134201, 0.02888702042400837, 0.0042638578452169895, 0.03660055249929428, -0.013133827596902847, -0.004706213250756264, 0.014281005598604679, 0.06505940854549408, -0.06643029302358627, 0.015836408361792564, -0.0202966146171093, -0.0355367437005043, 0.045361731201410294, -0.012789083644747734, -0.009212430566549301, -0.042694900184869766, 0.00898428913205862, -0.02829694375395775, 0.011072997935116291, -0.07107071578502655, 0.03484347090125084, -0.045710012316703796, -0.04329680651426315, 0.0397716648876667, 0.03788292035460472, 0.007548650726675987, 0.03340718150138855, 0.036164335906505585, -0.024414651095867157, -0.030583979561924934, -0.025624245405197144, 0.00849671196192503, 0.020343687385320663, -0.053653351962566376, -0.002105098217725754, -0.02638014405965805, 0.007444802206009626, -0.009138590656220913, 0.0323454923927784, 0.04006745666265488, 0.002927215304225683, 0.0010266710305586457, -0.004381189122796059, 0.04983264207839966, -0.08228462189435959, 0.0018546172650530934, 0.009627331979572773, -0.06193507835268974, -0.005936542060226202, -0.03835032135248184, 0.024924300611019135, -0.008927879855036736, -0.0022310959175229073, -0.05427713319659233, -0.029487207531929016, 0.002221456030383706, 0.0007640376570634544, 0.03019973821938038, 0.016279123723506927, 0.01516212709248066, -0.05563640594482422, -0.011445041745901108, 0.05502243712544441, -0.02269558236002922, -0.04798150435090065, 0.02729327604174614, 0.018783992156386375, 0.0500568225979805, -0.017654476687312126, -0.028346296399831772, -0.012637809850275517, 0.029051542282104492, 0.03374588489532471, -0.06169354170560837, -0.0056635853834450245, 0.02821175754070282, 0.003269878216087818, 0.053245943039655685, 0.009363207034766674, -0.018468709662556648, 0.022412726655602455, 0.020649069920182228, -0.02703769877552986, 0.05053414776921272, 0.04101336747407913, -0.03613429516553879, 0.012876843102276325, 0.02142900787293911, 0.03713822364807129, 0.006308889947831631, -0.006323104724287987, 0.07232115417718887, 0.004602236207574606, 0.0685855969786644, -0.03432071581482887, 0.026029301807284355, 0.025350451469421387, 0.010567874647676945, 0.009819957427680492, -0.016358377411961555, -0.010565507225692272, 0.007199313025921583, -0.06627915799617767, 0.01582944206893444, -0.016862228512763977, -0.0339091494679451, 0.0071908850222826, -0.05039074644446373, 0.0007793687400408089, 0.014424310065805912, -0.006430495530366898, 0.016730058938264847, -0.03385620564222336, -0.0026063495315611362, 0.01994057185947895, 0.034223489463329315, 0.03847633674740791, -0.07974031567573547, -0.030895082280039787, 0.008785443380475044, 0.005009956657886505, -0.0075497752986848354, -0.006779191084206104, -0.007960014045238495, 0.017063913866877556, -0.002423908794298768, -0.06288176774978638, -0.05226745083928108, -0.05160287395119667, 0.019983001053333282, -0.040376730263233185, -0.016671879217028618, 0.0010279796551913023, -0.02599276974797249, 0.07326182723045349, 0.0077574714086949825, 0.044784050434827805, 0.09499914944171906, -0.03197917342185974, -0.0363999679684639, -0.03158128634095192, 0.022224441170692444, 0.050698451697826385, -0.03904293477535248, -0.022216862067580223, 0.052102651447057724, 0.02104986272752285, 0.039983637630939484, 0.011595581658184528, 0.03187473118305206, -0.14923885464668274, 0.00029328936943784356, -0.0476672537624836, 0.0007858629105612636, 0.0011977757094427943, -0.0032918062061071396, -0.02340841107070446, -0.04553510248661041, 0.025898870080709457, 0.02146066166460514, 0.0030631190165877342, -0.08640238642692566, -0.0396423377096653, -0.007907501421868801, -0.06846819072961807, -0.019399089738726616, 0.025542283430695534, 0.0017917584627866745, -0.014469386078417301, -0.03603125736117363, -0.0005950745544396341, -0.014737134799361229, -0.00549091724678874, -0.015364118851721287, 0.013393827714025974, 0.040812939405441284, 0.00042251800186932087, -0.030674513429403305, -0.035131096839904785, 0.013980603776872158, 0.013446793891489506, -0.003285560989752412, 0.0025253640487790108, 5.630387386190705e-05, 0.002930194605141878, 0.02262198179960251, 4.661639832193032e-05, -0.01681777834892273, 0.025768784806132317, 0.01579182967543602, -0.020191451534628868, -0.03126833215355873, 0.06039918586611748, 0.007259619887918234, -0.005516592413187027, -0.04712771251797676, 0.02729889005422592, 0.01777181774377823, 0.018688246607780457, -0.005734303500503302, 0.01663563959300518, 0.03201231360435486, -0.015195132233202457, -0.029273709282279015, 0.0889265313744545, -0.0321492925286293, 0.027577852830290794, 0.014893715269863605, 0.008307117968797684, -0.04205895960330963, 0.011883075349032879, -0.027578260749578476, -0.02229846455156803, 0.019117843359708786, -0.060495954006910324, -0.005829770117998123, -0.05807867646217346, -0.03807301074266434, -0.010085774585604668, 0.027900850400328636, -0.03754166141152382, -0.011199369095265865, -0.002833211561664939, 0.05846569687128067, -0.06251027435064316, -0.0004017665924038738, -0.006575843784958124, -0.0347643680870533, 0.06785914301872253, 0.015631116926670074, 0.02503267303109169, 0.06278494745492935, 0.025311334058642387, -0.014893929474055767, -0.0016610989114269614, 0.020443301647901535, 0.004789798520505428, -0.07387899607419968, 0.026469940319657326, 0.02590096928179264, -0.05415639281272888, 0.0038165871519595385, -0.05433206260204315, -0.06872468441724777, 0.014813498593866825, 0.047768764197826385, 0.020496966317296028, 0.005726776551455259, -0.0393005833029747, -0.052343130111694336, -0.024355895817279816, 0.026198402047157288, 0.053779713809490204, 0.04629059508442879, 0.008940367959439754, 0.02510066330432892, -0.005211945623159409, -0.015994880348443985, -0.008212386630475521, 0.00919658038765192, 0.06395767629146576, 0.012010152451694012, -0.07786470651626587, -0.07143370062112808, -0.003668018151074648, -0.022907527163624763, 0.024751989170908928, 0.07789205759763718, 0.03293517231941223, 0.016416411846876144, -0.04952583089470863, 0.033791277557611465, 0.048168912529945374, 0.045028600841760635, -0.017096636816859245, -0.032154228538274765, 0.0036813870538026094, 0.026955442503094673, -0.0006719260127283633, -0.1060112714767456, 0.09394887089729309, -0.06465369462966919, 0.02507324144244194, -0.011579371988773346, -0.003558188444003463, 0.06897716224193573, -0.053247205913066864, -0.01600709930062294, -0.01486713532358408, 0.058036625385284424, -0.004256345331668854, 0.022557564079761505, -0.02284853719174862, 0.053602106869220734, -0.00020643442985601723, -0.016470104455947876, -0.0607253722846508, 0.04742371663451195, 0.025751277804374695, -0.011248991824686527, -0.04014738276600838, 0.018690533936023712, 0.04411500692367554, 0.019633712247014046, -0.04876615107059479, 0.010671879164874554, 0.017855489626526833, -0.05150848254561424, 0.051719214767217636, -0.00541685102507472, 0.006061118096113205, 0.018840372562408447, 0.023076137527823448, -0.01823127642273903, 0.005433050449937582, -0.01030694879591465, -0.015153178945183754, -0.02998763509094715, 0.06480847299098969, -0.04286600649356842, -0.009507146663963795, 0.021770674735307693, -0.05025021731853485, -0.004829402547329664, -0.042436569929122925, -0.00889987125992775, 0.028944911435246468, 0.019697293639183044, 0.08373145014047623, -0.009165934287011623, 0.005069346632808447, -0.0021405473817139864, 0.014339957386255264, -0.009327410720288754, -0.01694423332810402, 0.024020126089453697, 0.030187221243977547, 0.020110193639993668, 0.020838262513279915, -0.00868590921163559, -0.06377018988132477, -5.359438005859779e-33, 0.027203259989619255, -0.04148097708821297, 0.018955184146761894, 0.020937291905283928, -0.02423648163676262, 0.014847886748611927, 0.009690869599580765, 0.030873849987983704, 0.022212335839867592, -0.042911455035209656, -0.04397348314523697, -0.0003072975669056177, 0.022015204653143883, 0.04582400619983673, 0.03478211164474487, -0.059618692845106125, -0.0037353651132434607, -0.013921593315899372, 0.04175533354282379, 0.0197491142898798, 0.05416342243552208, 0.026153795421123505, 0.07373920828104019, -0.047973476350307465, -0.06790775060653687, 0.041589029133319855, 0.028327982872724533, -0.10247526317834854, -0.033343225717544556, -0.005217806436121464, -0.06287086009979248, 0.034700170159339905, 0.011305145919322968, -0.022535409778356552, 0.027928991243243217, 0.010289521887898445, -0.04326331615447998, -0.018503675237298012, -0.0757395550608635, 0.024242013692855835, -0.025188198313117027, -0.032082948833703995, 0.07237119227647781, -0.02519046887755394, -0.03269220143556595, 0.013350934721529484, 0.03818937763571739, -0.039993248879909515, -0.013289997354149818, -0.04681634157896042, 0.0032366791274398565, 0.010983169078826904, 0.05217333883047104, 0.03618509694933891, 0.02019019052386284, -0.0017851695884019136, -0.04082002118229866, -0.006336741615086794, -0.11754463613033295, 0.016054032370448112, 0.013446194119751453, 0.0312727615237236, -0.014958180487155914, 0.04249490797519684, 0.05113684758543968, 0.00424958486109972, 0.025160184130072594, -0.04416506737470627, -0.014716093428432941, 0.02136676385998726, 0.045107923448085785, 0.008279354311525822, 0.035631660372018814, 0.038506124168634415, 0.1020788848400116, -0.08799543976783752, -0.025091513991355896, 0.008177843876183033, 0.05090736225247383, -0.005929053295403719, 0.03970116376876831, 0.005305926315486431, -0.046053461730480194, -0.006989536806941032, 0.03553139790892601, 0.01579279825091362, -0.006371490191668272, -0.054464101791381836, 0.024733487516641617, 0.009686000645160675, 0.0033787612337619066, 0.018476882949471474, -0.0004453012370504439, -0.014529588632285595, 0.03863504156470299, -0.03790314495563507, 0.03503986820578575, 0.021881069988012314, 0.04924202710390091, -0.055231258273124695, -0.028648339211940765, -0.015604577958583832, -0.016228195279836655, -0.026481643319129944, 0.03612562268972397, 0.0009407107718288898, -0.016930457204580307, 0.02797345444560051, 0.004067929461598396, 0.01218301709741354, 0.017152883112430573, -0.029598718509078026, 0.05058242008090019, 0.04843084141612053, -0.0024374029599130154, -0.046207964420318604, 0.0015904427273198962, 0.01676345430314541, -0.028013281524181366, -0.012737203389406204, -0.0028452007099986076, -0.01793629676103592, -0.005930221173912287, 0.05002983286976814, -0.06555662304162979, 0.011250454932451248, -0.046938806772232056, 0.024152930825948715, -0.04839041084051132, -0.05536956712603569, 0.009973117150366306, 0.02630241960287094, 2.7098244004264416e-07, -0.06158581003546715, 0.011270195245742798, -0.0007698836270719767, -0.045287080109119415, 0.011110061779618263, 0.014307939447462559, 0.03295169025659561, 0.012904848903417587, -0.0015985555946826935, -0.04771793633699417, 0.005796107929199934, -0.015717091038823128, 0.028521474450826645, 0.03221806883811951, -0.03537963330745697, -0.04581789672374725, 0.008546159602701664, 0.09610731154680252, 0.012927766889333725, 0.03051932156085968, -0.03428196161985397, 0.04931170120835304, 0.06229061633348465, -0.005895507521927357, 0.08938656002283096, -0.0035708409268409014, 0.02832961268723011, 0.018887124955654144, 0.05893467366695404, -0.047925546765327454, 0.0018296194029971957, 0.03382489085197449, -0.02101481705904007, 0.008509086444973946, 0.024652335792779922, -0.014188266359269619, 0.0009891075314953923, -0.007867671549320221, -0.06622103601694107, 0.0619225949048996, 0.006533937528729439, -0.004548831842839718, 0.04075423255562782, -0.02501850202679634, 0.023638147860765457, 0.004226401448249817, -0.013117366470396519, -0.03536519408226013, 0.05422823131084442, 0.004543600138276815, 0.026349274441599846, -0.010480165481567383, 0.011052688583731651, -0.041538629680871964, 0.002375108189880848, -0.07102900743484497, -0.02341846190392971, -0.024676823988556862, 0.01025714073330164, -0.0054456498473882675, -0.02315337583422661, 0.0006500227027572691, -0.06243625655770302, 0.0039470987394452095, 0.05010081082582474, 0.0024937347043305635, 0.010522629134356976, 2.1235252642194333e-34, -0.04648970812559128, -0.03290250524878502, -0.004770940635353327, 0.019137388095259666, -0.017222711816430092, 0.0009453311213292181, 0.05105413496494293, -0.02236158400774002, -0.012489584274590015, -0.0041250670328736305, -0.03036557510495186]

['Joan Serrà', 'Dídac Surís', 'Marius Miron', 'Alexandros Karatzoglou']

1801.01423v2

Catastrophic forgetting occurs when a neural network loses the information learned in a previous task after training on subsequent tasks. This problem remains a hurdle for artificial intelligence systems with sequential learning capabilities. In this paper, we propose a task-based hard attention mechanism that preserves previous tasks' information without affecting the current task's learning. A hard attention mask is learned concurrently to every task, through stochastic gradient descent, and previous masks are exploited to condition such learning. We show that the proposed mechanism is effective for reducing catastrophic forgetting, cutting current rates by 45 to 80%. We also show that it is robust to different hyperparameter choices, and that it offers a number of monitoring capabilities. The approach features the possibility to control both the stability and compactness of the learned knowledge, which we believe makes it also attractive for online learning or network compression applications.

Overcoming catastrophic forgetting with hard attention to the task

http://arxiv.org/pdf/1801.01423v2

Title Overcoming catastrophic forgetting hard attention task Summary Catastrophic forgetting occurs neural network loses information learned previous task training subsequent task problem remains hurdle artificial intelligence system sequential learning capability paper propose taskbased hard attention mechanism preserve previous task information without affecting current task learning hard attention mask learned concurrently every task stochastic gradient descent previous mask exploited condition learning show proposed mechanism effective reducing catastrophic forgetting cutting current rate 45 80 also show robust different hyperparameter choice offer number monitoring capability approach feature possibility control stability compactness learned knowledge believe make also attractive online learning network compression application Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.037000950425863266, 0.03462167829275131, -0.007812450174242258, -0.01077504362910986, 0.009100215509533882, 0.009886335581541061, -0.023790210485458374, -0.0192704014480114, 0.002923540771007538, 0.01397237554192543, -0.0008448531734757125, 0.0033932134974747896, -0.004014899488538504, 0.05124600976705551, 0.03366876766085625, -0.04262276366353035, 0.05844298377633095, 0.03187687322497368, -0.006128997541964054, 0.003628125647082925, 0.053440261632204056, -0.04646865651011467, 0.017717672511935234, 0.01325336191803217, -0.03907063975930214, -0.05597076192498207, -0.006254839710891247, -0.0017077457159757614, 0.020675133913755417, -0.039549488574266434, 0.06863722950220108, -0.021363992244005203, 0.009321593679487705, 0.019486574456095695, 2.342397010579589e-06, -0.03414265811443329, -0.033754345029592514, -0.041184939444065094, -0.01097345631569624, -0.04478553682565689, -0.006831248290836811, -0.01176268607378006, -0.004574762657284737, 0.017500922083854675, -0.03096756711602211, 0.026086844503879547, 0.05950253829360008, 0.07235067337751389, 0.055247750133275986, 0.034623682498931885, 0.0048454999923706055, -0.050911013036966324, 0.05837644636631012, -0.012938864529132843, 0.013303790241479874, -0.02825767919421196, 0.008493117056787014, -0.01831471174955368, -0.07564351707696915, -0.06754211336374283, -0.012620643712580204, 0.04659654572606087, 0.02949553355574608, 0.03286362811923027, 0.05095934495329857, 0.02973628230392933, -0.0008115433738566935, -0.042522940784692764, -0.015677182003855705, -0.013302352279424667, -0.09252536296844482, -0.006958921905606985, 0.02579154446721077, -0.00598158361390233, -0.006280275993049145, -0.04940522834658623, -0.05346633493900299, 0.026190003380179405, -0.05717426910996437, 0.031246285885572433, -0.035287823528051376, -0.0018488202476873994, 0.011512014083564281, -4.1937109926948324e-05, 0.01667594537138939, -0.030284428969025612, -0.014780412428081036, -0.009902585297822952, -0.011395719833672047, -0.014113286510109901, -0.007069609593600035, 0.01886996440589428, 0.04745357483625412, 0.020489851012825966, -0.03692343086004257, 0.006990969181060791, -0.06141834706068039, -0.0921594500541687, 0.041284579783678055, -0.07391555607318878, 0.08038920164108276, -0.021852316334843636, -0.03515784069895744, 0.02634529210627079, -0.07471558451652527, 0.06061219796538353, -0.04091697558760643, 0.0017819582717493176, 0.017570583149790764, 0.03468434512615204, -0.04632314667105675, -0.0027819836977869272, -0.04235995188355446, 0.07023254036903381, 0.07319491356611252, 0.016135847195982933, -0.015159131027758121, 0.017142802476882935, -0.05704433470964432, 0.024741001427173615, 0.002214844571426511, 0.045586127787828445, -0.05802103504538536, -0.014375063590705395, -0.00160956138279289, 0.006081467028707266, -0.007013578899204731, -0.009720143862068653, 0.012680834159255028, 0.011248953640460968, 0.007373110391199589, -0.0013901025522500277, -0.004945858381688595, 0.0220172181725502, 0.018490560352802277, 0.0977262333035469, 0.018484190106391907, 0.016047153621912003, -0.08883865922689438, 0.010245914570987225, 0.025145141407847404, -0.021738575771450996, 0.02362513542175293, 0.0024226256646215916, -0.016578631475567818, -0.04646381363272667, -0.025144634768366814, -0.02032196708023548, 0.024975048378109932, 0.012440253980457783, -0.00751493452116847, 0.01803402602672577, -0.006534143351018429, -0.051482658833265305, 0.0810295045375824, 0.0075747291557490826, -0.03106333129107952, 0.029322104528546333, -0.01163669303059578, 0.009483156725764275, -0.003959651105105877, -0.002626223023980856, 0.01931218057870865, -0.011812056414783001, 0.05231921374797821, -0.016955023631453514, -0.009920558892190456, -0.04059159755706787, 0.06545241922140121, -0.003363403957337141, 0.022453919053077698, 0.057076647877693176, 0.014697503298521042, 0.0027023120783269405, 0.060167696326971054, -0.037011656910181046, 0.012739055790007114, 0.09862793982028961, -0.04483819007873535, -0.019205806776881218, -0.04202732443809509, 0.0106648625805974, -0.05672965943813324, 0.09009891748428345, -0.008245625533163548, 0.0019193370826542377, -0.04897364228963852, -0.007305892184376717, -0.04515792801976204, -0.03968313708901405, 0.0163675919175148, -0.02815701626241207, 0.01319256890565157, 0.003619416384026408, 0.057589415460824966, 0.014240271411836147, -0.037478648126125336, 0.04488309100270271, -0.015176990069448948, -0.007238204590976238, 0.011113825254142284, -0.025466443970799446, 0.005560146179050207, -0.02624155767261982, -0.0016052746213972569, -0.07764147222042084, -0.056700076907873154, -0.04275532811880112, -0.004292341880500317, -0.06790819764137268, -0.07016362249851227, 0.012188507243990898, 0.012751055881381035, -0.07105739414691925, 0.021247100085020065, 0.033923134207725525, -0.013175164349377155, 0.012590577825903893, -0.02753973752260208, -0.01078807096928358, 0.010010425932705402, 0.07625854015350342, -0.05367327481508255, 0.028067609295248985, -0.05607268586754799, -0.03174315392971039, -0.0010286677861586213, 0.023678602650761604, -0.011524866335093975, -0.007877832278609276, 0.03356357291340828, -0.00528386514633894, 0.058525681495666504, -0.054937850683927536, -0.027787750586867332, 0.00035145742003805935, -0.0809541642665863, 0.028890440240502357, 0.03527260571718216, -0.01790379360318184, 0.03618481382727623, 0.0617300346493721, -0.005276355892419815, -0.06799199432134628, 0.00426658196374774, -0.008256688714027405, 0.020689832046628, -0.008409978821873665, 0.026166103780269623, 0.0036433860659599304, 0.025210052728652954, -0.016652444377541542, 0.03891301527619362, -0.029787223786115646, -0.011190946213901043, -0.0013156577479094267, -0.007873563095927238, 0.025707431137561798, -0.06787510216236115, -0.013266026973724365, -0.013548227958381176, -0.03518572822213173, 0.024270230904221535, -0.017370950430631638, -0.001685087918303907, -0.057011473923921585, -0.002747040009126067, 0.0076649668626487255, -0.004141673911362886, -0.025409268215298653, -0.014989607967436314, -0.004042371176183224, -0.024102525785565376, 0.03044040873646736, -0.048546623438596725, -0.03419014438986778, 0.09826087951660156, -0.04212898761034012, -0.0028071983251720667, 0.027525588870048523, 0.022000102326273918, 0.03299541398882866, 0.01589471660554409, -0.02147340029478073, 0.01415511965751648, 0.01519847847521305, -0.011015297845005989, -0.054913029074668884, -0.0691109299659729, 0.02896006405353546, -0.007563339546322823, 0.03357183560729027, 0.0013906926615163684, 0.006359193008393049, -0.045921120792627335, -0.025246307253837585, 0.028377078473567963, 0.1437869668006897, 0.027105655521154404, -0.02321442775428295, 0.04042497277259827, -0.0049287681467831135, -0.002398093231022358, 0.006516714580357075, -0.012620262801647186, -0.0362294465303421, 0.0269221942871809, 0.031153572723269463, -0.024565543979406357, -0.007108950521796942, 0.020441388711333275, 0.021424666047096252, -0.004825724754482508, -0.023519987240433693, -0.031663861125707626, 0.0281659048050642, -0.026898274198174477, -0.023368192836642265, -0.037487201392650604, -0.047160472720861435, 0.002589896321296692, -0.013143626041710377, 0.0014977056998759508, 0.08286500722169876, 0.012458382174372673, -0.0068833366967737675, -0.018866151571273804, 0.016751866787672043, 0.02426580712199211, -0.016497300937771797, 0.029278067871928215, 0.06187012791633606, -0.06521385908126831, -0.057117655873298645, 0.0019273316720500588, 0.002765268785879016, -0.023180920630693436, -0.026037029922008514, 0.02511906810104847, -0.02968665212392807, -0.03203275427222252, -0.017508115619421005, -0.060551632195711136, 0.028758754953742027, 0.028477342799305916, 0.01696607656776905, -0.0271940678358078, 0.02123282290995121, 0.005728375166654587, -0.023041486740112305, 0.028485802933573723, 0.021237920969724655, -0.015538634732365608, -0.004951507784426212, 0.004596018232405186, 0.03133728727698326, 0.026724588125944138, 0.020145652815699577, 0.03277186304330826, -0.0027465447783470154, 0.03583080321550369, 0.07055182009935379, 0.07719958573579788, -0.010241839103400707, -0.04160439223051071, -0.023731525987386703, -0.011355816386640072, -0.018347514793276787, -0.009503234177827835, 0.02956475503742695, -0.014666613191366196, -0.0948285162448883, -0.030044086277484894, -0.0015585655346512794, -0.003878742689266801, -0.0997353345155716, -0.027677446603775024, -0.06478096544742584, -0.0015624595107510686, 0.005079359747469425, -0.018326222896575928, 0.005253610201179981, 0.012736727483570576, 0.013105195015668869, 0.04143300652503967, 0.01285842526704073, -0.026358094066381454, 0.026619073003530502, -0.0077258930541574955, 0.010329069569706917, 0.02495271898806095, 0.0004990881425328553, 0.0008013024344108999, 0.0023124092258512974, -0.02298840880393982, -0.018603593111038208, 0.03532068431377411, 0.03443921357393265, 0.014870721846818924, -0.02244303748011589, 0.05819692462682724, -0.015284384600818157, 0.013406774960458279, 0.03157834708690643, -0.05750631168484688, 0.02622346766293049, 0.05262329429388046, 0.011025723069906235, -0.006746313069015741, -0.05030953511595726, 0.07769706100225449, 0.0020550121553242207, 0.026492701843380928, 0.011328769847750664, 0.03005625307559967, 0.03402458503842354, -0.02873246744275093, -0.00829282309859991, 0.07502961903810501, -0.014794502407312393, -0.0031051957048475742, 0.03022727742791176, 0.052672483026981354, -0.009423993527889252, 0.01724637672305107, -0.015693016350269318, -0.05221142619848251, -0.015397843904793262, -0.021603191271424294, -0.0005207514623180032, -0.029188042506575584, -0.03768210858106613, 0.0010392810218036175, 0.04582123085856438, -0.041699282824993134, 0.005747136194258928, 0.028328148648142815, 0.017799867317080498, -0.02138330228626728, -0.06174006313085556, -0.01110184658318758, -0.026937324553728104, 0.06444139778614044, 0.03681623190641403, 0.007122330367565155, 0.05246400833129883, 0.009945995174348354, -0.06399862468242645, -0.01236308179795742, 0.008591805584728718, -0.011492453515529633, -0.04442661255598068, 0.04640646278858185, 0.018496273085474968, -0.013522537425160408, 0.026264378800988197, -0.03512951359152794, -0.08448255062103271, -0.009191743098199368, 0.042652569711208344, 0.07918001711368561, 0.003600239520892501, 0.03981500864028931, -0.0237237848341465, -0.04841862991452217, 0.01692112721502781, -0.03184986859560013, -0.002349789720028639, 0.007774923462420702, 0.08504872769117355, -0.02316536195576191, 0.010159731842577457, 0.029739398509263992, -0.023389548063278198, -0.017233770340681076, 0.02959281951189041, 0.0269662756472826, -0.015462039969861507, 0.08491090685129166, 0.03823811560869217, -0.02571544609963894, 0.01854122243821621, -0.017706114798784256, -0.006631346419453621, -0.007916049100458622, 0.03430173173546791, 0.03190116584300995, 0.014402489177882671, -0.015607508830726147, 0.07308700680732727, 0.008459054864943027, 0.020487168803811073, 0.04258568584918976, -0.03219068422913551, 0.0630081370472908, -0.07897577434778214, -0.03885722532868385, 0.004890077747404575, -0.041680727154016495, 0.06726694107055664, 0.002141777891665697, 0.010981367900967598, -0.055105265229940414, -0.0014930303441360593, -0.003978954162448645, 0.0190510842949152, -0.033797264099121094, 0.04793108254671097, 0.028757477179169655, -0.0004988039145246148, -0.05750317871570587, 0.009970991872251034, 0.030773650854825974, -0.03494369983673096, -0.04799000173807144, 0.007322462275624275, 0.09168930351734161, -0.003538183169439435, -0.031113440170884132, 0.016156552359461784, 0.005770223680883646, -0.030091239139437675, 0.007581566926091909, -0.03097892925143242, 0.01548326201736927, -0.03865582495927811, -0.02076507918536663, -0.004722790326923132, 0.01169378962367773, 0.027775386348366737, -0.028585659340023994, -0.01885243132710457, -0.013859190046787262, -0.0015165626537054777, -0.01376266498118639, 0.026333855465054512, 0.017449991777539253, 0.03241879120469093, -0.015319016762077808, -0.028242936357855797, 0.03919563814997673, -0.029479829594492912, 0.044382594525814056, 0.007655201014131308, 0.04847990348935127, -0.02049068734049797, 0.027950383722782135, -0.027996307238936424, 0.0021572881378233433, 0.023515090346336365, -0.007925882935523987, 0.020078925415873528, 0.0446808747947216, 0.032358404248952866, -0.028511859476566315, -6.321379563284212e-33, 0.021925315260887146, -0.0011306433007121086, -0.02041434496641159, -0.029095564037561417, -0.06118325889110565, 0.026835011318325996, -0.0169293824583292, -0.01387886144220829, 0.011752903461456299, -0.04133149981498718, -0.019803589209914207, 0.01618683524429798, -0.009786962531507015, 0.020707955583930016, 0.06989140063524246, -0.02608538791537285, -0.003349425969645381, 0.0072062695398926735, 0.024618247523903847, 0.04753328487277031, 0.07673722505569458, 0.07344044744968414, 0.0375223234295845, -0.05228906869888306, -0.029583752155303955, 0.002458749106153846, 0.01128824520856142, -0.036895643919706345, -0.02116575464606285, 0.01444979663938284, -0.013466056436300278, 0.020930500701069832, 0.02164979837834835, -0.05805317685008049, -0.04469919204711914, 0.013824299909174442, -0.08437243849039078, -0.006072381045669317, -0.07824454456567764, -0.01151606347411871, -0.03807784616947174, -0.00400893297046423, 0.07580963522195816, -0.006099218036979437, -0.0023714120034128428, 0.006416045129299164, 0.0335998460650444, -0.03390469402074814, -0.06795231252908707, -0.014197630807757378, -0.020065760239958763, -0.02920454740524292, 0.015216227620840073, 0.0018689046846702695, -0.01584661938250065, -0.012701747938990593, -0.03583386912941933, -0.025144731625914574, -0.11355508118867874, -0.04193544015288353, -0.04118752107024193, 0.029987696558237076, 0.0016144010005518794, 0.030935347080230713, 0.043069805949926376, 0.045884232968091965, 0.025280291214585304, 0.04870473966002464, -0.007008576299995184, -0.013367618434131145, 0.004541655536741018, -0.016214700415730476, 0.08975613862276077, -0.04486919194459915, 0.05189420282840729, -0.06359066069126129, -0.028589196503162384, -0.013041527941823006, -0.012719321995973587, 0.08430380374193192, 0.028028029948472977, 0.057885561138391495, 0.005501026753336191, -0.0017845865804702044, 0.03435764089226723, 0.04129014164209366, -0.03028607740998268, 0.009777773171663284, 0.01305252593010664, 0.010030189529061317, 0.0021940399892628193, 0.025821803137660027, 0.020057836547493935, -0.027558818459510803, 0.06813955307006836, -0.002004853682592511, 0.0517166368663311, 0.02453434281051159, 0.0102842403575778, 0.015846312046051025, -0.04765209183096886, -0.0009700654190964997, -0.04377828910946846, 0.017308276146650314, 0.004509996622800827, 0.02986399456858635, 0.043167341500520706, 0.026234736666083336, 0.015925254672765732, -0.03728099167346954, -0.00021334299526643008, -0.02782631851732731, 0.059194423258304596, 0.03597132861614227, 0.023107683286070824, -0.0025905005168169737, 0.026763346046209335, 0.06576644629240036, 0.033843811601400375, -0.025234341621398926, -0.06892278790473938, 0.020187821239233017, 0.02405252307653427, 0.014976526610553265, -0.020457299426198006, 0.007866268046200275, -0.07196308672428131, 0.0029606965836137533, -0.029845494776964188, -0.0808873325586319, 0.01913033239543438, 0.022472023963928223, 2.969050854062516e-07, -0.08815734833478928, 0.013760522939264774, -0.00886708777397871, -0.06555340439081192, 0.014859935268759727, 0.014295916073024273, 0.004570639226585627, 0.029571328312158585, -0.018133040517568588, 0.04063970223069191, 0.017637623474001884, -0.022109298035502434, 0.012359828688204288, -0.00011795418686233461, -0.07295383512973785, -0.02703692577779293, -0.01078495942056179, 0.040509749203920364, -0.019573770463466644, 0.026480747386813164, 0.03368288651108742, 0.05231451615691185, 0.042152952402830124, -0.0005863078986294568, 0.05811287835240364, -0.023659545928239822, -0.005903157871216536, 0.06456667184829712, 0.033366378396749496, -0.05780218169093132, 0.008834508247673512, 0.06691325455904007, -0.03802749887108803, -0.001035976456478238, -0.02724197506904602, -0.017878618091344833, 0.004633933771401644, -0.015122667886316776, -0.03926367312669754, -0.0829172357916832, 0.042118288576602936, 0.025799838826060295, 0.02864774875342846, -0.014639042317867279, 0.041347481310367584, -0.05092031508684158, -0.030865920707583427, 0.040354516357183456, -0.0012069899821653962, 0.004152127541601658, 0.0028629088774323463, 0.015484113246202469, -0.024720167741179466, -0.041156310588121414, -0.04011165723204613, 0.020057691261172295, -0.021411258727312088, -0.09902944415807724, 0.01858961582183838, 0.07236891984939575, -0.01772492751479149, -0.024330666288733482, -0.03296782076358795, -0.011166458949446678, 0.03505268692970276, -0.04999707639217377, -0.0059887985698878765, 2.545386768678032e-34, -0.0275424737483263, -0.04718105122447014, 0.010855323635041714, 0.05842425674200058, -0.020346343517303467, -0.022984009236097336, -0.008394274860620499, 0.01887926273047924, 0.033564772456884384, -0.004519698675721884, -0.0597735270857811]

['Zachary C. Lipton', 'Yu-Xiang Wang', 'Alex Smola']

1802.03916v2

Faced with distribution shift between training and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets), cause symptoms (observations), we focus on label shift, where the label marginal $p(y)$ changes but the conditional $p(x|y)$ does not. We propose Black Box Shift Estimation (BBSE) to estimate the test distribution $p(y)$. BBSE exploits arbitrary black box predictors to reduce dimensionality prior to shift correction. While better predictors give tighter estimates, BBSE works even when predictors are biased, inaccurate, or uncalibrated, so long as their confusion matrices are invertible. We prove BBSE's consistency, bound its error, and introduce a statistical test that uses BBSE to detect shift. We also leverage BBSE to correct classifiers. Experiments demonstrate accurate estimates and improved prediction, even on high-dimensional datasets of natural images.

Detecting and Correcting for Label Shift with Black Box Predictors

http://arxiv.org/pdf/1802.03916v2

Title Detecting Correcting Label Shift Black Box Predictors Summary Faced distribution shift training test set wish detect quantify shift correct classifier without test set label Motivated medical diagnosis disease target cause symptom observation focus label shift label marginal py change conditional pxy propose Black Box Shift Estimation BBSE estimate test distribution py BBSE exploit arbitrary black box predictor reduce dimensionality prior shift correction better predictor give tighter estimate BBSE work even predictor biased inaccurate uncalibrated long confusion matrix invertible prove BBSEs consistency bound error introduce statistical test us BBSE detect shift also leverage BBSE correct classifier Experiments demonstrate accurate estimate improved prediction even highdimensional datasets natural image Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0030144392512738705, 0.03700340911746025, -0.009759852662682533, -0.00436204532161355, -0.010795993730425835, 0.01528732106089592, 0.0360267236828804, 0.0810960903763771, -0.04707879573106766, -0.00498958257958293, 0.09225547313690186, 0.006553373299539089, 0.00669174874201417, 0.05810375139117241, -0.01896798051893711, -0.042747706174850464, -0.0033228008542209864, 0.03770951181650162, -0.030090637505054474, 0.0005942417192272842, 0.015336312353610992, -0.040710095316171646, -0.026962492614984512, 0.025892695412039757, -0.08030898123979568, -0.007315520197153091, -0.0057886382564902306, 0.014350248500704765, 0.03605714067816734, -0.05196631699800491, 0.03385316953063011, 0.012524317018687725, -0.0226700808852911, 0.03606243431568146, 2.382719230809016e-06, -0.05610262602567673, -0.03317097947001457, -0.02691005729138851, 0.010848603211343288, -0.051359448581933975, -0.016599945724010468, -0.059009112417697906, 0.010265699587762356, -0.03306993097066879, 0.008317087776958942, -0.05298253521323204, 0.06444143503904343, 0.07094451785087585, -0.014051266945898533, 0.06042789667844772, -0.0032393524888902903, 0.0016739324200898409, -0.0263105146586895, 0.01077237818390131, 0.0712379738688469, -0.053891509771347046, 0.05505288764834404, -0.029466936364769936, -0.05524086579680443, -0.04512602835893631, -0.05404235050082207, 0.05255334451794624, 0.024010296911001205, -0.012972249649465084, 0.05184789374470711, 0.0770992562174797, 0.002355910139158368, -0.017503637820482254, -0.03288386017084122, 0.04789682477712631, -0.045472316443920135, -0.00613759271800518, -0.004632694646716118, -0.018207255750894547, 0.021689388900995255, 0.01734684780240059, -0.0036961755249649286, -0.009341822937130928, -0.015093514695763588, -0.022958766669034958, -0.07318049669265747, 0.029142770916223526, 0.01956314407289028, -0.04668355733156204, -0.02329307794570923, 0.051083244383335114, -0.010902299545705318, -0.030186278745532036, -0.013743488118052483, -0.017656009644269943, 0.032427169382572174, -0.04052174836397171, 0.01362626627087593, 0.00706824567168951, -0.046939149498939514, -0.020423240959644318, 0.009791411459445953, -0.04320764169096947, 0.04774698242545128, -0.04171522706747055, 0.017752820625901222, -0.027430810034275055, -0.09572377055883408, 0.025610672309994698, 0.009106533601880074, 0.03074057772755623, -0.04848277196288109, 0.08895339071750641, -0.018738657236099243, 0.05285298824310303, -0.02384532429277897, 0.04164913296699524, -0.02294566109776497, -0.023121459409594536, 0.07735207676887512, 0.011349411681294441, -0.05333489924669266, -0.029717134311795235, -0.012716356664896011, 0.013453102670609951, 0.002006800612434745, 0.0674055889248848, 0.006853191647678614, -0.022902073338627815, 0.015287619084119797, 0.04711640626192093, 0.017798010259866714, -0.005534035153687, 0.0012035041581839323, 0.02248784713447094, 0.017656542360782623, 0.048585548996925354, -0.015389584004878998, -0.009688949212431908, 0.020898407325148582, 0.05356837064027786, 0.011707990430295467, 0.0018215462332591414, -0.05501518025994301, -0.0014434463810175657, -0.0806078389286995, 0.043168939650058746, 0.003171083750203252, -0.020180972293019295, -0.06017408147454262, -0.0015252599259838462, 0.015194163657724857, 0.008316542953252792, -0.0025927997194230556, -0.03314850106835365, 0.0015881642466410995, 0.08321689069271088, -0.03471730649471283, -0.00861415360122919, 0.10557053238153458, 0.00839908979833126, -0.019391892477869987, 0.04069700092077255, 0.029159709811210632, -0.007392593659460545, 0.05671834573149681, -0.05503520742058754, 0.01596379093825817, 0.014118902385234833, -0.03113793581724167, -0.023771213367581367, -0.03887952119112015, -0.03224651515483856, 0.021641045808792114, 0.04907388612627983, -0.01596318930387497, -0.05720333382487297, 0.04677374288439751, -0.026963679119944572, 0.03471461310982704, 0.04287252947688103, 0.006520663853734732, -0.024174688383936882, -0.02493533305823803, -0.03774796053767204, -0.0855993926525116, -0.0178071279078722, 0.002456067828461528, 0.028422825038433075, -0.05928835645318031, -0.029631946235895157, -0.06253720819950104, -0.0013233774807304144, 0.011770817451179028, -0.04310383275151253, -0.005731921177357435, -0.009954076260328293, -0.06629858165979385, -0.043447546660900116, 0.057267479598522186, -0.011402571573853493, -0.0010346060153096914, 0.0442679226398468, 0.03749394789338112, -0.019353359937667847, -0.042195577174425125, -0.044672057032585144, 0.026692865416407585, -0.03531685844063759, -0.03118276782333851, -0.0695023387670517, -0.023990284651517868, -0.021924488246440887, 0.034336064010858536, 0.01629556529223919, 0.005586639512330294, 0.025894861668348312, 0.006878198124468327, -0.03463004156947136, -0.008195610716938972, 0.057132184505462646, 0.015140771865844727, -0.019646281376481056, -0.0127304308116436, 0.022142445668578148, -0.008853771723806858, -0.011493274010717869, 0.0021123886108398438, 0.03310152888298035, 0.021901540458202362, 0.03114396147429943, 0.02583729289472103, 0.04929077625274658, -0.0026846760883927345, -0.04151533544063568, 0.009518910199403763, -0.03248700499534607, 0.0053242831490933895, -0.02081899903714657, -0.06702986359596252, 0.03066875785589218, 0.011522436514496803, -0.01539074257016182, 0.037019044160842896, -0.016534876078367233, 0.010706990957260132, -0.015381166711449623, -0.06223982945084572, -0.011617237702012062, -0.01630006730556488, -0.010205451399087906, -0.05053276941180229, 0.029838016256690025, 0.03917335718870163, -0.007864367216825485, 0.012086976319551468, -0.03869321942329407, 0.01807207055389881, -0.004023178480565548, -0.007524009793996811, -0.028629405423998833, -0.03858347609639168, 0.030083127319812775, 0.0167892724275589, 0.030148738995194435, 0.009706889279186726, -0.026051411405205727, 0.001128821400925517, -0.015082931146025658, 0.006336177699267864, -0.01591227576136589, 0.02921885810792446, 0.03323012962937355, -0.017377343028783798, -0.006544979754835367, -0.008345910347998142, 0.028351977467536926, -0.01250508613884449, -0.011612034402787685, -0.051992807537317276, -0.011724758893251419, 0.0164750088006258, -0.031998589634895325, -0.03735177218914032, 0.0578516349196434, 0.004409069661051035, -0.02719867043197155, -0.014032662846148014, 0.03071775659918785, -0.011046911589801311, 0.03435825556516647, 0.036625806242227554, -0.060423269867897034, -0.044193100184202194, -0.010309794917702675, -0.0033079935237765312, -0.006120046600699425, 0.016954125836491585, -0.021321551874279976, -0.04008187726140022, 0.000557977647986263, -0.04097394645214081, 0.05599299445748329, 0.04141309857368469, 0.025720668956637383, 0.01013316959142685, 0.07114441692829132, -0.00022240275575313717, -0.019881628453731537, -0.048201341181993484, -0.0069868918508291245, 0.006423767190426588, -0.079732745885849, 0.012258387170732021, 0.06825336068868637, 0.006908537819981575, 0.02376469410955906, -0.008847731165587902, -0.047207072377204895, 0.0024341901298612356, 0.016293451189994812, -0.07841650396585464, 0.03332337364554405, -0.0374971367418766, 0.024054257199168205, -0.025949332863092422, -0.04991364851593971, 0.03251507878303528, 0.0016651293262839317, 0.012489628046751022, 0.0029685443732887506, -0.0171522069722414, 0.01185173075646162, -0.02458590269088745, 0.002202357165515423, 0.024660494178533554, 0.05133960023522377, 0.009920534677803516, 0.0029038244392722845, -0.002793043153360486, 0.021319469437003136, -0.02070092223584652, -0.000458952272310853, -0.05104080215096474, 0.03038344345986843, 0.020639820024371147, -0.02515782043337822, -0.032148439437150955, -0.01943294145166874, 0.03336478769779205, -0.04636770859360695, -0.04243306815624237, -0.012114429846405983, -0.036541055887937546, 0.02072196640074253, -0.018902400508522987, 0.06341911107301712, -0.016952481120824814, -0.017994338646531105, 0.022135896608233452, 0.006540066562592983, 0.03389216586947441, -0.026940247043967247, -0.04613202437758446, -0.0319141261279583, -0.004992200993001461, 0.029830122366547585, -0.0608627088367939, 0.03444086015224457, -0.07489999383687973, 0.010162224993109703, -0.02470308355987072, 0.012695042416453362, -0.015286140143871307, -0.011171217076480389, 0.03851086273789406, -0.006346493493765593, -0.011845567263662815, 0.06006544083356857, 0.01817762665450573, -0.06784366071224213, -0.010348067618906498, -0.04645391181111336, -0.023893048986792564, -0.010149715468287468, -0.019215315580368042, -0.046330422163009644, -0.019055485725402832, -0.005450565833598375, -0.0016146632842719555, -0.0060508763417601585, -0.028465531766414642, 0.02552725002169609, -0.03459575027227402, 0.026275280863046646, 0.021463416516780853, -0.0318436399102211, -0.021031739190220833, 0.010090703144669533, 0.005446021445095539, -9.96433868749591e-07, -0.05438815802335739, 0.0028980274219065905, 0.032819390296936035, -0.02689054235816002, 0.05053569748997688, -0.06881166249513626, 0.01747215911746025, 0.0286069605499506, -0.026427770033478737, -0.043883539736270905, 0.025755761191248894, 0.017021384090185165, -0.032731540501117706, -0.03359145298600197, 0.03643975779414177, -0.005734844133257866, 0.035263095051050186, -0.0011733464198186994, 0.14850027859210968, 0.0016965839313343167, -0.00395415723323822, 0.004727592691779137, 0.008058929815888405, -0.021134506911039352, 0.02990262396633625, 0.05366375669836998, 0.0464048832654953, 0.012575649656355381, -0.01648881286382675, -0.04723444581031799, 0.03829416260123253, 0.005021956283599138, -0.033418189734220505, 0.02566348947584629, -0.025636453181505203, 0.007929797284305096, 0.007659078575670719, 0.04860451817512512, -0.01613735966384411, 0.03254617750644684, 0.06203474849462509, -0.07945389300584793, -0.09575672447681427, -0.06029006838798523, 0.06301973015069962, -0.015002361498773098, 0.04126451164484024, 0.0321684256196022, -0.029480909928679466, -0.01542225293815136, -0.0008667661459185183, -0.04886244237422943, 0.03999728709459305, 0.07734312862157822, 0.03948265686631203, -0.030287183821201324, 0.0017706333892419934, 0.02802436053752899, 0.021115431562066078, -0.001779528334736824, -0.06003282964229584, -0.039118148386478424, -0.021886074915528297, -0.01106841117143631, 0.047408994287252426, 0.016033712774515152, 0.009786974638700485, -0.0109003446996212, -0.015898242592811584, 0.015376752242445946, 0.039860647171735764, 0.05608411505818367, 0.016846442595124245, -0.007624341174960136, -0.06752263009548187, -0.010944163426756859, -0.0012201498029753566, 0.0005702454946003854, 0.05662301927804947, 0.02760815992951393, -0.08044262230396271, -0.05294226109981537, 0.0011762342182919383, -0.005687145050615072, -0.03853120282292366, 0.11115429550409317, -0.035458896309137344, -0.04081729054450989, -0.01857295259833336, 0.04739740863442421, 0.02328561246395111, -0.0028751117642968893, 0.016971362754702568, -0.016345767304301262, 0.015467571094632149, -0.028126699849963188, -0.01994745433330536, 0.024662809446454048, -0.03971361368894577, -0.05363813042640686, -0.060025252401828766, 0.010437042452394962, 0.00512071093544364, 0.06071082502603531, 0.04677286744117737, 0.014564254321157932, 0.040588244795799255, -0.012002821080386639, 0.04579323157668114, 0.06650623679161072, 0.042810264974832535, 0.07934363186359406, 0.05268613621592522, 0.020699163898825645, -0.021772662177681923, 0.00011505516886245459, 0.004724096041172743, 0.014517655596137047, -0.04746563732624054, 0.002661770675331354, 0.036394305527210236, -0.03430972248315811, 0.005956465844064951, 0.05320986360311508, -0.013190309517085552, 0.0016753977397456765, 0.08226017653942108, -0.020724091678857803, 0.010210167616605759, 0.04826997593045235, -0.01867285929620266, -0.011961685493588448, 0.012993439100682735, 0.04161059483885765, 0.04759230464696884, 0.00495939701795578, -0.03445468097925186, -0.02497371844947338, -0.01855061575770378, 0.06492085009813309, 0.05078737065196037, -0.02887878194451332, -0.010799724608659744, 0.02427808940410614, -0.03424866497516632, -0.020725734531879425, 0.04295165091753006, -0.024774186313152313, 0.06727927178144455, 0.048046208918094635, -0.021561497822403908, 0.025176437571644783, -0.010639745742082596, -0.07119980454444885, 0.006260142661631107, 0.014018462039530277, -8.048293966567144e-05, 0.007193889934569597, -0.03144241124391556, -6.177260282453553e-33, -0.011593220755457878, -0.06047412008047104, -0.04998791590332985, -0.033010851591825485, 0.02002028375864029, 0.024556849151849747, -0.019493911415338516, 0.008908693678677082, 0.040068767964839935, 0.04515490680932999, 0.0077656712383031845, 0.002439690986648202, 0.02607019618153572, 0.020344236865639687, 0.029810834676027298, -0.034618932753801346, -0.0025000860914587975, -0.01958712562918663, -0.032958220690488815, -0.005184388719499111, 0.01806185394525528, 0.07194003462791443, 0.0615135133266449, -0.04867111146450043, -0.06518465280532837, 0.04446929320693016, 0.004830351565033197, -0.014363686554133892, -0.04524809122085571, -0.01663004234433174, 0.04831612482666969, 0.013404838740825653, 0.00838957168161869, 0.015279081650078297, 0.014881453476846218, -0.022656958550214767, -0.008983050473034382, 0.0028775406535714865, -0.044671326875686646, 0.0738959014415741, -0.009107102639973164, 0.026796331629157066, 0.04679737985134125, -0.011571739800274372, -0.0003137352177873254, -0.028021754696965218, 0.04933932423591614, -0.07600322365760803, 0.014594043605029583, 0.010892219841480255, -0.03340953588485718, 0.030815621837973595, -0.026346130296587944, 0.004414998926222324, -0.0015790234319865704, -0.012026522308588028, 0.0030064908787608147, 0.0017453394830226898, -0.024982577189803123, 0.005850647110491991, 0.0696944147348404, 0.0152647215873003, 0.026099644601345062, 0.06705421209335327, -0.023502731695771217, 0.027294669300317764, 0.07237909734249115, -0.008244161494076252, 0.02115580625832081, -0.04942013695836067, -0.04406315088272095, 0.022882802411913872, 0.03826471418142319, 0.01668906956911087, 0.09995044767856598, -0.04383251443505287, -0.03642481565475464, 0.027704158797860146, -0.08436316251754761, -0.0020131284836679697, -0.06353896111249924, -0.011931786313652992, -0.024817829951643944, -0.009820613078773022, 0.04492607340216637, 0.0001782955223461613, -0.007288717199116945, 0.012562037445604801, 0.02220224030315876, -0.0021227276884019375, 0.014360866509377956, 0.052648644894361496, -0.0333399698138237, 0.0007126966957002878, 0.046041544526815414, -0.10007981956005096, 0.020304810255765915, 0.04756927117705345, -0.010259314440190792, -0.05049823224544525, -0.004280793480575085, -0.0335102342069149, 0.024485217407345772, 0.020243488252162933, 0.06900932639837265, 0.0019362122984603047, 0.06405851244926453, -0.028065791353583336, -0.03458752483129501, 0.0055566634982824326, 0.01103129144757986, -0.06465471535921097, 0.020946316421031952, 0.029683319851756096, -0.010991796851158142, 0.001851285109296441, -0.03363267332315445, 0.1172238364815712, 0.01784094050526619, -0.014884752221405506, -0.01154885720461607, -0.029232880100607872, -0.010168465785682201, 0.024121247231960297, -0.10084890574216843, -0.014909878373146057, 0.021198831498622894, -0.03341611102223396, 0.03881412371993065, -0.05615340918302536, -0.017638681456446648, -0.07695583999156952, 3.0151528562782914e-07, 0.05143006145954132, 0.04247976839542389, 0.01427367702126503, -0.04691309109330177, -0.0023697339929640293, 0.007370542269200087, -0.049903180450201035, 0.011974737979471684, -0.021349985152482986, -0.04314585030078888, 0.038060300052165985, -0.047851577401161194, 0.0156142208725214, -0.010876351036131382, 0.023004624992609024, -0.059626948088407516, -0.006499804090708494, 0.012692026793956757, -0.038808226585388184, 0.003882078221067786, 0.06355195492506027, 0.034850358963012695, 0.016096273437142372, -0.06528664380311966, 0.02776157669723034, 0.002858320716768503, 0.005596148781478405, -0.04258928820490837, 0.05425821244716644, -0.026335610076785088, -0.0022270791232585907, -0.023966006934642792, -0.013061242178082466, 0.047589126974344254, -0.010875493288040161, -0.018360091373324394, -0.020730435848236084, 0.011929069645702839, -0.06423898786306381, 0.04847633093595505, -0.024536756798624992, 0.05489957705140114, 0.006047507282346487, -0.034568801522254944, 0.04012854024767876, -0.03192862495779991, 0.007057775277644396, -0.04625729098916054, -0.05387076735496521, -0.0005140557768754661, 0.04559595510363579, 0.005036813672631979, 0.009665201418101788, 0.03220066800713539, 0.006586521398276091, 0.012477211654186249, -0.01133558340370655, -0.054009534418582916, 0.002406234620139003, 0.041658125817775726, 0.009973100386559963, 0.016350464895367622, 0.027370162308216095, -0.03638305142521858, -0.006908085662871599, -0.06572631746530533, -0.007557932287454605, 3.1577010872551404e-34, 0.0153967859223485, 0.024974742904305458, 0.019595783203840256, -0.018601348623633385, 0.006159599870443344, -0.017651036381721497, 0.029199248179793358, -0.01932706870138645, -0.0010934151941910386, 0.031026845797896385, -0.0028356502298265696]

['Kenji Kawaguchi', 'Yoshua Bengio']

1802.07426v1

This paper introduces a novel measure-theoretic learning theory to analyze generalization behaviors of practical interest. The proposed learning theory has the following abilities: 1) to utilize the qualities of each learned representation on the path from raw inputs to outputs in representation learning, 2) to guarantee good generalization errors possibly with arbitrarily rich hypothesis spaces (e.g., arbitrarily large capacity and Rademacher complexity) and non-stable/non-robust learning algorithms, and 3) to clearly distinguish each individual problem instance from each other. Our generalization bounds are relative to a representation of the data, and hold true even if the representation is learned. We discuss several consequences of our results on deep learning, one-shot learning and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. Because of the differences in the assumptions and the objectives, the proposed learning theory is meant to be complementary to previous learning theory and is not designed to compete with it.

Generalization in Machine Learning via Analytical Learning Theory

http://arxiv.org/pdf/1802.07426v1

Title Generalization Machine Learning via Analytical Learning Theory Summary paper introduces novel measuretheoretic learning theory analyze generalization behavior practical interest proposed learning theory following ability 1 utilize quality learned representation path raw input output representation learning 2 guarantee good generalization error possibly arbitrarily rich hypothesis space eg arbitrarily large capacity Rademacher complexity nonstablenonrobust learning algorithm 3 clearly distinguish individual problem instance generalization bound relative representation data hold true even representation learned discus several consequence result deep learning oneshot learning curriculum learning Unlike statistical learning theory proposed learning theory analyzes problem instance individually via measure theory rather set problem instance via statistic difference assumption objective proposed learning theory meant complementary previous learning theory designed compete Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04089696332812309, 0.010580497793853283, -0.04603782296180725, -0.009592321701347828, 0.004706556908786297, 0.004627256654202938, 0.006789667531847954, 0.010783826932311058, -0.05618637055158615, 0.03374860808253288, 0.06609243899583817, -0.017072129994630814, -0.003834246890619397, 0.05823005735874176, 0.024226350709795952, -0.04149449244141579, -0.018110143020749092, 0.01878628134727478, -0.01375460997223854, -0.026840191334486008, 0.004395852331072092, -0.06610071659088135, 0.01146567054092884, 0.03664315119385719, -0.036409083753824234, 0.032262030988931656, -0.015423569828271866, -0.07794155180454254, 0.015314102172851562, -0.0050442214123904705, 0.031587518751621246, -0.023240679875016212, -0.015813689678907394, -0.004444126505404711, 2.2139226985018468e-06, -0.05829647183418274, -0.0530671589076519, -0.015665439888834953, 0.047759197652339935, -0.05482226237654686, 0.01682017743587494, -0.001378295011818409, 0.030420182272791862, 0.035852715373039246, -0.02269655466079712, 0.030164293944835663, 0.027659868821501732, 0.03303825482726097, 0.029471397399902344, 0.04003264382481575, -0.0050367750227451324, -0.0636746808886528, 0.00784879270941019, -0.009279792197048664, 0.012273833155632019, -0.008184467442333698, -0.002991116838529706, 0.05367141589522362, -0.02848818339407444, -0.050327982753515244, -0.020182477310299873, 0.02800043486058712, 0.0421794094145298, 0.029964327812194824, 0.07816025614738464, 0.01245975960046053, -0.018839862197637558, 0.009934796020388603, 0.025378141552209854, 0.031043706461787224, -0.02702593244612217, -0.0033695348538458347, 0.010885978117585182, -0.011482138186693192, -0.011013898998498917, -0.011253711767494678, -0.06279850751161575, 0.010723970830440521, 0.01243758574128151, 0.012096394784748554, -0.044020820409059525, 0.027504630386829376, 0.0005860471865162253, -0.011547081172466278, -0.05135297775268555, 0.06647221744060516, -0.02549736760556698, 0.0012520182644948363, 0.01920868270099163, -0.002810669830068946, -0.04746239632368088, 0.051537252962589264, -0.01565779373049736, 0.058151956647634506, -0.05180840194225311, -0.04058830812573433, 0.02583480440080166, -0.07477300614118576, 0.05353860557079315, -0.06866096705198288, 0.05481787398457527, -0.0018500201404094696, -0.008724705316126347, -0.00946873053908348, -0.016507962718605995, 0.09515267610549927, -0.011869302950799465, 0.022779066115617752, -0.04823337867856026, 0.03119480423629284, -0.07091518491506577, 0.00851791724562645, -0.0015686452388763428, 0.10696879774332047, 0.023694481700658798, 0.009167125448584557, -0.08737072348594666, 0.021480794996023178, -0.04710059612989426, -0.013480929657816887, -0.0033310779836028814, 0.05660242214798927, -0.01697400212287903, 0.035359837114810944, -0.006681845523416996, 0.0034336058888584375, -0.054578982293605804, 0.04359326884150505, -0.033583205193281174, 0.026161685585975647, 0.0528586320579052, -0.006381200160831213, 0.011605707928538322, 0.08737877756357193, 0.030506517738103867, 0.08361872285604477, -0.0036308106500655413, 0.014816686511039734, -0.0520276241004467, 0.004670104943215847, -0.010296073742210865, -0.014595789834856987, -0.04418361559510231, -0.0585138201713562, 0.0008192754467017949, -0.03186424449086189, -0.002266667317599058, 0.001205085194669664, -0.03741215169429779, -0.05479911342263222, 0.001993682002648711, 0.022123854607343674, 0.014534530229866505, 0.014756280928850174, 0.07681668549776077, -0.0035136144142597914, 0.0014055046485736966, 0.029277337715029716, 0.03528013452887535, 0.00788069423288107, 0.02959691360592842, -0.03512050211429596, 0.0246016513556242, 0.031097419559955597, 0.0021314008627086878, -0.06439999490976334, -0.011631399393081665, -0.02298515848815441, -0.019758693873882294, -0.013896875083446503, 0.009610049426555634, 0.02329372614622116, 0.0013285621535032988, -0.05082816258072853, -0.008887519128620625, 0.05807044357061386, 0.005741188768297434, 0.04750899225473404, 0.01994088664650917, -0.007174461614340544, 0.02513899840414524, 0.041037749499082565, 0.047994114458560944, 0.00863919872790575, -0.021564742550253868, -0.0361291766166687, -0.002602311782538891, -0.055622648447752, -0.05385151505470276, -0.07112281769514084, 0.0373745858669281, -0.02495814673602581, -0.03377049043774605, -0.03582675755023956, 0.08175455033779144, -0.0037353348452597857, 0.031092774122953415, -0.04888761416077614, 0.03456393629312515, 0.010991321876645088, -0.013592950999736786, -0.053428471088409424, 0.06769231706857681, -0.05780990049242973, -0.0018658945336937904, -0.07101121544837952, 0.024213258177042007, -0.05557379126548767, -0.04689216613769531, -0.08843666315078735, 0.009786346927285194, -0.050672054290771484, 0.016102461144328117, -0.010101393796503544, -0.01049856934696436, 0.014270714484155178, 0.013208386488258839, 0.0035188626497983932, -0.02068290114402771, -0.02027249149978161, 0.014910348691046238, 0.015649089589715004, -0.0670919194817543, 0.008542594499886036, 0.007537659723311663, -0.02645205706357956, 0.08428768813610077, 0.04434416815638542, 0.05463738366961479, -0.00553144421428442, 0.006730497814714909, -0.021861974149942398, 0.009219672530889511, -0.0326622910797596, -0.0646076574921608, -0.008859272114932537, 0.018286829814314842, 0.022840816527605057, 0.0272056981921196, -0.05142462998628616, 0.03805800899863243, -0.008598466403782368, -0.03544731065630913, -0.08353368192911148, 0.0016318680718541145, -0.05351148545742035, 0.0038987051229923964, 0.005105499643832445, 0.04656502231955528, -0.037960201501846313, 0.031609389930963516, -0.03748899698257446, 0.039750367403030396, 0.0029185533057898283, 0.02414928376674652, -0.04788506031036377, -0.028269562870264053, 0.05933806672692299, -0.044566504657268524, -0.051446594297885895, 0.016401497647166252, -0.05840751528739929, 0.03276895731687546, 0.07619498670101166, 0.0037806618493050337, -0.014851326122879982, 0.04477052763104439, 0.014796513132750988, -0.0022929394617676735, 0.016643987968564034, -0.0044211228378117085, 0.00829007662832737, 0.02233973704278469, 0.030731920152902603, 0.01995403878390789, -0.047652970999479294, 0.017680803313851357, 0.05087593197822571, -0.038806818425655365, 0.04190441593527794, 0.009883050806820393, -0.010062459856271744, -0.01093494426459074, -0.026701435446739197, -0.026587607339024544, 0.05424458906054497, 0.04704514518380165, -0.007074320688843727, -0.010961216874420643, 0.057212840765714645, -0.008609168231487274, -0.014169206842780113, -0.01998576708137989, -0.03971416503190994, 0.001945359050296247, -0.05754256248474121, -0.053224604576826096, 0.09078431874513626, -0.013574542477726936, -0.005275263916701078, 0.003599270712584257, 0.0906805694103241, -0.05161692202091217, 0.01395438238978386, -0.04546156898140907, -0.012938338331878185, 0.03628363460302353, -0.014476470649242401, 0.01966148056089878, 0.011135336942970753, 0.030692558735609055, -0.01819145679473877, -0.028159024193882942, 0.012650242075324059, -0.016234733164310455, 0.004752099514007568, -0.08867423236370087, 0.02953581139445305, 0.01448593195527792, 0.01608099602162838, -0.017205141484737396, -0.062353890389204025, 0.021853547543287277, 0.04463880509138107, 0.011479946784675121, -0.03387582302093506, -0.06032742187380791, 0.03263867646455765, 0.0317041389644146, 0.043562766164541245, 0.030979998409748077, -0.04623761773109436, -0.019264429807662964, -0.0440557636320591, -0.01833835244178772, -0.01255534216761589, -0.04747731238603592, 0.04066803678870201, -0.0039635272696614265, -0.03595428541302681, 0.020213037729263306, 0.012533726170659065, -0.020190710201859474, 0.049270544201135635, 0.041672512888908386, -0.012930602766573429, -0.022293752059340477, -0.022215992212295532, -0.007057089824229479, 0.011414647102355957, 0.011244836263358593, 0.022089647129178047, -0.024395061656832695, -0.043164465576410294, -0.005728145595639944, 0.015839209780097008, 0.012790277600288391, -0.05488348379731178, -0.026743674650788307, 0.004033701494336128, 0.044634342193603516, 0.02719000168144703, 0.0004287630436010659, 0.03794325143098831, -0.10629764944314957, 0.03519323095679283, -0.04473090544342995, -0.04021754115819931, -0.018754897639155388, 0.03855201229453087, -0.024450179189443588, -0.02676491253077984, 0.037021953612565994, 0.0606270395219326, -0.004496047273278236, -0.02721717394888401, -0.004538340959697962, -0.011989094316959381, -0.04122154042124748, 0.0055207679979503155, 0.03966013714671135, -0.020643752068281174, 0.03260668367147446, -0.025099636986851692, -0.0025051813572645187, -0.05177563056349754, -0.06355477124452591, 0.047319196164608, -0.0720527172088623, -0.026208000257611275, 0.020822321996092796, -0.06947485357522964, -0.04966171458363533, -0.0012859455309808254, 0.021278250962495804, -0.06538720428943634, -0.022418765351176262, -0.008900086395442486, 0.02082618698477745, 0.003110988065600395, 0.07054635137319565, -0.06749680638313293, -0.022445326671004295, -0.0010606503346934915, -0.053868990391492844, -0.012593698687851429, 0.01353610772639513, 0.04564371705055237, -0.052257146686315536, 0.0023779445327818394, -0.041117943823337555, 0.056706469506025314, -0.0014053903287276626, -0.011426093988120556, 0.05138633772730827, 0.06763801723718643, -0.020166859030723572, 0.022853635251522064, 0.05493633449077606, 0.018772443756461143, 0.05410757288336754, 0.00424499437212944, 0.08474680781364441, -0.011859565041959286, -0.0019164902623742819, -0.030909810215234756, -0.038363005965948105, -0.011106343939900398, 0.010331081226468086, -0.022874051705002785, -0.022996943444013596, -0.007147022057324648, -0.02149946242570877, 0.04009006544947624, -0.01765599474310875, 0.01388443261384964, 0.01171706523746252, 0.011016938835382462, -0.030758904293179512, -0.05254468694329262, 0.008590715005993843, -0.015155432745814323, 0.08662043511867523, 0.019373701885342598, -0.01818113587796688, -0.005344079341739416, -0.0014128668699413538, -0.030082112178206444, -0.03642188012599945, 0.03368480131030083, 0.023266198113560677, 0.017804434522986412, -0.003437794977799058, -0.001001012627966702, -0.021949419751763344, -0.051669664680957794, -0.07037816941738129, -0.014184875413775444, -0.05224163457751274, -0.021608198061585426, 0.05313245579600334, 0.02550656348466873, -0.022909577935934067, -0.03282077983021736, -0.07352572679519653, 0.061713483184576035, -0.017502114176750183, 0.006081920582801104, -0.00428940961137414, 0.056761786341667175, 0.012803992256522179, -0.007361478637903929, 0.0011230959789827466, -0.006269797682762146, 0.05527976155281067, -0.00950685702264309, -0.015547748655080795, -0.0581592433154583, 0.00757999811321497, 0.007122837472707033, 0.02966400794684887, 0.0377701036632061, 0.04859250411391258, -0.03433747962117195, -0.012854308821260929, -0.009967608377337456, 0.06827326864004135, -0.017004655674099922, -0.02555709518492222, 0.021090742200613022, 0.060068000108003616, 0.08128836005926132, -0.029866088181734085, -0.059140436351299286, 0.016435371711850166, -0.05264907702803612, 0.02824539877474308, 0.003995462320744991, 0.048931628465652466, 0.066048763692379, -0.013943727128207684, 0.03261365741491318, -0.01143892202526331, -0.029012052342295647, 0.05134143307805061, 0.006410706788301468, 0.018089327961206436, 0.0020486488938331604, 0.006500457879155874, 0.0779019147157669, -0.04355185851454735, -0.03877328336238861, 0.0007101808441802859, 0.0007422253838740289, -0.04424982890486717, 0.04615052044391632, 0.0009541605832055211, -0.021771660074591637, -0.05112843960523605, 0.017749328166246414, 0.03515079990029335, -0.015698518604040146, 0.020540514960885048, -0.021382279694080353, 0.033437516540288925, 0.008479294367134571, -0.03316022455692291, 0.008803377859294415, 0.004168582148849964, 0.04793328046798706, -0.028527500107884407, -0.0225049015134573, -0.08746417611837387, -0.01888808235526085, -0.040814902633428574, 0.0540732704102993, 0.041458744555711746, 0.009196268394589424, -0.01144945714622736, 0.019935986027121544, 0.004351102747023106, -0.042401306331157684, 0.010130072012543678, 0.017480721697211266, 0.09074676036834717, 0.007131769321858883, -0.010465365834534168, 0.04860136657953262, -0.010709772817790508, 0.01623896136879921, -0.01399986445903778, -0.07204578071832657, -0.0014099624240770936, 0.02508002705872059, -0.059392672032117844, -5.260119018790865e-33, 0.018907055258750916, -0.020388716831803322, -0.058812227100133896, -0.012859169393777847, 0.004546173848211765, 0.013066922314465046, -0.0007913224399089813, 0.0006193427834659815, 0.003706831717863679, -0.0011055158684030175, -0.022631002590060234, 0.010915844701230526, -0.013040694408118725, 0.006104778964072466, 0.06988036632537842, 0.01619293913245201, 0.0018484151223674417, -0.022771192714571953, 0.016153879463672638, 0.019435936585068703, 0.04797903075814247, 0.028268273919820786, 0.01113713625818491, -0.022602293640375137, -0.021146699786186218, 0.004800601862370968, -0.02407178282737732, 0.002763190073892474, -0.00031091185519471765, 0.008373557589948177, 0.008988814428448677, 0.04939066246151924, 0.04162128269672394, -0.010113855823874474, -0.012259913608431816, 0.001606774516403675, -0.025465084239840508, -0.059690192341804504, -0.025921091437339783, -0.00922099407762289, 0.0002978490956593305, -0.0029570620972663164, 0.0783076286315918, -0.026063239201903343, -0.029374707490205765, -0.018733130767941475, 0.07543831318616867, -0.030664192512631416, -0.005378940608352423, -0.04812072589993477, 0.010378745384514332, -0.015138665214180946, -0.05993732064962387, 0.03524354100227356, -0.0005522337160073221, 0.02965529076755047, -0.016474276781082153, -0.02578996680676937, -0.027562055736780167, 0.03262166306376457, 0.017105644568800926, -0.0146083515137434, -0.0099351080134511, 0.024833371862769127, 0.026273656636476517, 0.037845052778720856, 0.056376371532678604, -0.05072994902729988, -0.009483090601861477, -0.016447391360998154, -0.006128577049821615, 0.03155900910496712, 0.021178780123591423, 0.009616956114768982, 0.05805037170648575, -0.07548563927412033, -0.08929882943630219, 0.0763491541147232, 0.039190251380205154, 0.05127786472439766, -0.04936419427394867, -0.0020567600149661303, -0.05052954703569412, -0.003400282235816121, 0.00490801315754652, -0.05295891687273979, -0.0014702532207593322, -0.011251142248511314, 0.02574831247329712, -0.01390861812978983, -0.009517280384898186, 0.03633881360292435, -0.016519801691174507, -0.05754949897527695, 0.05279621481895447, 0.004612444434314966, -0.00927144568413496, 0.03694478049874306, 0.042439430952072144, -0.02819257788360119, -0.02210676670074463, -0.03838406503200531, -0.05573878809809685, 0.005589804612100124, 0.048467960208654404, 0.0020677116699516773, 0.05220586806535721, 0.04226238653063774, -0.006899441592395306, -0.01026768609881401, 0.0044884090311825275, -0.07324828207492828, -0.0036777937784790993, 0.028376370668411255, 0.0017165534663945436, -0.02027970552444458, -0.00154319335706532, 0.06267683953046799, -0.023828912526369095, 0.019176604226231575, -0.032183270901441574, -0.019574949517846107, 0.04240605607628822, 0.026161914691329002, -0.016426322981715202, -0.040759045630693436, 0.007467828691005707, -0.007087530568242073, 0.05041974410414696, -0.06046203151345253, -0.007313498295843601, -0.04408857226371765, 2.7227599730395013e-07, -0.01712222397327423, -0.037505101412534714, -0.02577071078121662, -0.03712954744696617, 0.004940706770867109, 0.007135896012187004, -0.012049276381731033, 0.028337571769952774, -0.02625902183353901, 0.019673993811011314, 0.05165316164493561, -0.05373666062951088, 0.01382419653236866, -0.015794716775417328, -0.015327378176152706, -0.03138646483421326, -0.04909444972872734, 0.02795470878481865, 0.012390109710395336, 0.05391048267483711, 0.025089852511882782, 0.06731126457452774, 0.07009456306695938, -0.055632539093494415, 0.036591459065675735, -0.043089818209409714, 0.02635606750845909, 0.012312648817896843, 0.06107569485902786, 0.040338896214962006, 0.05445633456110954, 0.029409123584628105, 0.035201702266931534, 0.020813215523958206, -0.004848797339946032, 0.09771313518285751, 0.04228726774454117, 0.0038504411932080984, 0.02818198874592781, 0.03714592382311821, 0.02485433593392372, -0.01963069476187229, 0.053920578211545944, -0.03321986272931099, 0.03796970844268799, -0.05584614723920822, -0.018971674144268036, -0.013253791257739067, -0.014754747040569782, 0.04452047497034073, 0.03438054025173187, 0.022790098562836647, 0.016088882461190224, -0.019880417734384537, -0.016909077763557434, -0.044880855828523636, 0.00374293583445251, -0.034233443439006805, 0.024789929389953613, 0.05592799559235573, -0.011927802115678787, -0.0062820566818118095, 0.03496512398123741, -0.0032813246361911297, 0.05977366864681244, -0.021575039252638817, 0.018412571400403976, 2.571854906614467e-34, 0.011386900208890438, -0.008619840256869793, 0.017285946756601334, -0.026757309213280678, -0.02052251063287258, -0.02189689502120018, -0.017667556181550026, -0.015223467722535133, 0.039706118404865265, -0.015148905105888844, -0.01380221638828516]

['Roman Novak', 'Yasaman Bahri', 'Daniel A. Abolafia', 'Jeffrey Pennington', 'Jascha Sohl-Dickstein']

1802.08760v1

In practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor smaller models. In this work, we investigate this tension between complexity and generalization through an extensive empirical exploration of two natural metrics of complexity related to sensitivity to input perturbations. Our experiments survey thousands of models with various fully-connected architectures, optimizers, and other hyper-parameters, as well as four different image classification datasets. We find that trained neural networks are more robust to input perturbations in the vicinity of the training data manifold, as measured by the norm of the input-output Jacobian of the network, and that it correlates well with generalization. We further establish that factors associated with poor generalization $-$ such as full-batch training or using random labels $-$ correspond to lower robustness, while factors associated with good generalization $-$ such as data augmentation and ReLU non-linearities $-$ give rise to more robust functions. Finally, we demonstrate how the input-output Jacobian norm can be predictive of generalization at the level of individual test points.

Sensitivity and Generalization in Neural Networks: an Empirical Study

http://arxiv.org/pdf/1802.08760v1

Title Sensitivity Generalization Neural Networks Empirical Study Summary practice often found large overparameterized neural network generalize better smaller counterpart observation appears conflict classical notion function complexity typically favor smaller model work investigate tension complexity generalization extensive empirical exploration two natural metric complexity related sensitivity input perturbation experiment survey thousand model various fullyconnected architecture optimizers hyperparameters well four different image classification datasets find trained neural network robust input perturbation vicinity training data manifold measured norm inputoutput Jacobian network correlate well generalization establish factor associated poor generalization fullbatch training using random label correspond lower robustness factor associated good generalization data augmentation ReLU nonlinearities give rise robust function Finally demonstrate inputoutput Jacobian norm predictive generalization level individual test point Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.008312312886118889, 0.009196307510137558, -0.05233009159564972, 0.021689528599381447, 0.03583923727273941, -0.023269161581993103, 0.03057517297565937, -0.006933005526661873, -0.021818634122610092, 0.027232104912400246, -0.00268950336612761, 0.030916081741452217, 0.00390625512227416, 0.02507195994257927, 0.027891039848327637, -0.06729602068662643, -0.005113866180181503, 0.02149549126625061, -0.01703927293419838, -0.0402652807533741, -0.009031816385686398, -0.038637250661849976, 0.006761504802852869, 0.025429975241422653, -0.0673317015171051, 0.03326594829559326, 0.0174584798514843, 0.0027488507330417633, 0.021020080894231796, -0.0002990586799569428, 0.02135549671947956, 4.074988828506321e-05, 0.012434502132236958, 0.0111659811809659, 2.1815062609675806e-06, -0.049463484436273575, -0.010827475227415562, -0.00796664971858263, 0.04767148569226265, 0.028638679534196854, 0.02160860225558281, -0.04908540099859238, 0.01090024784207344, -0.00901594664901495, -0.006046079099178314, -0.015352156944572926, 0.037324920296669006, 0.04645949974656105, 0.01171950064599514, 0.05877715349197388, -0.008454977534711361, -0.02916276454925537, 0.03490723296999931, 0.012456260621547699, -0.032537322491407394, -0.04465005174279213, -0.015791133046150208, 0.0018590855179354548, -0.01684277504682541, 0.0008281240588985384, -0.03326116129755974, 0.038355108350515366, 0.057444170117378235, 0.011330695822834969, 0.05041433870792389, 0.020125580951571465, -0.03118998371064663, 0.013842952437698841, -0.004461108241230249, 0.03163670003414154, -0.07307511568069458, 0.021593818441033363, -0.02505086362361908, -0.0277636107057333, -0.004131957422941923, 0.01717277616262436, -0.03190835565328598, -0.028229709714651108, 0.029538093134760857, -0.015801506116986275, -0.08972100168466568, 0.034945301711559296, 0.01866542547941208, 0.012721378356218338, -0.0006439585122279823, 0.05034572258591652, 0.0013854402350261807, 0.04856250807642937, 0.003306278493255377, -0.030285628512501717, -0.05798840895295143, 0.0004748558276332915, 0.01421512570232153, 0.02070499025285244, -0.01676359958946705, -0.046656813472509384, -0.04166238009929657, -0.07883497327566147, 0.04104263335466385, -0.09966450184583664, 0.09914519637823105, -0.014824857003986835, 0.0024730321019887924, -0.014700345695018768, -0.03713043034076691, 0.08585227280855179, -0.06565138697624207, 0.08531937748193741, -2.921189434346161e-06, -0.008760936558246613, -0.011083475314080715, 0.01405075378715992, -0.007891443558037281, 0.0625821202993393, 0.022485598921775818, -0.008427273482084274, -0.06046189367771149, 0.02678253874182701, 0.006035987287759781, -0.024509986862540245, -0.03236091136932373, 0.05336861312389374, 0.018377743661403656, -0.05061611905694008, 0.004365690518170595, -0.0004684804589487612, -0.028189972043037415, 0.057055141776800156, -0.0236789770424366, 0.023722529411315918, 0.00786664430052042, 0.003672269405797124, 0.03485030680894852, 0.0045517305843532085, 0.03010820969939232, 0.08960632979869843, -0.002687047468498349, 0.02009640634059906, -0.07541677355766296, -0.026060884818434715, -0.005246439948678017, -0.01109234243631363, -0.012378237210214138, -0.027379708364605904, -0.029704278334975243, 0.007951668463647366, -0.012650943361222744, -0.024002747610211372, -0.024690384045243263, -0.03571049124002457, -0.05494857206940651, 0.03412160649895668, 0.02207326889038086, -0.02635614201426506, 0.10923592001199722, -0.018239296972751617, -0.04438557103276253, 0.03939340263605118, 0.011542226187884808, 0.036706700921058655, 0.035950638353824615, -0.03245211020112038, 0.018418271094560623, 0.02272915467619896, -0.01825859397649765, -0.016462447121739388, -0.03994068503379822, -0.031922340393066406, 0.01639981009066105, 0.015863874927163124, 0.04278373345732689, 0.017278438434004784, -0.006931622978299856, -0.049721088260412216, 0.04577898979187012, 0.029617182910442352, 0.027476288378238678, 0.03155103698372841, -0.021911820396780968, 0.004336467478424311, 0.0014429755974560976, 0.003354767570272088, -0.03250700235366821, 0.055587295442819595, -0.05507125332951546, -0.04180674999952316, -0.03112383373081684, -0.031232738867402077, -0.048262447118759155, -0.055660974234342575, -0.00566887529566884, -0.0005223075277172029, -0.016806630417704582, -0.02398567460477352, 0.05459248274564743, -0.006809233222156763, -0.005245639011263847, -0.028255706652998924, -0.007687212899327278, 0.003960920497775078, -0.02018395997583866, -0.013190384954214096, -0.008652333170175552, -0.07780992239713669, -0.03947536647319794, -0.027058463543653488, 0.012513957917690277, -0.00012763582344632596, 0.02423255331814289, -0.044886477291584015, 0.03490549698472023, 0.016887599602341652, 0.05607938766479492, -0.004845620598644018, 0.000727145466953516, 0.015073023736476898, 0.033995673060417175, 0.03844517096877098, -0.00801611877977848, -0.02554287202656269, 0.015784485265612602, -0.011841881088912487, -0.031391583383083344, 0.010796650312840939, -0.026682259514927864, -0.027504663914442062, 0.052584052085876465, 0.040448546409606934, 0.00594018679112196, 0.008291647769510746, 0.015420034527778625, -0.027229322120547295, 0.0001632929634070024, -0.04190251976251602, -0.02047928236424923, -0.038326412439346313, 0.0033208192326128483, 0.05353907495737076, 0.006628414150327444, 0.004147363360971212, 0.047474827617406845, 0.05965748801827431, -0.010044768452644348, -0.06216264143586159, 0.05333060771226883, 0.013231777586042881, -0.01988348923623562, 0.0003969190292991698, 0.0030314845498651266, -0.03577204421162605, 0.06901038438081741, 0.0057950858026742935, -0.03779398277401924, 0.022122468799352646, 0.02869829162955284, -0.0336855985224247, 0.018941743299365044, 0.04268977791070938, -0.007352709770202637, -0.06435617804527283, -0.0002924842410720885, -0.05425911396741867, 0.0024656523019075394, 0.010891054756939411, 0.00012821266136597842, 0.04620775580406189, 0.016189629212021828, 0.01886923424899578, -0.04410933703184128, -0.005330871790647507, -0.005315062589943409, -0.002834160113707185, 0.01340138167142868, 0.007157836575061083, -0.007421887945383787, 0.03313901647925377, 0.10332014411687851, -0.013563827611505985, -0.029229136183857918, 0.06770726293325424, 0.028348511084914207, -0.01738942787051201, -0.03647150099277496, -0.03351235017180443, 0.033769067376852036, 0.05780530348420143, 0.07035920768976212, -0.03018316812813282, -0.004475416149944067, -0.013662537559866905, 0.02431834489107132, 0.026245703920722008, 0.007370426785200834, -0.09771152585744858, -0.0445854552090168, -0.026342783123254776, -0.034546732902526855, 0.109681136906147, -0.02093072235584259, -0.08253668248653412, 0.0017762627685442567, 0.1047467514872551, -0.014068973250687122, 0.018977323547005653, -0.042033083736896515, -0.05614380165934563, 0.02473945915699005, -0.026480019092559814, 0.004145376849919558, 0.01839081384241581, 0.0007919140625745058, -0.04184655100107193, -0.008767712861299515, 0.02217339538037777, 0.016637319698929787, 0.01284410897642374, -0.03892212361097336, 0.02902280166745186, 0.014873463660478592, 0.011982531286776066, 0.002808104967698455, -0.04293796047568321, -0.02888384461402893, 0.023956455290317535, 0.035359226167201996, 0.04201309755444527, -0.04689621552824974, 0.01892729476094246, 0.02582547254860401, 0.03759900480508804, 0.020319901406764984, -0.007545000407844782, -0.028949396684765816, -0.026920391246676445, 0.004291612189263105, 0.02013678289949894, 0.01491356361657381, -0.011499259620904922, -0.023068828508257866, -0.03874410688877106, -0.030091840773820877, 0.004153335466980934, -0.014180472120642662, 0.008319033309817314, 0.028678128495812416, 0.025258993729948997, -0.02287549152970314, -0.041972577571868896, 0.027564721181988716, -0.010286998003721237, -0.023528805002570152, 0.06213180348277092, -0.04450758546590805, -0.022807655856013298, 0.014574814587831497, 0.015056053176522255, -0.00797973945736885, -0.004968228284269571, 0.004485627170652151, 0.03394271805882454, 0.02603868953883648, 0.003340490162372589, -0.04979180917143822, 0.023477351292967796, -0.08148262649774551, -0.005919144954532385, -0.026815030723810196, 0.008393430151045322, -0.021008212119340897, 0.027494078502058983, 0.03376547247171402, -0.022472243756055832, 0.02978195808827877, -0.008290110155940056, -0.020611481741070747, -0.05199657380580902, -0.005975532345473766, 0.0030358212534338236, 0.01479276455938816, 0.023921750485897064, 0.007982281036674976, 0.06815735250711441, 0.02473166584968567, -0.011179829947650433, -0.0043819681741297245, -0.02634696289896965, -0.05271364003419876, 0.022587547078728676, -0.03155587986111641, -0.00880133081227541, 0.004539984744042158, -0.0605318658053875, -0.04407277703285217, -4.6187746193027124e-05, 0.03055569902062416, -0.03358292207121849, 0.033178918063640594, -0.02745993435382843, 0.03847033530473709, -0.0342833511531353, 0.041017211973667145, -0.022232113406062126, -0.02801891788840294, -0.025023523718118668, -0.07931811362504959, -0.03974252566695213, -0.014843105338513851, -0.013471822254359722, -0.0694705992937088, 0.008920017629861832, 0.058145277202129364, 0.05204164981842041, 0.04608149081468582, -0.003748713294044137, 0.071516253054142, 0.07481465488672256, 0.007420460693538189, 0.03537286818027496, 0.06120796501636505, 0.004047565162181854, 0.06959868967533112, 0.005753944627940655, 0.03190387412905693, 0.018172385171055794, 0.04155208170413971, -0.06575997918844223, -0.025218600407242775, -0.027211902663111687, -0.04691609367728233, 0.014106173068284988, -0.04044530913233757, -0.038487304002046585, -0.014972737990319729, 0.027136053889989853, -0.030670084059238434, 0.017110517248511314, -0.001768434070982039, 0.005230896174907684, -0.06455458700656891, -0.049024831503629684, 0.07254098355770111, -0.06355323642492294, 0.05295403301715851, 0.010645147413015366, -0.05247548595070839, -0.007405539508908987, 0.020675312727689743, -0.008005439303815365, 0.014402580447494984, 0.08879128843545914, 0.012694899924099445, -0.02217983454465866, 0.07684363424777985, 0.016604015603661537, -0.03450248762965202, -0.02223237417638302, -0.03598346188664436, -0.026945656165480614, -0.03874816372990608, -0.009005238302052021, 0.06520729511976242, 0.008881162852048874, 0.006227284669876099, -0.04339734464883804, -0.08851812779903412, 0.022714925929903984, 0.016250312328338623, -0.0229465514421463, 0.03041355311870575, 0.10511978715658188, -0.0037905173376202583, -0.03682481870055199, 0.01003866083920002, -0.014862249605357647, 0.05661921575665474, 0.04220796003937721, -0.0714179128408432, 0.003999175503849983, -0.006602274253964424, -0.030190063640475273, -0.0011946404119953513, 0.06678751111030579, 0.046724025160074234, -0.012677720747888088, -0.021549846976995468, 0.031089698895812035, 0.024472415447235107, 0.029002642259001732, -0.03558673337101936, 0.011565635912120342, 0.07343937456607819, 0.03776116669178009, -0.03646828234195709, -0.05606226995587349, 0.07260855287313461, 0.01596074178814888, -0.03154226765036583, 0.013562933541834354, -0.01014848705381155, 0.037518784403800964, -0.01802143268287182, 0.04471791163086891, -0.04483567923307419, -0.03062986209988594, 0.016916310414671898, -0.018642157316207886, 0.004286478739231825, 0.000834656588267535, -0.019269943237304688, 0.03446710854768753, -0.0812755823135376, -0.017416564747691154, -0.053116630762815475, -0.008631632663309574, -0.05002255737781525, 0.021481042727828026, 0.04050108417868614, -0.0058959671296179295, -0.0318792499601841, 0.011413219384849072, -0.030729563906788826, -0.036698803305625916, 0.013557787984609604, 0.010873028077185154, 0.03262683004140854, 0.04219060018658638, -0.03168387711048126, 0.03321077674627304, 0.024282556027173996, 0.03263825550675392, 0.010187827982008457, -0.027234453707933426, -0.010797402821481228, 0.014908402226865292, -0.010327765718102455, 0.04437234625220299, 0.05019211769104004, 0.04191000387072563, 0.009547071531414986, 0.03626193851232529, 0.026630323380231857, -0.01358520332723856, 0.027161497622728348, -0.03641638904809952, 0.023847663775086403, -0.0032970760948956013, -0.011903868988156319, -0.007938954047858715, -0.01547521073371172, -0.021778317168354988, 0.0011722370982170105, -0.035315338522195816, -0.007940041832625866, 0.034396808594465256, -0.03638722375035286, -5.4215779433221066e-33, 0.022349616512656212, 0.020749637857079506, -0.07074807584285736, -0.015879176557064056, -0.0053916932083666325, 0.007438143249601126, 0.01562666893005371, -0.001562547287903726, -0.039791639894247055, -0.0038819836918264627, -0.01811354048550129, 0.00621966365724802, -0.020327270030975342, 0.027255956083536148, 0.013427170924842358, 0.0007937413756735623, -0.010611297562718391, -0.01263649296015501, 0.034932732582092285, -0.007899230346083641, 0.025748230516910553, 0.019753163680434227, 0.0395628847181797, -0.09995702654123306, -0.03373633325099945, 0.019005022943019867, -0.039067789912223816, -0.03867550194263458, -0.00501213688403368, 0.005372495390474796, 0.008357072249054909, 0.07330480217933655, -0.024394167587161064, -0.0317239984869957, -0.003934886772185564, 0.012790295295417309, -0.03204379975795746, -0.05985299497842789, -0.060404740273952484, 0.014998129568994045, 0.014136374928057194, -0.009652545675635338, 0.08553621172904968, -0.02985905297100544, -0.0404123030602932, -0.06608706712722778, 0.05754509195685387, -0.024859629571437836, -0.03231764957308769, -0.033970557153224945, 0.011053066700696945, 0.01844738982617855, -0.02528468146920204, 0.036600347608327866, -0.009582865051925182, 0.062123123556375504, -0.019797857850790024, 0.00820282381027937, -0.01991845853626728, -0.0050047170370817184, 0.04172060638666153, 0.007029888220131397, -0.03555169701576233, 0.033840011805295944, 0.0349627360701561, 0.021008461713790894, 0.045364413410425186, -0.007314592134207487, -0.012029810808598995, -0.004542665556073189, -0.015920490026474, 0.0177932046353817, 0.07563473284244537, 0.06888394057750702, 0.06802234798669815, -0.07897250354290009, -0.06884472817182541, 0.008715029805898666, -0.07080661505460739, -0.00808695051819086, -0.013029518537223339, -0.011537803336977959, -0.04093119874596596, -0.014753592200577259, 0.01473829336464405, -0.05166251212358475, -0.01719365082681179, -0.0274801068007946, 0.025422004982829094, -0.019946249201893806, 0.03506864234805107, -0.038668982684612274, -0.05665978416800499, -0.0262907724827528, 0.05715886503458023, -0.014303398318588734, 0.0001506418047938496, 0.054004691541194916, 0.05040176957845688, 0.00063322763890028, 0.018249832093715668, 0.0009598348988220096, -0.02752518840134144, -0.0033148066140711308, 0.0337182991206646, -0.009130008518695831, 0.029682254418730736, 0.045394472777843475, -0.010055238381028175, -0.04572098329663277, 0.014399401843547821, -0.01896180585026741, 0.04308781027793884, 0.08576545864343643, 0.006127530243247747, -0.064395010471344, 0.01474116463214159, 0.09756796061992645, -0.025129634886980057, 0.05535304918885231, -0.014126334339380264, -0.025203051045536995, -0.018650339916348457, 0.024485427886247635, -0.024693533778190613, -0.021582473069429398, 0.010146187618374825, -0.02915392629802227, 0.009929177351295948, -0.0769987627863884, -0.018001770600676537, 0.012229954823851585, 2.72632973974396e-07, -0.012404189445078373, 3.538008968462236e-05, -0.022831840440630913, -0.05890721455216408, 0.009967903606593609, -0.008964171633124352, -0.00716406898573041, 0.04451367259025574, -0.04699016362428665, 0.009583299979567528, 0.01342748012393713, -0.07142383605241776, 0.0016498974291607738, -0.0041936482302844524, -0.03357165306806564, -0.04749482125043869, -0.014324150048196316, 0.09358327090740204, -0.009993912652134895, 0.0511874295771122, 0.050294917076826096, 0.04955935850739479, 0.025583472102880478, -0.011640301905572414, 0.02581094019114971, -0.028914624825119972, -0.012508457526564598, -0.05926881358027458, 0.08343605697154999, 0.002563471905887127, 0.03566771373152733, -0.0030054841190576553, 0.033670902252197266, 0.02428969368338585, -0.00797793734818697, 0.06498889625072479, -0.0033130801748484373, 0.018962793052196503, -0.01947365142405033, -0.02474919520318508, 0.0351155549287796, 0.004420462064445019, 0.0505402572453022, -0.09007526189088821, 0.04538480192422867, -0.06610981374979019, -0.03691485896706581, 0.015121624805033207, 0.007117828819900751, 0.02476470172405243, 0.08825653791427612, -0.02489629201591015, 0.03196852654218674, -0.04437611624598503, 0.031060652807354927, -0.0384172685444355, 0.010912447236478329, -0.05167487636208534, 0.025752728804945946, 0.06377463042736053, -0.03691818565130234, 0.002486740704625845, -0.0033284195233136415, -0.0007859023753553629, 0.08436017483472824, 0.03040749952197075, -0.0140371797606349, 2.304497670480813e-34, -0.015042744576931, -0.030170220881700516, 0.020620444789528847, -0.03861936181783676, -0.020434454083442688, -0.009097229689359665, -0.038781289011240005, -0.012843816541135311, 0.045068737119436264, -0.02977321855723858, -0.011865894310176373]

['Ari S. Morcos', 'David G. T. Barrett', 'Neil C. Rabinowitz', 'Matthew Botvinick']

1803.06959v1

Despite their ability to memorize large datasets, deep neural networks often achieve good generalization performance. However, the differences between the learned solutions of networks which generalize and those which do not remain unclear. Additionally, the tuning properties of single directions (defined as the activation of a single unit or some linear combination of units in response to some input) have been highlighted, but their importance has not been evaluated. Here, we connect these lines of inquiry to demonstrate that a network's reliance on single directions is a good predictor of its generalization performance, across networks trained on datasets with different fractions of corrupted labels, across ensembles of networks trained on datasets with unmodified labels, across different hyperparameters, and over the course of training. While dropout only regularizes this quantity up to a point, batch normalization implicitly discourages single direction reliance, in part by decreasing the class selectivity of individual units. Finally, we find that class selectivity is a poor predictor of task importance, suggesting not only that networks which generalize well minimize their dependence on individual units by reducing their selectivity, but also that individually selective units may not be necessary for strong network performance.

On the importance of single directions for generalization

http://arxiv.org/pdf/1803.06959v1

Title importance single direction generalization Summary Despite ability memorize large datasets deep neural network often achieve good generalization performance However difference learned solution network generalize remain unclear Additionally tuning property single direction defined activation single unit linear combination unit response input highlighted importance evaluated connect line inquiry demonstrate network reliance single direction good predictor generalization performance across network trained datasets different fraction corrupted label across ensemble network trained datasets unmodified label across different hyperparameters course training dropout regularizes quantity point batch normalization implicitly discourages single direction reliance part decreasing class selectivity individual unit Finally find class selectivity poor predictor task importance suggesting network generalize well minimize dependence individual unit reducing selectivity also individually selective unit may necessary strong network performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.025508176535367966, 0.058791566640138626, -0.02577769011259079, 0.013703260570764542, 0.011755692772567272, 0.011057221330702305, 0.06269649416208267, -0.022969113662838936, -0.06650397926568985, 0.03535652160644531, -0.004868027754127979, -0.016830842941999435, -0.001781700411811471, 0.06200243905186653, 0.012779345735907555, -0.04720601812005043, -0.003730174619704485, 0.04232672229409218, -0.0044092945754528046, -0.04109179973602295, 0.008065599948167801, -0.0397895984351635, -0.0064690131694078445, 0.04128613322973251, -0.05019534379243851, 0.0009635612950660288, 0.023379642516374588, -0.017019281163811684, 0.004353964701294899, -0.02536030299961567, 0.053563397377729416, 0.042124733328819275, 0.049160491675138474, -0.017210375517606735, 2.551262468841742e-06, -0.03828692436218262, -0.034142669290304184, -0.05249473452568054, -0.002386678010225296, -0.01308705285191536, -0.0468052476644516, 0.004195760004222393, 0.01608908548951149, -0.02842186950147152, -0.01793958991765976, -0.012666783295571804, 0.053648851811885834, 0.09299090504646301, -0.013722315430641174, 0.011557736434042454, -0.006027350202202797, -0.0809810683131218, 0.008332028985023499, -0.026609133929014206, 0.02350781485438347, -0.0016533674206584692, 0.0018301807576790452, 0.019064687192440033, -0.053167857229709625, -0.009083055891096592, -0.04278372973203659, 0.02959391102194786, 0.07613524794578552, 0.026699591428041458, 0.06593749672174454, 0.06622569262981415, -0.004479424562305212, -0.027274737134575844, 0.0069808922708034515, 0.08266531676054001, -0.01692817360162735, 0.019814634695649147, -0.004356253892183304, -0.025411896407604218, -0.0005632017855532467, -0.019185855984687805, -0.020198749378323555, 0.003773349104449153, 0.0005230914102867246, 0.02615208551287651, -0.064874067902565, 0.026641009375452995, 0.025855597108602524, 0.01976107992231846, -0.03358481824398041, 0.030049612745642662, -0.004768903832882643, 0.0014802363002672791, 0.04360492154955864, -0.00997522845864296, -0.013144344091415405, 0.011876929551362991, 0.03284188359975815, -0.003911981359124184, -0.034920305013656616, -0.023440927267074585, 0.020957397297024727, -0.05780889466404915, 0.03502747043967247, -0.037769876420497894, 0.06202375888824463, 0.0037697884254157543, -0.05276388302445412, -0.024064023047685623, -0.007068421225994825, 0.08241274207830429, -0.014794030226767063, 0.05074424669146538, -0.0017638327553868294, 0.033378966152668, -0.04740357771515846, -0.013053272850811481, -0.017207907512784004, 0.07728492468595505, 0.03793025761842728, -0.0031528088729828596, -0.06166635453701019, -0.033169571310281754, -0.014934840612113476, -0.0011468215379863977, 0.019154934212565422, 0.08801954239606857, -0.0037135642487555742, 0.009642256423830986, 0.002942341146990657, 0.03516393154859543, -0.06425459682941437, 0.04446801170706749, -0.001677530468441546, -0.013767754659056664, 0.010005120187997818, -0.011133071966469288, 0.007080020383000374, 0.007576650474220514, 0.046664755791425705, 0.05006562918424606, -0.02386399358510971, 0.015218891203403473, -0.08430423587560654, -0.010760071687400341, -0.009494096972048283, -0.026400327682495117, 0.007959678769111633, -0.05809731408953667, -0.008511878550052643, 0.013192052952945232, -0.0031324317678809166, -0.018440568819642067, -0.00836887490004301, -0.037691228091716766, -0.0030222320929169655, 0.03137227147817612, 0.01401545014232397, -0.03299302980303764, 0.10731242597103119, 0.016337169334292412, 0.029989348724484444, 0.035653986036777496, 0.022212326526641846, 0.032549794763326645, -0.0016252739587798715, -0.030398445203900337, 0.021338392049074173, -0.007096405606716871, -0.01052415743470192, -0.047474347054958344, -0.06921470165252686, -0.05196842551231384, -0.006651466712355614, 0.006307047791779041, 0.0409778356552124, 9.380838309880346e-05, -0.02935091219842434, -0.049538325518369675, 0.03741828352212906, 0.020509440451860428, 0.0734507143497467, 0.035221848636865616, 0.0037468960508704185, -0.003684467636048794, -0.0226746853441, 0.003964549396187067, -0.008172032423317432, 0.05926114320755005, 0.04527495428919792, -0.03885474056005478, -0.0207388736307621, -0.009098343551158905, -0.057457104325294495, -0.08118357509374619, 0.03197315335273743, -0.03149677440524101, -0.045158546417951584, -0.02514098770916462, 0.07559112459421158, 0.005432441830635071, -0.01734050363302231, -0.007800470571964979, 0.03646938502788544, 0.02261548675596714, -0.020381253212690353, -0.006471632979810238, 0.01240535732358694, -0.022321611642837524, -0.029378997161984444, -0.025066452100872993, -0.03657624125480652, -0.010186679661273956, -0.030374493449926376, -0.013323062099516392, 0.014988288283348083, 0.0016110497526824474, 0.07993192225694656, -0.06356306374073029, -0.003148979041725397, -0.0014233527472242713, 0.016120364889502525, 0.05253284424543381, -0.03778272494673729, -0.006404473911970854, 0.009769096039235592, 0.00504161836579442, -0.0005601041484624147, 0.019703544676303864, 0.002197584602981806, -0.05702168121933937, 0.05321640148758888, 0.043427515774965286, 0.02055615372955799, 0.010910296812653542, 0.0093691386282444, -0.02669505774974823, 0.006539559923112392, -0.027378829196095467, -0.07349347323179245, -0.025278659537434578, -0.10064487904310226, 0.019083209335803986, -0.010030885227024555, -0.014685530215501785, -0.006308501586318016, 0.04174427315592766, -0.02068818360567093, -0.05079594627022743, 0.03729250654578209, 0.01883097179234028, -0.03441902995109558, -0.008496621623635292, -0.03246878832578659, 0.010968982242047787, 0.0512191504240036, 0.00392920384183526, 0.022677535191178322, -0.0012075634440407157, 0.02513972483575344, -0.044255632907152176, 0.004093398340046406, 0.04572355002164841, -0.027196122333407402, -0.012580128386616707, 0.004838882479816675, -0.0636131688952446, 0.009991545230150223, -0.004727902356535196, 0.0140116261318326, -0.030274903401732445, 0.05502471700310707, -0.0025321217253804207, 0.017125051468610764, -0.031186716631054878, -0.031985074281692505, -0.034893397241830826, -0.011058870702981949, 0.017591383308172226, -0.04182371869683266, -0.03802885860204697, 0.03597681596875191, -0.022759974002838135, -0.026424024254083633, 0.053099390119314194, 0.010088440030813217, 0.0158198531717062, -0.023762445896863937, -0.02785058319568634, 0.013197443448007107, 0.02224630117416382, 0.02687140554189682, 0.015683632344007492, 0.008134319446980953, 0.012928835116326809, -0.009096367284655571, 0.024420758709311485, -0.004512777552008629, -0.07071469724178314, -0.003330647712573409, -0.03760549798607826, 0.007334154099225998, 0.07459817081689835, 0.0017840873915702105, -0.012757334858179092, 0.0032093802001327276, 0.057688381522893906, -0.04236839339137077, -0.0004120004887226969, -0.027967065572738647, 0.019796548411250114, 0.0367840901017189, 0.020267246291041374, -0.05303258076310158, 0.06328034400939941, 0.056131962686777115, 0.01139030046761036, 0.030694959685206413, -0.005931403953582048, -0.004050290212035179, -0.043929945677518845, -0.07667102664709091, 0.0015313823241740465, 0.02063106745481491, -0.02953364886343479, 0.011134539730846882, -0.013013881631195545, 0.04499088227748871, 0.038368672132492065, -0.024732276797294617, 0.010751942172646523, -0.03692226856946945, 0.012823803350329399, 0.020656989887356758, -0.0029739905148744583, -0.012765486724674702, -0.009468941949307919, -0.040563397109508514, -0.004683719482272863, -0.025546686723828316, -0.012182636186480522, -0.004824681207537651, 0.05145047605037689, -0.037281036376953125, -0.04381085932254791, -0.03424020856618881, -0.04090696945786476, -0.05219946801662445, 0.04191366583108902, 0.019243240356445312, 0.027816042304039, 0.004009328782558441, 0.007929059676826, -0.019597357138991356, -0.03772430121898651, 0.018779341131448746, 0.04917098581790924, -0.05080658569931984, -0.010018081404268742, 0.015246453694999218, 0.054221898317337036, -0.018509354442358017, 0.033251628279685974, -0.026151880621910095, -0.005115616135299206, 0.026537038385868073, 0.03066125512123108, 0.015108216553926468, 0.004676252603530884, -0.11842075735330582, 0.03850992023944855, -0.01902935467660427, -0.014404292218387127, -0.008684070780873299, -0.012637395411729813, 0.024501679465174675, -0.08357380330562592, 0.021316001191735268, 0.025462748482823372, -0.008368710055947304, -0.07334323972463608, -0.00887488666921854, 0.0009608222753740847, 0.011701309122145176, 0.00018797705706674606, -0.017048118636012077, 0.0038386816158890724, -0.016572607681155205, -0.03876486048102379, -0.015389344654977322, 0.007010413333773613, -0.034407321363687515, 0.0324341244995594, -0.045721281319856644, 0.0010879139881581068, -0.00874276366084814, -0.0656253844499588, -0.03197861090302467, -0.034694451838731766, -0.02763066627085209, -0.05844859033823013, 0.04668877646327019, -0.016129614785313606, 0.03865659981966019, -0.025214461609721184, 0.06904798746109009, -0.030879585072398186, 0.023722782731056213, 0.013239111751317978, -0.06521888077259064, 0.005965429358184338, 0.029733678326010704, 0.005244721192866564, -0.07058737426996231, -0.014446302317082882, 0.045396771281957626, 0.007040142547339201, 0.043630506843328476, -0.00572966318577528, 0.11134487390518188, 0.04990273341536522, 0.008363507688045502, 0.015509194694459438, 0.03562609478831291, -0.04190618172287941, 0.019561385735869408, 0.0007722991867922246, 0.031998492777347565, -0.027118073776364326, 0.00020053739717695862, -0.051497939974069595, -0.015082038007676601, 0.007733447477221489, -0.034245967864990234, -0.0011192616075277328, -0.057301342487335205, -0.06473136693239212, -0.024081043899059296, 0.05380912870168686, -0.09243425726890564, -0.0060185594484210014, 0.017475774511694908, 0.030863825231790543, -0.07736918330192566, -0.037674084305763245, -0.010930085554718971, -0.016663437709212303, 0.03461455553770065, 0.004498436115682125, -0.029354963451623917, -0.009050436317920685, 0.0069071040488779545, -0.019165419042110443, 0.014770038425922394, 0.039497002959251404, 0.00914788618683815, -0.033921122550964355, 0.001340455375611782, 0.04366440698504448, -0.03618679940700531, -0.014826907776296139, -0.03770916908979416, -0.011344377882778645, 0.004156938754022121, -0.0008669407689012587, 0.017957214266061783, 0.00982139352709055, -0.013180323876440525, -0.011759762652218342, -0.05411309003829956, 0.04459649324417114, 0.01874653622508049, 0.0014521685661748052, 0.0033798329532146454, 0.0733819231390953, -0.026982061564922333, -0.003588809398934245, -0.003028266131877899, -0.008268971927464008, 0.118013396859169, 0.04554577171802521, -0.04333352670073509, -0.013372134417295456, 0.039455629885196686, 0.0034411572851240635, -0.01676854118704796, 0.0973159447312355, 0.04704767093062401, 0.04525816813111305, -0.04903127998113632, 0.03727255389094353, 0.05010044947266579, 0.02096545137465, -0.024312647059559822, 0.0064144073985517025, 0.03674374520778656, 0.03331609070301056, -0.0259367898106575, -0.019052457064390182, 0.07701219618320465, -0.0035595998633652925, -0.02604847215116024, 0.008208204992115498, 0.02021550014615059, 0.030691789463162422, -0.005314808804541826, 0.03161392733454704, -0.04984918236732483, 0.04882313683629036, 0.053369466215372086, 0.0035952208563685417, 0.015252695418894291, 0.028777791187167168, 0.018166931346058846, 0.03648445010185242, -0.049868810921907425, -0.01311988104134798, -0.014628024771809578, -0.04479615390300751, -0.03808251768350601, -0.011564046144485474, 0.0542798712849617, -0.05881735309958458, -0.022202810272574425, 0.018750319257378578, 0.02492169849574566, -0.033791638910770416, 0.01797144114971161, -0.029302112758159637, 0.026127994060516357, 0.030179573222994804, -0.018751895055174828, 0.015456423163414001, 0.02887442149221897, 0.06809715926647186, -0.0004581832909025252, -0.0004317107959650457, -0.05137013643980026, 0.030097443610429764, -0.039541635662317276, 0.04158339276909828, 0.040417078882455826, 0.0076997666619718075, -0.013217424042522907, 0.019272729754447937, 0.018925052136182785, -0.034534551203250885, 0.016760779544711113, 0.015497418120503426, 0.06960443407297134, 0.010910131968557835, 0.03990104794502258, 0.05566500499844551, -0.016603603959083557, -0.022882021963596344, -0.013184319250285625, -0.007245014421641827, 0.007612374611198902, 0.014971963129937649, -0.017329294234514236, -6.942979506631099e-33, 0.005539881531149149, -0.016495386138558388, -0.02252270095050335, -0.019200533628463745, -0.004113051109015942, -0.0005807732813991606, -0.016491511836647987, 0.02334626019001007, -0.03664940595626831, 0.03006119653582573, -0.04328589513897896, 0.008511858992278576, 0.00678717577829957, 0.037751875817775726, 0.09345053881406784, -0.0019515840103849769, 0.029283719137310982, 0.008222063072025776, 0.028790801763534546, 0.011880355887115002, 0.05795213580131531, 0.04285755380988121, 0.08329806476831436, -0.08226540684700012, -0.04074186086654663, 0.005236245226114988, -0.034054748713970184, -0.036155443638563156, -0.06280727684497833, -0.009940514340996742, -0.011671287007629871, 0.041894927620887756, 0.0292681697756052, -0.08112030476331711, -0.045593734830617905, -0.005694493185728788, -0.05989668518304825, -0.08633971214294434, -0.07276255637407303, 0.009530490264296532, -0.03583470359444618, -0.009181810542941093, 0.11723912507295609, -0.004959508776664734, -0.02301068790256977, -0.01858069747686386, 0.06814184039831161, -0.014922254718840122, -0.021182678639888763, -0.03770162910223007, -0.02503350004553795, 0.02440406009554863, -0.02021818980574608, 0.017120180651545525, -0.021663321182131767, 0.0016178799560293555, -0.04602671414613724, 0.026767009869217873, -0.0892905592918396, 0.025769786909222603, 0.018353596329689026, 0.03181951865553856, -0.0033636533189564943, 0.03272431343793869, 0.013683028519153595, 0.05751965939998627, 0.0752420499920845, -0.03771884739398956, -0.008928132243454456, -0.06207685172557831, 0.005844389088451862, 0.04314896836876869, 0.0478755421936512, 0.005333445500582457, 0.10843554139137268, -0.07941833138465881, -0.07240709662437439, 0.020582664757966995, -0.028273766860365868, -0.010252546519041061, -0.009479681961238384, 0.029770443215966225, -0.0009794837096706033, -0.008385085500776768, 0.010597563348710537, -0.044378988444805145, -0.02636856958270073, -0.028575606644153595, 0.008217807859182358, -0.0025679918471723795, 0.032457973808050156, 0.029928866773843765, -0.01126671489328146, -0.04474687576293945, 0.038131918758153915, -0.016263648867607117, 0.004870649427175522, 0.044112835079431534, 0.05905593931674957, -0.04641362652182579, -0.07440581917762756, -0.020431138575077057, -0.020068492740392685, 0.0064348080195486546, 0.0317901186645031, 0.05323972553014755, 0.06398400664329529, 0.02449933812022209, -0.016783762723207474, -0.04627364128828049, 0.0112216267734766, -0.06716486066579819, 0.053836092352867126, 0.06604734063148499, 0.011114569380879402, -0.04071464389562607, -0.02143547125160694, 0.07997453957796097, 0.0034682988189160824, 0.006356795784085989, -0.06221884861588478, -0.004508383106440306, 0.0010683333966881037, 0.04332488030195236, -0.044358763843774796, -0.04132770374417305, -0.04375879839062691, -0.031023986637592316, 0.03966662660241127, -0.05885752663016319, -0.009015388786792755, 0.0006567495292983949, 3.110151851615228e-07, -0.012565542943775654, -0.0019619856029748917, -0.016189301386475563, -0.06848230957984924, 0.013235585764050484, 0.04818817600607872, -0.053712572902441025, 0.009550248272716999, -0.021125299856066704, -0.027786951512098312, 0.05818849802017212, 0.016896022483706474, 0.005982585716992617, 0.019230905920267105, -0.03271090239286423, -0.0010464779334142804, -0.012307570315897465, 0.028082216158509254, -0.017193997278809547, 0.026821190491318703, 0.0011730000842362642, 0.07779599726200104, 0.03375536948442459, -0.03978053852915764, 0.046876464039087296, 0.030208822339773178, 0.001128586707636714, 0.0031082332134246826, 0.050427310168743134, 0.00601259944960475, 0.01724192127585411, 0.014678028412163258, -0.02779664471745491, 0.017244065180420876, -0.0367017462849617, 0.029956378042697906, 0.0032734456472098827, 0.035794902592897415, -0.014984476380050182, -0.027887500822544098, 0.03033803030848503, 0.02525172010064125, 0.05332795903086662, -0.031240010634064674, 0.04369702562689781, -0.045791272073984146, -0.03499152511358261, 0.007058971561491489, 0.011702509596943855, 0.050131697207689285, 0.05958271026611328, 0.018536558374762535, 0.013646692037582397, -0.02205645479261875, -0.017147565260529518, -0.021330317482352257, -0.03334459289908409, -0.04608284682035446, 0.02489837072789669, 0.04669931158423424, -0.04705528914928436, -0.0173153355717659, -0.00519170518964529, -0.0408502034842968, 0.06273210793733597, 0.029247233644127846, -0.03237765282392502, 2.6283029718604187e-34, -0.01271750032901764, 0.000761744799092412, 0.010683167725801468, 0.007821952924132347, -0.023454170674085617, -0.04104170575737953, -0.029030529782176018, 0.0007851950940676033, -0.012885714881122112, 0.0030283783562481403, -0.03433233126997948]

['Srinivas C. Turaga', 'Kevin L. Briggman', 'Moritz Helmstaedter', 'Winfried Denk', 'H. Sebastian Seung']

0911.5372v1

Images can be segmented by first using a classifier to predict an affinity graph that reflects the degree to which image pixels must be grouped together and then partitioning the graph to yield a segmentation. Machine learning has been applied to the affinity classifier to produce affinity graphs that are good in the sense of minimizing edge misclassification rates. However, this error measure is only indirectly related to the quality of segmentations produced by ultimately partitioning the affinity graph. We present the first machine learning algorithm for training a classifier to produce affinity graphs that are good in the sense of producing segmentations that directly minimize the Rand index, a well known segmentation performance measure. The Rand index measures segmentation performance by quantifying the classification of the connectivity of image pixel pairs after segmentation. By using the simple graph partitioning algorithm of finding the connected components of the thresholded affinity graph, we are able to train an affinity classifier to directly minimize the Rand index of segmentations resulting from the graph partitioning. Our learning algorithm corresponds to the learning of maximin affinities between image pixel pairs, which are predictive of the pixel-pair connectivity.

Maximin affinity learning of image segmentation

http://arxiv.org/pdf/0911.5372v1

Title Maximin affinity learning image segmentation Summary Images segmented first using classifier predict affinity graph reflects degree image pixel must grouped together partitioning graph yield segmentation Machine learning applied affinity classifier produce affinity graph good sense minimizing edge misclassification rate However error measure indirectly related quality segmentation produced ultimately partitioning affinity graph present first machine learning algorithm training classifier produce affinity graph good sense producing segmentation directly minimize Rand index well known segmentation performance measure Rand index measure segmentation performance quantifying classification connectivity image pixel pair segmentation using simple graph partitioning algorithm finding connected component thresholded affinity graph able train affinity classifier directly minimize Rand index segmentation resulting graph partitioning learning algorithm corresponds learning maximin affinity image pixel pair predictive pixelpair connectivity Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.026119409129023552, -0.0805911123752594, -0.007136921398341656, 0.028323953971266747, -0.02615479752421379, -0.021099906414747238, 0.008177189156413078, 0.014270447194576263, 0.04525921121239662, 0.029587985947728157, 0.014500692486763, 0.0403924323618412, 0.018854228779673576, -0.03336678072810173, 0.014648486860096455, -0.10915450006723404, -0.007662664633244276, 0.025502396747469902, -0.03349555283784866, -0.02192748337984085, 0.04543359950184822, 0.004421973135322332, 0.033355820924043655, -0.01434229128062725, -0.07914731651544571, 0.02385137230157852, 0.015610438771545887, 0.022297395393252373, 0.010387890040874481, -0.03257741034030914, -0.006674788426607847, -0.02432010881602764, -0.01434363704174757, -0.006817607209086418, 2.2574142803932773e-06, -0.053813546895980835, -0.043892502784729004, -0.016880834475159645, 0.06506837904453278, -0.022312114015221596, 0.06313295662403107, -0.02911183051764965, 0.013688490726053715, -0.054405681788921356, -0.011624176055192947, 0.03625549003481865, 0.028526699170470238, 0.045847248286008835, 0.04656544700264931, 0.033001601696014404, -0.027551066130399704, -0.05193858966231346, 0.03119765780866146, -0.0007066321559250355, 0.03016113117337227, -0.01879982091486454, 0.011185816489160061, 0.04673925042152405, 0.011442368850111961, -0.07092328369617462, -0.03523062914609909, 0.020494837313890457, 0.03191559389233589, 0.030444765463471413, 0.08310853689908981, 0.04201708734035492, -0.01188917737454176, -0.052923765033483505, -0.027083076536655426, 0.032820407301187515, -0.08077114075422287, 0.045021090656518936, 0.01542800571769476, -0.009885653853416443, -0.027145415544509888, 0.004923670552670956, 0.013906900770962238, 0.00855862908065319, -0.02015465870499611, 0.03375408053398132, -0.022449485957622528, 0.03848729282617569, -0.011184846051037312, -0.017494693398475647, -0.04138689115643501, 0.053874023258686066, -0.0028205919079482555, 0.029875757172703743, 0.019270284101366997, 0.011440214700996876, -0.042163871228694916, 0.0032798524480313063, -0.0028757748659700155, -0.006692429073154926, -8.953418000601232e-05, -0.019407430663704872, 0.0059126815758645535, -0.040796082466840744, 0.014727264642715454, 0.04032376408576965, -0.006976133678108454, -0.07068648934364319, 0.00271437456831336, 0.029541220515966415, -0.021755600348114967, -0.04160526767373085, -0.02193761244416237, 0.11546257138252258, -0.04463209956884384, 0.017244651913642883, -0.03007969632744789, 0.036685191094875336, -0.03104768507182598, 0.03794579952955246, 0.041699521243572235, -0.0038096036296337843, -0.03344547748565674, 0.018949270248413086, -0.029264478012919426, -0.03588759899139404, 0.017339762300252914, 0.038836654275655746, -0.009290479123592377, -0.04005590081214905, -0.00023799399787094444, -0.015286740846931934, -0.041075076907873154, 0.03094913624227047, 0.01220775581896305, -0.0049320971593260765, 0.07393355667591095, 0.04179948940873146, 0.03320516273379326, -0.002307175425812602, 0.0067969923838973045, -0.002993285423144698, -0.010337297804653645, -0.00885697826743126, -0.09881548583507538, -0.022734763100743294, 0.007688799407333136, -0.021305833011865616, -0.007150096818804741, -0.0341586172580719, 0.004482204560190439, -0.04331545531749725, -0.00536487577483058, 0.008295097388327122, -0.03811504319310188, -0.053933270275592804, -0.03258061036467552, 0.05931790545582771, -0.035955533385276794, -0.01122632622718811, 0.09081569314002991, -0.0025382486637681723, 0.01512096542865038, 0.0359179750084877, -0.005517852026969194, 0.03685813024640083, 0.012553474865853786, -0.016402289271354675, -0.014309794642031193, -0.02166169323027134, -0.015700537711381912, -0.03937617316842079, -0.06301480531692505, -0.04576253518462181, 0.024298474192619324, -0.0330282486975193, 0.0151292709633708, 0.03270254284143448, -0.0116543835029006, -0.06641288846731186, -0.033137332648038864, 0.06395848095417023, -0.008160210214555264, 0.009070747531950474, -0.040059756487607956, 0.004848021548241377, -0.04805045202374458, 0.014019487425684929, 0.016501177102327347, 0.059660349041223526, 0.0365368016064167, -0.02276819385588169, 0.025196686387062073, -0.007985415868461132, -0.024269862100481987, -0.02088981680572033, 0.008492028340697289, -0.026250947266817093, 0.03912022337317467, -0.03778595104813576, 0.0608186349272728, -0.017759980633854866, -0.017994072288274765, -0.06827399879693985, 0.023276163265109062, 0.021230991929769516, -0.013218353502452374, -0.05233870819211006, 0.029472727328538895, -0.030456196516752243, -0.05059223249554634, -0.039429184049367905, 0.03275877609848976, 0.010713128373026848, 0.016544299200177193, -0.04818197339773178, -0.05196494981646538, 0.03164588660001755, -0.014476021751761436, -0.05291960388422012, -0.007358061149716377, -0.012877978384494781, -0.006929731462150812, -0.0072398860938847065, -0.010730544105172157, -0.0006893686950206757, -0.017559006810188293, -0.028823122382164, -0.006531473249197006, 0.03219437599182129, 0.048728782683610916, 0.09532073885202408, 0.013431360013782978, 0.05609240010380745, -0.022034229710698128, -0.021140078082680702, 0.0069093406200408936, -0.055095020681619644, 0.019294679164886475, 0.02471853978931904, 0.03980737924575806, -0.021593378856778145, -0.001400874461978674, 0.007611941080540419, -0.0030811431352049112, -0.05335701256990433, -0.03282087296247482, -0.06270744651556015, -0.02558441273868084, 0.00379392271861434, 0.02121509611606598, 0.0003635227039922029, 0.010191629640758038, -0.015728788450360298, -0.0016471750568598509, -0.01855870895087719, 0.02492675557732582, -0.007265510968863964, 0.05720551311969757, -0.0013596644857898355, -0.0207783542573452, -0.007945084013044834, 0.011022231541574001, 0.0035855735186487436, -0.027800926938652992, 0.03821653872728348, -0.05175500363111496, -0.033908694982528687, 0.0012278889771550894, 0.005218669772148132, 0.009629511274397373, -0.020610386505723, -0.008309162221848965, 0.022318163886666298, -0.021350672468543053, -0.01523094717413187, -0.03940925747156143, -0.007471083663403988, -0.0070563433691859245, 0.02198069915175438, -0.009605412371456623, 0.02622445486485958, 0.11605063080787659, -0.013923116959631443, -0.040453195571899414, 0.043119773268699646, 0.012945743277668953, 0.007915723137557507, -0.007178116124123335, -0.038305580615997314, 0.0034201028756797314, 0.025716999545693398, 0.10924341529607773, -0.06702923774719238, -3.3443948268541135e-06, 0.06022954359650612, 3.625376905347366e-07, -0.03434247151017189, 0.032839905470609665, -0.036105845123529434, -0.02419612929224968, -0.04967381805181503, -0.04693556949496269, 0.10315696895122528, 0.027130665257573128, -0.00743047846481204, -0.022346125915646553, 0.0293580275028944, 0.05212490260601044, -0.02720559388399124, -0.03340452164411545, 0.06483497470617294, 0.022100448608398438, -0.0315365269780159, -0.0038969346787780523, -0.010733477771282196, 0.026875045150518417, 0.006313455291092396, 0.02458995394408703, -0.028769049793481827, -0.021724717691540718, 0.0001583173725521192, 0.015471771359443665, -0.0036127499770373106, 0.011790281161665916, -0.03371722996234894, -0.057515643537044525, -0.04636494442820549, 0.04029291868209839, 0.055622026324272156, -0.016084950417280197, 0.026100972667336464, -0.05208767578005791, 0.012590575963258743, -0.02094123139977455, 0.05441414192318916, 0.04634558781981468, -0.037652913480997086, -0.01243849378079176, -0.024706540629267693, -0.04091237112879753, -0.01822054758667946, 0.02787802927196026, 0.04034142196178436, 0.024435922503471375, -0.008827734738588333, 0.017611656337976456, 0.01280110515654087, -0.011789082549512386, 0.08954926580190659, 0.010784901678562164, 0.013894100673496723, -0.0036493241786956787, -0.011644120328128338, 0.05799723044037819, 0.037448227405548096, -0.020501654595136642, 0.001382546848617494, -0.04044359549880028, -0.029260948300361633, 0.025613296777009964, 0.0610315166413784, -0.022013401612639427, -0.06137893721461296, -0.05484559386968613, -0.026773754507303238, 0.0318659283220768, 0.01764705777168274, 0.023626811802387238, -0.02858714573085308, -0.08448486030101776, 0.01666843332350254, -0.05668381601572037, 0.011217016726732254, -0.030246013775467873, -0.020611127838492393, 0.022412963211536407, -0.005077978130429983, 0.03180514648556709, -0.0013457101304084063, 0.006579602602869272, -0.06903212517499924, -0.044516388326883316, 0.008762149140238762, -0.04233792796730995, 0.009771255776286125, -0.012280053459107876, 0.015866100788116455, -0.005431133788079023, -0.037043798714876175, 0.014932235702872276, 0.0339360311627388, -0.02688075602054596, 0.02670256420969963, -0.016303911805152893, 0.07676100730895996, 0.032823484390974045, -0.05752855911850929, -0.004847256932407618, -0.04374650493264198, -0.004070183727890253, -0.04546279460191727, -0.02232642099261284, -0.00750059075653553, 0.012332850135862827, -0.03431938588619232, 0.028603654354810715, -0.03875213861465454, 0.08712092787027359, -0.015322268940508366, -0.07934268563985825, -0.0538368821144104, 0.03844447433948517, 0.010748798958957195, 0.0063771274872124195, -0.05530017614364624, 0.08642423152923584, -0.061131514608860016, 0.01470225490629673, -0.03700021281838417, 0.029133036732673645, 0.0371471606194973, 0.023875221610069275, -0.009675968438386917, 0.03926757350564003, 0.05023173242807388, 0.04375341534614563, 0.0028089401312172413, 0.062260329723358154, -0.00296220020391047, 0.013255732133984566, -0.022128384560346603, -0.0016695937374606729, -0.019037680700421333, -0.05170021578669548, 0.006414797622710466, -0.015953024849295616, -0.0475710965692997, -0.021928176283836365, 0.09177988022565842, -0.05638990178704262, 0.05666082352399826, 0.002483689459040761, -0.022956350818276405, -0.07733950763940811, -0.0512029305100441, 0.004708398599177599, 0.010594150982797146, 0.05728110298514366, 0.010780811309814453, -0.0448346845805645, -0.018433647230267525, 0.011096672154963017, -0.011657564900815487, -0.00041065653203986585, 0.03343082219362259, 0.0069776601158082485, -0.044371042400598526, -0.0034076424781233072, -0.007387245073914528, -0.005964014679193497, -0.0003319532552268356, -0.047195710241794586, 0.017081113532185555, -0.0384296253323555, 0.011492966674268246, 0.08258381485939026, -0.005156338214874268, 0.019711678847670555, -0.030974479392170906, -0.0269735436886549, 0.0016101350774988532, 0.05480809137225151, 0.010838361456990242, 0.013025535270571709, 0.01125642005354166, -0.024356931447982788, -0.016103914007544518, 0.014493239112198353, -0.013177121989428997, 0.03378548100590706, 0.022668365389108658, -0.08042639493942261, -0.08581610769033432, -0.01701516844332218, -0.051305390894412994, 0.03262804076075554, 0.056967757642269135, 0.015837864950299263, 0.02217966876924038, -0.04529990255832672, 0.012579194270074368, 0.05317265912890434, 0.010716515593230724, 0.025877660140395164, -0.038276806473731995, 0.04760194569826126, 0.03327568620443344, 0.01682489551603794, -0.04126613959670067, 0.042853474617004395, -0.02612229622900486, 0.042524244636297226, 0.05068903788924217, 0.004296552389860153, 0.04771658778190613, -0.045676495879888535, 0.020778335630893707, 0.029885075986385345, -0.029023006558418274, 0.048751287162303925, 0.05107541009783745, -0.003394761588424444, 0.007554409559816122, 0.027040675282478333, 0.0015569970710203052, -0.03052450716495514, 0.0468752458691597, 0.03953593596816063, 0.0599677748978138, -0.04228483885526657, -0.0005072196945548058, 0.010756051167845726, -0.003548266598954797, -0.019490430131554604, 0.014625387266278267, 0.02052147127687931, -0.0345788411796093, 0.04822205752134323, 0.006214292719960213, -0.06542038917541504, 0.02285158261656761, -0.009435975924134254, 0.019820377230644226, 0.02713737078011036, -0.038525983691215515, -0.11021217703819275, -0.029969794675707817, 0.028465082868933678, -0.003949034959077835, -0.023083405569195747, 0.06424864381551743, -0.0322294756770134, -0.05743865668773651, 0.0017904898850247264, 0.04865928366780281, 0.0025669094175100327, 0.017497573047876358, 0.031849030405282974, 4.1311483073513955e-05, 0.046127863228321075, 0.06329700350761414, 0.01695377193391323, -0.0017457135254517198, -0.007527789566665888, 0.0006808724137954414, -0.006988947745412588, -0.059825651347637177, -0.013233160600066185, 0.0013939251657575369, 0.06066565588116646, -6.349559836293269e-33, 0.00396833335980773, -0.022034471854567528, -0.03386307880282402, -0.020893333479762077, -0.019518211483955383, 0.016436344012618065, 0.006722217425704002, -0.030664315447211266, -0.005727104377001524, -0.013948173262178898, -0.014262987300753593, -0.020384805276989937, -0.012220996432006359, 0.006967995315790176, -0.022853873670101166, -0.016260569915175438, -0.007529268506914377, 0.006978936027735472, 0.011516532860696316, 0.02880379743874073, -0.012588354758918285, 0.022725865244865417, -0.008156866766512394, 0.016132352873682976, -0.08270063251256943, 0.04184796288609505, -0.027122803032398224, -0.02041161060333252, 0.049914516508579254, -0.00910605676472187, 0.009645766578614712, 0.004675192758440971, -0.0008479201351292431, -0.04336623102426529, 0.0067352293990552425, -0.03706761449575424, -0.053297802805900574, -0.030669184401631355, -0.031380146741867065, 0.05010863021016121, -0.020929725840687752, 0.019307870417833328, 0.037022657692432404, -0.025456666946411133, 0.02588839642703533, -0.017869381234049797, 0.08065778017044067, -0.021793661639094353, -0.017703352496027946, 0.05345810577273369, 0.02230042964220047, 0.03332004323601723, -0.01941945217549801, 0.013327240943908691, 0.09531890600919724, -0.05088897421956062, 0.016422919929027557, 0.014664839021861553, -0.05408977344632149, 0.04077591001987457, -0.013260760344564915, 0.01043610367923975, 0.0021459825802594423, 0.0618027001619339, 0.033439259976148605, 0.02874048240482807, 0.06749752908945084, -0.05430250242352486, 0.06701191514730453, 0.009267304092645645, -0.005441394634544849, 0.06026570126414299, -0.01958092860877514, -0.0651356503367424, -0.0383102148771286, -0.06383223086595535, -0.02981540933251381, 0.05567306652665138, 0.025048604235053062, 0.0031546917743980885, -0.04172492027282715, 0.011541381478309631, 0.016829639673233032, -0.010272469371557236, 0.08450629562139511, -0.08699863404035568, -0.021358607336878777, -0.05006653442978859, -0.05016250163316727, 0.022516530007123947, -0.05897625908255577, 0.08047061413526535, 0.0006888189818710089, -0.015281779691576958, 0.01710510440170765, -0.02019888535141945, -0.029093243181705475, 0.08215988427400589, 0.04317491129040718, -0.030795477330684662, -0.014665967784821987, -0.01942000538110733, 0.016913529485464096, 0.003494022646918893, 0.0007320565637201071, 0.027445534244179726, 0.013458937406539917, -0.026046020910143852, 0.004262029659003019, -0.004380142316222191, 0.005352952517569065, 0.003546625142917037, 0.01253477856516838, 0.003388794371858239, -0.000686084502376616, -0.006303102243691683, -0.012121753767132759, 0.11295224726200104, -0.007401308510452509, 0.008548581972718239, -0.002595515688881278, -0.004884364549070597, -0.06016458198428154, 0.029303452000021935, -0.0644792765378952, 0.008599063381552696, 0.012651961296796799, -0.020118769258260727, -0.03230353444814682, -0.022574545815587044, -0.04372219741344452, 0.002391664544120431, 2.8296105369918223e-07, 0.010415652766823769, 0.023161768913269043, 0.01169612631201744, -0.08398769050836563, -0.04688672348856926, 0.0215060543268919, -0.02140280231833458, -0.03327489644289017, -0.017208149656653404, -0.05578639730811119, 0.027989516034722328, 0.019274722784757614, -0.02517732046544552, 0.0014724439242854714, -0.033966533839702606, 0.12148123979568481, 0.0385645367205143, 0.036143895238637924, 0.001298733172006905, 0.04729866981506348, -0.03702940791845322, 0.044107694178819656, 0.0283439252525568, -0.005681411828845739, 0.028600260615348816, -0.041640836745500565, -0.043825626373291016, -0.015162810683250427, 0.037013839930295944, 0.0006284954724833369, -0.02524535171687603, 0.025402460247278214, -0.022753864526748657, 0.015845097601413727, -0.007861200720071793, -0.02627766877412796, -0.0012282676761969924, -0.031225072219967842, -0.007896138355135918, 0.0004470529966056347, 0.07416177541017532, 0.04306010156869888, 0.042117889970541, -0.046215880662202835, 0.04965505376458168, -0.0262198057025671, -0.017950527369976044, -0.017801892012357712, -0.0005851833848282695, 0.005086001940071583, 0.028778018429875374, 0.01766318455338478, -0.019933875650167465, 0.03562934324145317, -0.00454879691824317, -0.03655225783586502, 0.0212238859385252, -0.00945645198225975, 0.0386006236076355, 0.03670894727110863, 0.047497574239969254, -0.027941441163420677, 0.03889373317360878, 0.0837584063410759, 0.03532782942056656, 0.045624252408742905, -0.04752402380108833, 2.253328309554023e-34, 0.00021659616322722286, 0.024328239262104034, -0.012332855723798275, 0.03498946875333786, -0.004113275557756424, 0.013553199358284473, -0.05421409383416176, -0.01709272898733616, -0.02550205960869789, 0.0036780121736228466, -0.012178242206573486]

['Sergey S. Tarasenko']

1102.2739v1

This study is focused on the development of the cortex-like visual object recognition system. We propose a general framework, which consists of three hierarchical levels (modules). These modules functionally correspond to the V1, V4 and IT areas. Both bottom-up and top-down connections between the hierarchical levels V4 and IT are employed. The higher the degree of matching between the input and the preferred stimulus, the shorter the response time of the neuron. Therefore information about a single stimulus is distributed in time and is transmitted by the waves of spikes. The reciprocal connections and waves of spikes implement predictive coding: an initial hypothesis is generated on the basis of information delivered by the first wave of spikes and is tested with the information carried by the consecutive waves. The development is considered as extraction and accumulation of features in V4 and objects in IT. Once stored a feature can be disposed, if rarely activated. This cause update of feature repository. Consequently, objects in IT are also updated. This illustrates the growing process and dynamical change of topological structures of V4, IT and connections between these areas.

A General Framework for Development of the Cortex-like Visual Object Recognition System: Waves of Spikes, Predictive Coding and Universal Dictionary of Features

http://arxiv.org/pdf/1102.2739v1

Title General Framework Development Cortexlike Visual Object Recognition System Waves Spikes Predictive Coding Universal Dictionary Features Summary study focused development cortexlike visual object recognition system propose general framework consists three hierarchical level module module functionally correspond V1 V4 area bottomup topdown connection hierarchical level V4 employed higher degree matching input preferred stimulus shorter response time neuron Therefore information single stimulus distributed time transmitted wave spike reciprocal connection wave spike implement predictive coding initial hypothesis generated basis information delivered first wave spike tested information carried consecutive wave development considered extraction accumulation feature V4 object stored feature disposed rarely activated cause update feature repository Consequently object also updated illustrates growing process dynamical change topological structure V4 connection area Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0009064223268069327, 0.0021670248825103045, -0.025190727785229683, 0.04891321063041687, -0.002613988472148776, 0.014427641406655312, 0.01968766376376152, 0.008697547018527985, 0.03644901141524315, 0.005616879090666771, -0.037766337394714355, 0.014864770695567131, 0.00046208896674215794, 0.08074658364057541, 0.014535075053572655, -0.05890842154622078, 0.011744770221412182, 0.03551391512155533, -0.03899148106575012, -0.03382934257388115, 0.00682171992957592, -0.06582438200712204, -0.0013559249928221107, 0.0271848626434803, -0.03150560334324837, 0.009813005104660988, -0.03334445133805275, -0.0389079824090004, -0.013864698819816113, -0.05478328838944435, 0.014303140342235565, 0.009562712162733078, 0.020361097529530525, 0.016109850257635117, 2.184260210924549e-06, -0.03603314235806465, 0.030396979302167892, -0.027180520817637444, 0.019471442326903343, -0.06433354318141937, -0.010733609087765217, 0.002348407870158553, -0.0019000988686457276, -0.04628146067261696, -0.015091078355908394, 0.02147761732339859, 0.1042194664478302, 0.07884954661130905, -0.01681884191930294, -0.0021861849818378687, -0.023679086938500404, -0.07841729372739792, 0.06856364756822586, 0.016578134149312973, 0.0006432067602872849, 0.04134810343384743, -0.0028345317114144564, 0.02190045826137066, 0.035076189786195755, -0.014965765178203583, -0.023350510746240616, 0.005524234380573034, 0.03784063085913658, 0.007626284379512072, 0.0657987892627716, 0.034762270748615265, -0.04353589192032814, -0.03256260231137276, -0.04139130562543869, 0.02860250324010849, -0.036845024675130844, -0.035056207329034805, -0.005441870540380478, 0.01241187285631895, -0.021548286080360413, -0.006534936372190714, 0.0047473181039094925, -0.006703340448439121, -0.054643016308546066, 0.03977035731077194, -0.0007156996871344745, 0.012100236490368843, -0.030449027195572853, -0.012267779558897018, 0.03311435505747795, -0.049344830214977264, 0.000512809376232326, 0.013400072231888771, -0.0027826360892504454, -0.029621081426739693, 0.02329878695309162, -0.005843689665198326, 0.031672727316617966, 0.008913560770452023, 0.015473967418074608, -0.03782951459288597, -0.020750535652041435, -0.03928752988576889, -0.007357282098382711, -0.08181586116552353, 0.05401506647467613, 0.018314654007554054, -0.061372507363557816, 0.030346518382430077, -0.04731003940105438, 0.06447484344244003, -0.07048942893743515, 0.06210445240139961, -0.01893458515405655, 0.013869031332433224, -0.057035140693187714, 0.005123431328684092, 0.00930213462561369, 0.08939158916473389, 0.036428723484277725, -0.021295497193932533, -0.04422556608915329, 0.007198733743280172, 0.0068464744836091995, -0.0674266442656517, -0.02126842737197876, 0.030035540461540222, 0.0325159952044487, -0.0004632683121599257, -0.046975720673799515, -0.014791281893849373, 0.023312818259000778, -0.029270589351654053, -0.0358077734708786, 0.026584183797240257, 0.033053990453481674, 0.04379207640886307, -0.008386969566345215, 0.04296867176890373, 0.0011037095682695508, 0.034279149025678635, -0.034597430378198624, -0.01870819367468357, -0.06755609810352325, 0.0517592690885067, 0.03496351093053818, 0.03076532483100891, 0.04956546053290367, -0.025585554540157318, -0.011916586197912693, 0.004975803662091494, -0.060943178832530975, 0.0028752079233527184, -0.006207195110619068, -0.04004225879907608, -0.03593992814421654, 0.029797643423080444, -0.0648297518491745, -0.0191279798746109, 0.07174544036388397, -0.005536268465220928, 0.023792043328285217, -0.006176571827381849, 0.03059498593211174, 0.031500641256570816, -0.06470140814781189, -0.023228058591485023, 0.028728356584906578, -0.012682287022471428, -0.037704627960920334, -0.07610958814620972, -0.09802688658237457, -0.05098522827029228, -0.010527899488806725, -0.008751976303756237, 0.029914502054452896, 0.025494130328297615, -0.001132335513830185, 0.002182846190407872, 0.012507867068052292, 0.06877710670232773, -0.01339318510144949, 0.0461437851190567, 0.015043037943542004, -0.04567800089716911, 0.02070445939898491, 0.013043849729001522, -0.003757194383069873, 0.1010184958577156, -0.026651479303836823, -0.062840536236763, -0.0687372237443924, -0.01858089491724968, -0.025647791102528572, -0.02757643721997738, 0.014374738559126854, -0.004569228272885084, -0.02989237569272518, 0.010043494403362274, 0.031325481832027435, -0.014193176291882992, -0.005608896724879742, -0.06585992872714996, -0.0061866831965744495, 0.028860997408628464, -0.009157595224678516, -0.07904458791017532, 0.03803267702460289, 0.02121708169579506, 0.004061682615429163, -0.01438161265105009, 0.030359160155057907, 0.0386926643550396, -0.022300610318779945, 0.025362007319927216, -0.016903452575206757, -0.019217390567064285, 0.00472415704280138, -0.008720573969185352, -0.04562857747077942, 0.03838352486491203, -0.016156962141394615, 0.024598129093647003, -0.00957860890775919, -0.01933666691184044, -0.032207660377025604, 0.06644000113010406, -0.02938816137611866, 0.011990878731012344, 0.038946010172367096, 0.03632420673966408, -0.013698558323085308, 0.010392631404101849, 0.018104150891304016, -0.02684990130364895, 0.00852549821138382, -0.020637281239032745, 0.02353602647781372, -0.04795704036951065, 0.03151620924472809, -0.01697497069835663, -0.031206490471959114, 0.013324456289410591, 0.023363294079899788, 0.05891585350036621, 0.04030715301632881, 5.191554919292685e-06, 0.026137862354516983, -0.03964943811297417, 0.050896722823381424, 0.027388297021389008, 0.03609621524810791, -0.02496919594705105, 0.06597182154655457, -0.002323924330994487, 0.0360126830637455, 0.000530553050339222, 0.06334476917982101, 0.006145096849650145, -0.018901458010077477, -0.021464364603161812, -0.016867224127054214, 0.02209414355456829, -0.03570503741502762, -0.00906222965568304, 0.06286383420228958, -0.05736890435218811, -0.017057225108146667, -0.005468619521707296, 0.024907803162932396, -0.008793461136519909, -0.014552310109138489, -0.026173021644353867, -0.03733019530773163, 0.03363588824868202, -0.019113264977931976, -0.00246412493288517, -0.031435277312994, 0.025855183601379395, -0.03389604762196541, -0.012885436415672302, 0.11474417895078659, -0.017444457858800888, -0.0332660973072052, 0.02101258561015129, -0.0038160672411322594, -0.013869458809494972, -0.03700942173600197, -0.014248143881559372, 0.0003373347863089293, 0.04686906933784485, 0.03449774160981178, -0.07639236748218536, -0.019067496061325073, 0.0409182533621788, 0.004597894847393036, 0.0582994669675827, 0.026629919186234474, -0.016637245193123817, -0.013758781366050243, -0.010160689242184162, 0.027635609731078148, 0.05977142974734306, 0.03329431638121605, 0.02224305272102356, -0.002387144137173891, 0.0218199472874403, 0.017747199162840843, 0.0029850401915609837, -0.016446836292743683, 0.008858747780323029, 0.012496397830545902, 0.045855555683374405, -0.014083449728786945, 0.059743933379650116, 0.0541008785367012, 0.016217254102230072, -0.01697874255478382, -0.0030616510193794966, 0.018365327268838882, -0.022898735478520393, -0.046898629516363144, -0.035208266228437424, -0.02869885228574276, 0.009536235593259335, -0.04427848756313324, -0.040114182978868484, 0.018829021602869034, 0.029769156128168106, 0.04100445285439491, 0.04753422737121582, -0.01213035173714161, 0.02427561767399311, 0.029066313058137894, 0.05105912312865257, 0.025800906121730804, -0.013924704864621162, -0.01889793388545513, -0.006182004231959581, -0.008810988627374172, -0.040060270577669144, -0.018339233472943306, -0.04601606726646423, -0.06037162244319916, -0.015757547691464424, -0.06203072890639305, -0.022202111780643463, -0.06794159859418869, 0.05651837959885597, 0.016596637666225433, 0.03923070803284645, 0.01694743148982525, -0.0006041303859092295, 0.0348883718252182, 0.04230787605047226, 0.03836308792233467, 0.05639741197228432, -0.033124133944511414, -0.02614472061395645, -0.021653305739164352, 0.05208468809723854, 0.004559413529932499, 0.010244958102703094, -0.03486497700214386, 0.045049332082271576, 0.018465518951416016, 0.008687196299433708, -0.022354062646627426, 0.011617766693234444, -0.12565778195858002, 0.044594407081604004, 0.01065043918788433, 0.04801814258098602, -0.02623557113111019, 0.005051507614552975, 0.03568381443619728, -0.04198337346315384, 0.02436278946697712, -0.012672343291342258, -0.020348088815808296, -0.10264252871274948, -0.043400999158620834, -0.006202847696840763, -0.053875476121902466, 0.003938411828130484, 0.009053822606801987, 0.049338895827531815, 0.01472846232354641, -0.039677929133176804, -0.04412134736776352, -0.001033694832585752, -0.0367141030728817, 0.020934583619236946, -0.004013314843177795, 0.024823088198900223, -0.02457640878856182, -0.0433339960873127, -0.04311680421233177, 0.02739008143544197, 0.006120231002569199, 0.03340340033173561, -0.0743633508682251, 0.04234907031059265, -0.00041221181163564324, -0.020308267325162888, 0.02755083702504635, 0.04118692874908447, 0.03125758096575737, 0.044747233390808105, -0.0510825477540493, -0.010180889628827572, 0.07079630345106125, 0.004457601346075535, -0.006180610042065382, -0.01700510084629059, -0.05883727967739105, 0.00716199679300189, 0.05645167827606201, -0.00525203812867403, -0.04256519675254822, 0.03532232716679573, -0.02038276568055153, -0.01752678118646145, 0.047363802790641785, 0.03227851539850235, -0.005421228241175413, -0.06492975354194641, 0.025525681674480438, -0.008079346269369125, -0.008935446850955486, -0.051302291452884674, 0.006712417118251324, -0.010665688663721085, -0.017589302733540535, 0.0037036053836345673, -0.037776365876197815, -0.006471588276326656, 0.03832870349287987, 0.019490288570523262, -0.03206236660480499, -0.02143048495054245, 0.020293090492486954, -0.024837099015712738, -0.049453869462013245, -0.0335819274187088, 0.03577903285622597, -0.017070479691028595, 0.022317197173833847, 0.0447937548160553, -0.02013619802892208, 0.03657472878694534, -0.02227477915585041, -0.04530526325106621, 0.003116387641057372, 0.05358543619513512, -0.06306853890419006, -0.0790962427854538, -0.015619569458067417, 0.014351936057209969, -0.056656189262866974, -0.007224013563245535, -0.017070366069674492, -0.03426022455096245, -0.006033121142536402, 0.041171591728925705, 0.038418639451265335, -0.0031719589605927467, -0.04452579468488693, 0.010732079856097698, -0.03167001157999039, -0.012027747929096222, 0.03810526430606842, 0.04008621349930763, 0.022462384775280952, -0.03721199184656143, 0.0018203320214524865, -0.03703419491648674, -0.023814979940652847, -0.0018940092995762825, 0.08875147998332977, 0.011278785765171051, -0.07345874607563019, -0.028765102848410606, 0.02865358255803585, 0.013898048549890518, -0.022658994421362877, 0.10900644958019257, 0.03007161058485508, 0.030431006103754044, -0.02252020873129368, 0.0030312989838421345, 0.04993290454149246, 0.06204931437969208, -0.03141370043158531, 0.0046099708415567875, 0.008040191605687141, 0.014256547205150127, 0.026781992986798286, -0.04599032178521156, 0.06520774960517883, -0.024483926594257355, 0.06246764585375786, -0.0001831941626733169, -0.05626530945301056, -0.012902074493467808, -0.08303425461053848, 0.020756065845489502, -0.004644781816750765, 0.020813846960663795, 0.010623980313539505, 0.038643479347229004, -0.021107142791152, 0.05917704477906227, 0.001792228315025568, -0.02622186578810215, -0.02183247171342373, 0.02273494191467762, 0.025965502485632896, -0.0013054471928626299, -0.026768261566758156, 0.007335023023188114, 0.042816486209630966, 0.005105819087475538, -0.04966435208916664, 0.019529113546013832, 0.02777785062789917, -0.03503131493926048, 0.03872775286436081, 0.005264608189463615, 0.028237460181117058, 0.048902228474617004, 0.01822330430150032, 0.007467827294021845, -0.056768640875816345, -0.010145503096282482, -0.01864043064415455, -0.04915044456720352, -4.803905994776869e-06, 0.020519381389021873, -0.0036716340109705925, 0.041893959045410156, 0.018128521740436554, 0.014634005725383759, -0.029161270707845688, 0.027193892747163773, 0.011221548542380333, 0.022683382034301758, 0.025136226788163185, 0.025657987222075462, 0.056125979870557785, -0.0010421862825751305, 0.019583361223340034, -0.004705521278083324, 0.012605409137904644, -0.05097198858857155, 0.022902434691786766, -0.04975534975528717, 0.053852830082178116, 0.013544155284762383, -0.04327902942895889, -5.932120119139181e-33, -0.0033875182271003723, -0.0011135073145851493, 0.011619254015386105, -0.007024702616035938, 0.01096627302467823, -0.006028382107615471, -0.0015353667549788952, 0.014450137503445148, -0.025313302874565125, -0.050893668085336685, -0.04163951799273491, -0.005663413088768721, 0.019406914710998535, 0.014562082476913929, 0.04330359399318695, 0.015002237632870674, -0.030683796852827072, -0.04305209591984749, 0.06952348351478577, -0.029427744448184967, 0.08353347331285477, 0.015032028779387474, 0.10970179736614227, -0.0630907416343689, -0.08188532292842865, 0.054008178412914276, 0.04538554698228836, -0.02694959193468094, 0.023827724158763885, -0.048532530665397644, -0.0693783387541771, -0.007682097610086203, 0.017132384702563286, 0.020019352436065674, 0.016453783959150314, -0.041249390691518784, -0.03940104320645332, 0.006262574810534716, -0.028791554272174835, 0.014666371047496796, -0.06357147544622421, -0.014057258144021034, 0.05130590870976448, -0.028466323390603065, -0.048945650458335876, 0.04204951599240303, 0.030541682615876198, -0.05138321965932846, -0.0007923413650132716, 0.030593888834118843, -0.018366048112511635, 0.009279868565499783, -0.007182256318628788, -0.02972121722996235, 0.06721613556146622, -0.023006217554211617, -0.02605963684618473, 0.04340089112520218, -0.037532344460487366, 0.0449107326567173, -0.011159256100654602, 0.06945407390594482, -0.0020273400004953146, 0.04181915894150734, 0.09071767330169678, 0.0545363686978817, 0.07833527773618698, -0.025607969611883163, -0.010403801687061787, -0.02927878499031067, 0.011115719564259052, 0.05358162894845009, 0.037440814077854156, 0.036103442311286926, 0.12581874430179596, -0.055689163506031036, -0.01636827550828457, 0.015437370166182518, -0.0049149952828884125, 0.014958290383219719, -0.037981171160936356, 0.005892072804272175, -0.04439917579293251, 0.003173157339915633, 0.06687764823436737, -0.04060456529259682, -0.03430713713169098, -0.03188619017601013, 0.00835847482085228, -0.030695108696818352, 0.014087763614952564, 0.01809610053896904, 0.007511903531849384, -0.012970688752830029, 0.06989141553640366, -0.029902489855885506, 0.023934729397296906, 0.04426981508731842, 0.04922981187701225, -0.03800931200385094, -0.04924287647008896, -0.024995094165205956, 0.004909852519631386, -0.024353550747036934, 0.018354151397943497, 0.05013567954301834, -0.026224274188280106, 0.03468243032693863, 0.028040137141942978, -0.01620848849415779, 0.013774939812719822, -0.06104001775383949, 0.05610061436891556, -0.008742490783333778, -0.010486114770174026, -0.04277365654706955, 0.016305655241012573, 0.00883204024285078, -0.019902341067790985, -0.025224769487977028, -0.03191400319337845, -0.020979272201657295, 0.00789192970842123, 0.0742323249578476, 0.03781309723854065, 0.01830465905368328, -0.09974130243062973, 0.026700250804424286, -0.008393379859626293, -0.04257303476333618, 0.0005885715363547206, 0.05988078564405441, 2.925495721228799e-07, -0.0665242075920105, -0.0074041071347892284, -0.012851915322244167, -0.0010059453779831529, 0.021918607875704765, -0.020489029586315155, 0.036026474088430405, 0.046867795288562775, -0.007116736378520727, -0.06161940097808838, -0.03170331194996834, 0.003959162160754204, -0.027307584881782532, 0.00911510270088911, -0.055543966591358185, -0.015232127159833908, -3.537642987794243e-05, 0.020153505727648735, -0.015749868005514145, -0.00353521341457963, 0.06648687273263931, 0.011763930320739746, 0.011173253878951073, 0.00020484528795350343, 0.033568352460861206, 0.028115691617131233, 0.02656630240380764, 0.02594788745045662, 0.04902378469705582, -0.014201773330569267, -0.03687432408332825, -0.0058736237697303295, -0.008060453459620476, 0.07088632136583328, -0.0022753491066396236, 0.0006253694300539792, -0.008713657036423683, -0.059038832783699036, -0.0491805300116539, -0.0015698156785219908, 0.03444003313779831, 0.024242300540208817, 0.01181620080024004, -0.020744582638144493, 0.0152666000649333, -0.03407398983836174, -0.024659257382154465, -0.01537875086069107, 0.04368392005562782, -0.003382529364898801, -0.02481880411505699, -0.011870277114212513, -0.011695713736116886, -0.03026842325925827, -0.044972363859415054, -0.04828091710805893, -0.030231734737753868, -0.0037471295800060034, 0.03842280060052872, 0.01845131814479828, 0.005279787350445986, 0.01443603914231062, -0.013251463882625103, -0.062103454023599625, 0.06038440763950348, 0.019529052078723907, -0.041405677795410156, 2.1412407906057906e-34, -0.04317237436771393, 0.0003181748616043478, -0.0009403181029483676, 0.00388120929710567, -0.021142777055501938, -0.02261177822947502, 0.013209771364927292, -0.01730894297361374, -0.024174561724066734, -0.0054396758787333965, -0.027620406821370125]

['Dan C. Cireşan', 'Ueli Meier', 'Luca M. Gambardella', 'Jürgen Schmidhuber']

1103.4487v1

The competitive MNIST handwritten digit recognition benchmark has a long history of broken records since 1998. The most recent substantial improvement by others dates back 7 years (error rate 0.4%) . Recently we were able to significantly improve this result, using graphics cards to greatly speed up training of simple but deep MLPs, which achieved 0.35%, outperforming all the previous more complex methods. Here we report another substantial improvement: 0.31% obtained using a committee of MLPs.

Handwritten Digit Recognition with a Committee of Deep Neural Nets on GPUs

http://arxiv.org/pdf/1103.4487v1

Title Handwritten Digit Recognition Committee Deep Neural Nets GPUs Summary competitive MNIST handwritten digit recognition benchmark long history broken record since 1998 recent substantial improvement others date back 7 year error rate 04 Recently able significantly improve result using graphic card greatly speed training simple deep MLPs achieved 035 outperforming previous complex method report another substantial improvement 031 obtained using committee MLPs Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.009414189495146275, 0.0630563497543335, 0.0035463629756122828, 0.09012654423713684, -0.010637854225933552, 0.0219058096408844, 0.08015017956495285, 0.023462682962417603, -0.002985337283462286, 0.03166167810559273, 0.02365194261074066, -0.023339396342635155, 0.050962645560503006, 0.022648407146334648, -0.013197244144976139, -0.023370739072561264, -0.04702203720808029, -0.01464968454092741, -0.027541134506464005, -0.020363589748740196, -0.007811545394361019, -0.04378782957792282, -0.01833508349955082, 0.03152117505669594, -0.07515443116426468, -0.0007940374780446291, -0.03549964353442192, -0.007022838108241558, 0.0014912127517163754, -0.00038458770723082125, -0.015164253301918507, 0.015677351504564285, 0.021886076778173447, 0.08417461812496185, 2.069000629489892e-06, -0.056022338569164276, -0.022110003978013992, -0.022715609520673752, -0.010465795174241066, -0.01621699333190918, 0.07265137881040573, -0.0414525531232357, -0.04534681886434555, -0.03599151223897934, -0.015100160613656044, -0.040223825722932816, 0.061782918870449066, 0.07986459136009216, 0.007794609759002924, 0.027422938495874405, 0.0015128942904993892, -0.0014756066957488656, 0.033893536776304245, -0.023242246359586716, 0.006734245456755161, -0.00859962310642004, 0.020994972437620163, -0.019811924546957016, -0.03699496388435364, -0.053965047001838684, 0.03710702061653137, 0.04471209645271301, 0.03304577246308327, -0.044276583939790726, 0.006166396662592888, 0.026189422234892845, 0.01053828839212656, -0.010167996399104595, 0.016082342714071274, 0.06277844309806824, -0.059851761907339096, 0.04171914607286453, 0.012250183150172234, -0.02679317630827427, -0.0624665841460228, -0.014593062922358513, -0.007703169248998165, 0.04184567555785179, -0.04641539230942726, -0.02042376436293125, -0.04165168106555939, -0.0049282549880445, 0.024520762264728546, 0.026117272675037384, 0.006967175751924515, -0.028769169002771378, 0.001128596835769713, -0.003489937400445342, 0.034603897482156754, -0.006236462388187647, -0.006409800611436367, -0.022024381905794144, 0.058224525302648544, 0.004787199664860964, 0.044079575687646866, -0.011382286436855793, -0.0058611910790205, -0.07839226722717285, -0.01071710605174303, -0.01880647800862789, 0.06302236020565033, 0.029076408594846725, -0.005760577041655779, 0.008336592465639114, -0.07831287384033203, 0.060711223632097244, -0.05736077204346657, 0.02762889489531517, 0.00496338214725256, 0.018782958388328552, -0.0051455749198794365, -0.030429329723119736, -0.03956616669893265, 0.01978202909231186, 0.03294874727725983, 0.013723638840019703, -0.07705250382423401, -0.0224776454269886, -0.004297998733818531, -0.018832964822649956, 0.02941632829606533, 0.03777988255023956, 0.006117682438343763, -0.0063704317435622215, -0.010406306944787502, -0.0027085510082542896, -0.017568912357091904, 0.0005171545199118555, -0.02287345379590988, -0.031166348606348038, 0.03364605829119682, 0.019773263484239578, 0.015977561473846436, 0.014430318959057331, 0.0461113341152668, 0.04615504667162895, 0.001469212002120912, -0.003231716575101018, -0.03324861079454422, 0.07689227908849716, -0.004343594890087843, -0.013174722902476788, 0.04315264895558357, -0.03844344988465309, 0.019690219312906265, -0.021533608436584473, -0.016191085800528526, -0.017702888697385788, 0.011969111859798431, -0.03648217394948006, 0.030079035088419914, 0.0833393782377243, -0.0658763200044632, -0.05443025752902031, 0.11598203331232071, -0.016874229535460472, -0.015582840889692307, -0.05870163440704346, 0.050655536353588104, 0.05592550337314606, -0.026488380506634712, -0.032641030848026276, 0.01356890145689249, 0.006664676126092672, -0.04060322791337967, -0.06906460970640182, -0.015487754717469215, -0.03624052181839943, 0.01201255340129137, 0.03792446851730347, 0.041568249464035034, 0.04041549190878868, 0.0010050400160253048, -0.03602695092558861, 0.022203462198376656, 0.0884849950671196, 0.03635764867067337, 0.06058092042803764, -0.00011464230919955298, -0.04269911348819733, 0.008083553053438663, -0.03724909946322441, -0.013179519213736057, 0.03854978829622269, 0.029995635151863098, -0.027002966031432152, -0.0146373575553298, -0.011774647049605846, -0.025381023064255714, -0.05437672138214111, 0.014458918012678623, -0.05161062628030777, 0.0096741933375597, -0.013554830104112625, 0.06773111969232559, -0.04983087629079819, -0.015321106649935246, -0.07052052021026611, -0.003652840619906783, -0.002006024122238159, -0.04290398955345154, -0.06301040202379227, 0.04332040622830391, 0.05328851938247681, -0.008345876820385456, -0.06289099156856537, -0.026069477200508118, 0.0027232146821916103, -0.027056733146309853, -0.00270889513194561, -0.034433092921972275, 0.016742736101150513, 0.07441800087690353, -0.08307170122861862, -0.01716325804591179, 0.04869421571493149, -0.03243296220898628, 0.04983038827776909, -0.0135736633092165, 0.012241791933774948, 0.015668794512748718, 0.03290148079395294, -0.020131511613726616, 0.02148965187370777, 0.033767424523830414, -0.04111607372760773, 0.035719938576221466, 0.05418701842427254, 0.007071806117892265, -0.004936003126204014, 0.009347662329673767, -0.05699160695075989, 0.04148155450820923, -0.05769331753253937, 0.018522197380661964, -0.0551021508872509, -0.06294555217027664, 0.021826965734362602, 0.05177679285407066, -0.03139273077249527, 0.0008049755124375224, 0.05694141983985901, -0.045809805393218994, -0.04762503132224083, 0.0036926555912941694, 0.02408151514828205, -0.012203140184283257, -0.038129474967718124, -0.002626449801027775, 0.006908182054758072, -0.022487429901957512, -0.01411377266049385, 0.05854314938187599, 0.007312085013836622, -0.008470283821225166, 0.028892578557133675, -0.027862662449479103, 0.008842425420880318, -0.06651417165994644, 0.0338134802877903, 0.012874508276581764, -0.03511425852775574, 0.03192024305462837, 0.006585066672414541, 0.047106143087148666, -0.008452040143311024, -0.03669728711247444, -0.016080176457762718, -0.02731282077729702, 0.0037477491423487663, -0.010840091854333878, 0.02669355273246765, -0.008053505793213844, 0.012497699819505215, -0.07301611453294754, -0.004948716145008802, 0.03605728968977928, 0.015928195789456367, -0.042306702584028244, 0.033520713448524475, 0.021413367241621017, 0.045153532177209854, 0.014717558398842812, -0.07163221389055252, 0.005093353800475597, 0.01860419102013111, 0.03344236686825752, -0.05731963738799095, -0.017167361453175545, -0.00038364334614016116, -0.0189101193100214, 0.03436201438307762, -0.0009367667371407151, 0.010341718792915344, 0.004927241243422031, -0.008504349738359451, -0.047383107244968414, 0.06239055097103119, 0.011862881481647491, -0.006954716984182596, -0.007952431216835976, 0.025219103321433067, 0.03035961650311947, 0.01014640275388956, 0.00112384173553437, 0.0431675985455513, -0.0024572471156716347, 0.034669484943151474, -0.061301764100790024, 0.006379430647939444, -0.039892688393592834, 0.04055371880531311, 0.0003348898608237505, -0.0359237939119339, 0.002759943250566721, 0.01468753907829523, -0.061560798436403275, -0.006724867504090071, 0.0006559768808074296, 0.009465273469686508, -0.017596708610653877, -0.055658008903265, 0.0172884464263916, -0.0284871906042099, -0.002003240631893277, 0.0495198518037796, -0.03799921274185181, 0.005737499333918095, 0.011196228675544262, 0.007885891944169998, 0.03654542565345764, -0.05751938000321388, -0.08229713141918182, -0.0002544239105191082, 0.0199762973934412, 0.004900804720818996, -0.0292469784617424, 0.004524607211351395, -0.002841222332790494, 0.025072544813156128, -0.06971201300621033, -0.0724034458398819, -0.05124053731560707, 0.020268984138965607, -0.04355557635426521, 0.01328999362885952, -0.02186565287411213, -0.016637757420539856, -0.0002656688739079982, 0.011786149814724922, 0.038440145552158356, 0.09750086814165115, -0.0012165297521278262, -0.024206968024373055, -0.019932987168431282, 0.0747712031006813, -0.01768822781741619, -0.006023344583809376, 0.0037229503504931927, 0.0010798886651173234, 0.012605239637196064, 0.00736059807240963, -0.014233127236366272, 0.04983602836728096, -0.1233506128191948, -0.011542897671461105, -0.024726927280426025, 0.00035001416108570993, -0.004258996341377497, -0.018600627779960632, 0.0037362421862781048, -0.049393583089113235, 0.029402490705251694, 0.025849640369415283, -0.028734229505062103, -0.08294031769037247, -0.046669851988554, 0.01805788464844227, -0.06708087772130966, -0.02449137158691883, 0.017141221091151237, -0.02580036036670208, -0.028341930359601974, 0.03293006494641304, 0.017359381541609764, -0.03015769273042679, -0.05253031477332115, 0.010839753784239292, -0.004871395416557789, 0.023917261511087418, 0.00944378599524498, -0.04903123900294304, -0.033708006143569946, -0.03776334226131439, -0.004813568200916052, -0.023062365129590034, 0.0032029463909566402, -0.014472917653620243, 0.014531569555401802, -0.03256566822528839, 0.007869213819503784, -0.026014188304543495, 0.044509407132864, 0.02017444558441639, -0.015146216377615929, -0.07056120038032532, 0.025480225682258606, 0.02614711783826351, 0.021505840122699738, -0.03173542395234108, 0.019808022305369377, -0.014318573288619518, 0.017841795459389687, -0.008808152750134468, 0.026174847036600113, 0.006963242311030626, -0.008070697076618671, -0.02619006298482418, 0.07111181318759918, -0.01827189326286316, 0.030624056234955788, 0.022142356261610985, -0.009744007140398026, -0.008573283441364765, 0.03801235184073448, 0.015258142724633217, -0.02197517640888691, -0.013283687643706799, -0.0553290992975235, 0.02307720109820366, -0.008184078149497509, -0.06816606223583221, -0.036775216460227966, 0.06095131114125252, -0.026431994512677193, 0.013043507933616638, 0.016083132475614548, 0.06306566298007965, -0.05991336703300476, 0.012842575088143349, -0.04413152486085892, -0.022801393643021584, 0.06630834192037582, 0.019931821152567863, -0.05199367180466652, 0.0713828057050705, 0.0007618718082085252, -0.033046040683984756, 0.03351912647485733, -0.034765128046274185, 0.021579843014478683, -0.0682959258556366, 0.043473903089761734, -0.013656829483807087, -0.05876458063721657, -0.007240740582346916, -0.02985033392906189, -0.07170556485652924, -0.01059005782008171, 0.019402701407670975, 0.06341630965471268, 0.010871456004679203, -0.024977724999189377, -0.03794219717383385, -0.09162987768650055, 0.00546433636918664, 0.01613635942339897, 0.03864716738462448, -0.02282399870455265, -0.007923894561827183, -0.0169698353856802, -0.028112584725022316, 0.008907653391361237, 0.027054468169808388, 0.05272533744573593, 0.0505405031144619, -0.07665777951478958, -0.06440632790327072, -0.013501442037522793, -0.00965801626443863, 0.006055864971131086, 0.055732376873493195, 0.01353190653026104, 0.005191271658986807, -0.05221593752503395, 0.06078851968050003, 0.05073334649205208, 0.024954915046691895, 0.011179570108652115, -0.04369577765464783, 0.026407886296510696, 0.044260259717702866, 0.015090872533619404, -0.08284811675548553, 0.0824773907661438, -0.016284652054309845, -0.01655139960348606, 0.02907676249742508, -0.0050385482609272, 0.08128970861434937, -0.05281878262758255, -0.008907160721719265, -0.004484290257096291, 0.09098199009895325, 0.01631392352283001, 0.05114378780126572, 0.0004234928928781301, 0.03186239302158356, -0.020196134224534035, -3.994363942183554e-05, -0.017607556656003, 0.04558423534035683, -0.0198229793459177, -0.034489117562770844, -0.053319450467824936, 0.039249908179044724, 0.07611404359340668, -0.019003838300704956, -0.060884520411491394, -0.024721132591366768, 0.005355290602892637, -0.05322917550802231, 0.013485122472047806, 0.026802076026797295, 0.006853948347270489, -0.008174050599336624, 0.03639069199562073, -0.024766506627202034, 0.005914362613111734, -0.01487645786255598, 0.004117701202630997, 0.005153710953891277, 0.051699381321668625, -0.02126183733344078, -0.050461675971746445, -0.008292394690215588, -0.0026050808373838663, 0.017314935103058815, -0.04071160405874252, -0.01930955983698368, 0.021704286336898804, 0.009784932248294353, 0.08283495903015137, -0.022954287007451057, 0.021573780104517937, 0.014586037956178188, -0.005625964142382145, -0.022258995100855827, -0.03139974921941757, 0.031178859993815422, 0.03546013683080673, 0.044939715415239334, 0.024848829954862595, 0.015273752622306347, -0.06992365419864655, -5.482109657575716e-33, 0.03081331215798855, -0.016805008053779602, 0.018080636858940125, -0.033862218260765076, -0.025853201746940613, 0.025937989354133606, 0.007072719279676676, 0.02240694873034954, -0.00072318414459005, -0.03149470314383507, -0.042247891426086426, -0.009011485613882542, 0.05019119009375572, 0.0443129800260067, 0.00018589130195323378, -0.031057707965373993, 0.03312641382217407, -0.03125733882188797, -0.005406337324529886, -0.0016487252432852983, 0.02007335051894188, 0.067470483481884, 0.07481256872415543, -0.05967829003930092, -0.033578190952539444, 0.009584170766174793, 0.006773022003471851, -0.040665049105882645, -0.019674019888043404, -0.028559191152453423, -0.03569699078798294, -0.012905065901577473, 0.018740875646471977, -0.03252270072698593, 0.04213609918951988, 0.015973521396517754, -0.057158712297677994, 0.012701264582574368, -0.08790083229541779, 0.0630275085568428, 0.00992131419479847, -0.06144997477531433, 0.06071072816848755, -0.015049486421048641, -0.045287370681762695, -0.014163987711071968, 0.0021002027206122875, -0.01690095290541649, -0.023613404482603073, -0.0411524772644043, -0.00805455818772316, 0.028272254392504692, -0.012577374465763569, -0.004573002923280001, 0.05490851402282715, -0.0437825545668602, -0.019694307819008827, 0.017784448340535164, -0.08213908970355988, 0.04926977679133415, 0.038984641432762146, 0.00851164385676384, 0.030260592699050903, 0.044149644672870636, 0.0051642064936459064, 0.018690023571252823, 0.05052843317389488, -0.03131657466292381, -0.010437561199069023, -0.04097561165690422, 0.027788862586021423, -0.005763924680650234, 0.04208963364362717, 0.02092345990240574, 0.10749635100364685, -0.03802727535367012, -0.029956508427858353, 0.019887009635567665, 0.043013084679841995, 0.012478501535952091, -0.001428319956175983, -0.006419596262276173, -0.050455112010240555, 0.03744271397590637, 0.03566087409853935, -0.027291517704725266, -0.013371709734201431, -0.013628494925796986, 0.02418222650885582, 0.011714121326804161, 0.0027914298698306084, 0.03380073606967926, -0.001099207205697894, -0.008442448452115059, 0.03503099083900452, -0.041494496166706085, 0.06032188981771469, 0.05258767306804657, 0.02694794535636902, -0.04218003898859024, -0.013585230335593224, -0.06362821161746979, -0.0074545033276081085, 0.028754131868481636, 0.004909994546324015, -0.0047103604301810265, 0.030038896948099136, 0.006011118181049824, -0.0329657606780529, 0.007748708128929138, -0.011610818095505238, -0.013563745655119419, 0.036266401410102844, 0.06942097097635269, 0.029101066291332245, -0.047329746186733246, 0.05926506966352463, 0.010429443791508675, -0.008602607063949108, -0.012176339514553547, 0.03886027634143829, -0.04033895954489708, 0.015327252447605133, 0.022553199902176857, -0.038610488176345825, 0.01747307926416397, -0.030292201787233353, 0.005875669419765472, -0.0273856483399868, -0.017664391547441483, 0.01444836426526308, 0.001557024079374969, 2.5400998993063695e-07, -0.02504621632397175, 7.406605436699465e-05, 0.04870535805821419, -0.046114467084407806, -0.023964526131749153, -0.004956262186169624, 0.00023422112280968577, 0.0006489145453087986, -0.03366151079535484, -0.008560249581933022, 0.0533561073243618, 0.012047240510582924, 0.05341667681932449, 0.01609032414853573, -0.027558056637644768, 0.021686982363462448, 0.007073229178786278, 0.045204341411590576, -0.03431050479412079, 0.058830294758081436, -0.00851998757570982, 0.0850532129406929, 0.013078639283776283, -0.03429771214723587, 0.04740982875227928, -0.018537577241659164, 0.010376550257205963, 0.019596124067902565, 0.06986767053604126, -0.05587783828377724, 0.02626853622496128, 0.042153891175985336, -0.03693031892180443, 0.016491789370775223, 0.039587926119565964, -0.021758683025836945, 0.04394116997718811, 0.04233677685260773, -0.04147210717201233, 0.06492038071155548, 0.003964725416153669, 0.03497865051031113, 0.007164657115936279, -0.0028318441472947598, 0.002408110536634922, 0.05273639038205147, 0.015185968019068241, -0.049141086637973785, 0.01132600475102663, -0.012244646437466145, 0.027463765814900398, -0.010346982628107071, 0.06311201304197311, 0.011747391894459724, 0.010837447829544544, -0.07813143730163574, -0.014092634432017803, -0.022869078442454338, 0.026809636503458023, -0.03608139976859093, 0.006331279873847961, -0.0021935473196208477, -0.022977150976657867, 0.012127160094678402, 0.09453258663415909, 0.011626345105469227, -0.005880742333829403, 1.859915834683987e-34, -0.028929084539413452, -0.0035912583116441965, -0.0026933990884572268, -0.0029493626207113266, -0.0077985371463000774, -0.00038651557406410575, 0.014008449390530586, -0.016346119344234467, -0.0093061039224267, -0.03108135238289833, -0.010881273075938225]

['Ridwan Al Iqbal']

1110.0214v1

Artificial Neural Network is among the most popular algorithm for supervised learning. However, Neural Networks have a well-known drawback of being a "Black Box" learner that is not comprehensible to the Users. This lack of transparency makes it unsuitable for many high risk tasks such as medical diagnosis that requires a rational justification for making a decision. Rule Extraction methods attempt to curb this limitation by extracting comprehensible rules from a trained Network. Many such extraction algorithms have been developed over the years with their respective strengths and weaknesses. They have been broadly categorized into three types based on their approach to use internal model of the Network. Eclectic Methods are hybrid algorithms that combine the other approaches to attain more performance. In this paper, we present an Eclectic method called HERETIC. Our algorithm uses Inductive Decision Tree learning combined with information of the neural network structure for extracting logical rules. Experiments and theoretical analysis show HERETIC to be better in terms of speed and performance.

Eclectic Extraction of Propositional Rules from Neural Networks

http://arxiv.org/pdf/1110.0214v1

Title Eclectic Extraction Propositional Rules Neural Networks Summary Artificial Neural Network among popular algorithm supervised learning However Neural Networks wellknown drawback Black Box learner comprehensible Users lack transparency make unsuitable many high risk task medical diagnosis requires rational justification making decision Rule Extraction method attempt curb limitation extracting comprehensible rule trained Network Many extraction algorithm developed year respective strength weakness broadly categorized three type based approach use internal model Network Eclectic Methods hybrid algorithm combine approach attain performance paper present Eclectic method called HERETIC algorithm us Inductive Decision Tree learning combined information neural network structure extracting logical rule Experiments theoretical analysis show HERETIC better term speed performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0367228165268898, 0.029489461332559586, -0.013720064423978329, 0.011697973124682903, -0.06896384060382843, -0.0035867507103830576, -0.007628391031175852, 0.046477969735860825, 0.011711702682077885, 0.007252187933772802, 0.04214801266789436, 0.019037997350096703, 0.02832217514514923, 0.028179598972201347, -0.021316105499863625, -0.0280145276337862, 0.0035659184213727713, 0.046268437057733536, 0.049925509840250015, 0.026493726298213005, 0.005755240097641945, -0.019548073410987854, -0.04019283130764961, 0.04263567551970482, 0.00966070219874382, -0.030022570863366127, 0.010496941395103931, -0.07112693041563034, -0.0009708833531476557, -0.04302867874503136, 0.03722405806183815, -0.0017192193772643805, -0.04778153821825981, 0.01508091576397419, 2.1556884348683525e-06, -0.0555398054420948, -0.04591923952102661, -0.022498736158013344, 0.029045643284916878, -0.036323729902505875, -0.0032902290113270283, 0.014444740489125252, 0.006635729689151049, -0.006302120164036751, -0.0565035305917263, -0.006565690040588379, 0.036457449197769165, 0.0978592112660408, 0.04266892373561859, 0.05028314143419266, -0.006786508951336145, -0.047279566526412964, -0.0046006846241652966, 0.01538407988846302, -0.013174544088542461, -0.0016828194493427873, 0.052919529378414154, -0.016612615436315536, -0.0015046083135530353, -0.04886694625020027, 0.014581046998500824, 0.0012054787948727608, 0.009011863730847836, 0.024247359484434128, -0.020854925736784935, 0.0229747723788023, 0.00019001204054802656, -0.03763046860694885, -0.0029907533898949623, 0.060108449310064316, -0.0174117349088192, 0.005624249577522278, 0.016611019149422646, -0.004087917972356081, -0.012857618741691113, -0.004645372740924358, 0.0009342175326310098, 0.010183523409068584, -0.09159807115793228, 0.007335098925977945, 0.0813845694065094, 0.05813215672969818, -0.010471991263329983, 0.007324864622205496, -0.04492731764912605, 0.053748805075883865, -0.022271674126386642, -0.022163689136505127, 0.05200440436601639, -0.044895660132169724, 0.011386196129024029, -0.021929161623120308, 0.05064896121621132, 0.03401878476142883, -0.012257404625415802, -0.008051533252000809, 0.01811903528869152, -0.024451900273561478, 0.08105684816837311, -0.08952692896127701, 0.0499982088804245, -0.006349093746393919, 0.014857217669487, 0.006975154392421246, -0.013283967971801758, -0.03429662063717842, -0.012985738925635815, 0.07775439321994781, -0.040242750197649, 0.05511907860636711, -0.07036910206079483, -0.009438781067728996, -0.020761102437973022, 0.07138895988464355, -0.02224784716963768, 0.002575183054432273, -0.09251115471124649, -0.03256743773818016, -0.032752588391304016, -0.014086009934544563, 0.030739810317754745, 0.03465963155031204, 0.02111775055527687, 0.011827780865132809, -0.046040866523981094, -0.008933582343161106, -0.03611738979816437, 0.04653889313340187, -0.00406921049579978, 0.011987358331680298, 0.038180019706487656, 0.004103602841496468, 0.0029295110143721104, 0.018130240961909294, 0.006612227763980627, 0.08264816552400589, 0.009848988614976406, 0.03315840661525726, -0.07187595218420029, -0.023470954969525337, 0.004859637469053268, -0.006732331123203039, 0.009797465056180954, -0.03910690173506737, 0.01136977132409811, -0.032416146248579025, -0.038639310747385025, -0.0543719083070755, -0.0035354853607714176, -0.0019406031351536512, -0.03302105888724327, 0.036785367876291275, -0.045401681214571, -0.006954025011509657, 0.028202679008245468, 0.013544299639761448, -0.02806028164923191, -0.0353173166513443, 0.01619645021855831, 0.018514219671487808, 0.0037386000622063875, -0.038464345037937164, 0.025147108361124992, -0.019442416727542877, -0.012484529055655003, -0.08547759056091309, -0.036765165627002716, -0.010623062029480934, -0.03781743347644806, 0.014427604153752327, -0.07504117488861084, 0.0588153637945652, 0.0016208268934860826, 0.0032780738547444344, 0.02838250994682312, 0.025717558339238167, 0.10834969580173492, 0.019167859107255936, 0.007526814937591553, -0.008127317763864994, 0.0541587732732296, 0.0026742166373878717, 0.024764500558376312, -0.011979070492088795, -0.05196389555931091, -0.02104862965643406, -0.08272261917591095, 0.005298597272485495, 0.00807156041264534, -0.07787558436393738, 0.00614260695874691, 0.0044358596205711365, -0.012123402208089828, -0.02670927345752716, 0.053068727254867554, 0.0033584549091756344, 0.0047440677881240845, -0.0029281897004693747, 0.060549329966306686, 0.0234821867197752, -0.060907550156116486, -0.046229880303144455, 0.0450119748711586, -0.0006625654059462249, -0.012687135487794876, -0.07302084565162659, -0.018003541976213455, -0.010278552770614624, -0.03278543800115585, -0.04399224370718002, -0.03125624731183052, -0.02358158864080906, 0.0028643859550356865, -0.0492919497191906, 0.016038477420806885, 0.05934841185808182, 0.015824981033802032, -0.0021654488518834114, -0.053076084703207016, 0.013758073560893536, -0.021402480080723763, 0.053585465997457504, -0.005122622009366751, 0.049028430134058, 0.007164360024034977, 0.020025450736284256, 0.025491531938314438, 0.02337564341723919, 0.04174099490046501, 0.020701071247458458, 3.550701194399153e-06, 0.02822723425924778, 0.02619931474328041, -0.03634190186858177, -0.06022510677576065, 0.0014640111476182938, -0.032329387962818146, -0.024861281737685204, 0.037215642631053925, -0.02111893706023693, 0.0158725343644619, -0.09784634411334991, -0.029345430433750153, -0.0013392549008131027, -0.019325928762555122, -0.03687509149312973, 0.006290379911661148, -0.030391467735171318, -0.005990886129438877, 0.030561715364456177, 0.001806396059691906, -0.04614964500069618, 0.04278528690338135, -0.013942197896540165, -0.027950139716267586, -0.017621459439396858, -0.08568989485502243, 0.019434159621596336, 0.009920093230903149, 0.04160705581307411, 0.01797131635248661, -0.06024034693837166, -0.0022660652175545692, -0.06152397766709328, 0.06825781613588333, -0.02188125252723694, -0.03049243614077568, -0.04209968447685242, -0.015517103485763073, 0.02704080007970333, -0.019045868888497353, -0.01873408816754818, -0.009447469376027584, 0.0010732930386438966, -0.022669028490781784, -0.022880088537931442, 0.03267427533864975, -0.01922709308564663, -0.010249876417219639, 0.05198416858911514, 0.023416811600327492, -0.026451684534549713, -0.011532658711075783, -0.02611638233065605, -0.04357067123055458, 0.02978072687983513, 0.018104899674654007, -0.04539938643574715, 0.004281190223991871, -0.03637116029858589, 0.0040199775248765945, 0.015787802636623383, 0.001087877550162375, -0.038308385759592056, -0.0386224128305912, -0.03592891991138458, -0.04280081391334534, 0.05004148557782173, 0.045342836529016495, -0.006807358004152775, 0.01389409601688385, 0.002906185109168291, 0.001747749513015151, 0.006480389274656773, -0.0230205450206995, 0.06435426324605942, 0.029411837458610535, -0.011307296343147755, 0.0009635260212235153, 0.006537747569382191, 0.06799006462097168, 0.02336392179131508, 0.011415509507060051, 0.09277372062206268, -0.005535244010388851, -0.008793375454843044, -0.07157893478870392, -0.017061688005924225, -0.006990534253418446, 0.0431242436170578, 0.03581254556775093, 0.011286254040896893, 0.0881265178322792, 0.03351617604494095, 0.045462559908628464, -0.06034799665212631, -0.07078763097524643, -0.026584943756461143, -0.03590412437915802, -0.011573687195777893, 0.026181260123848915, 0.05660605803132057, -0.027795936912298203, 0.0012018762063235044, -0.028036100789904594, 0.03920372575521469, -0.049787309020757675, 0.05547603592276573, -0.024332132190465927, -0.012387002818286419, -0.0156887024641037, -0.02934037521481514, -0.04139469936490059, -0.04304250702261925, 0.03231470659375191, -0.0045364126563072205, -0.03602582961320877, 0.04323652759194374, -0.00560374790802598, 0.03146323934197426, -0.014773694798350334, 0.028216073289513588, -0.026758350431919098, -0.008490189909934998, -0.015792394056916237, -0.0052930694073438644, 0.017692044377326965, -0.01322806067764759, -0.013784796930849552, 0.040929943323135376, 0.025315718725323677, 0.05632631853222847, -0.08183072507381439, -0.004124544560909271, -0.044249434024095535, 0.03392694517970085, -0.036088988184928894, -0.02030724659562111, 0.02999439835548401, 0.03190740942955017, -0.03685950115323067, -0.051858704537153244, 0.058539096266031265, 0.041972607374191284, 0.012341678142547607, -0.02207685075700283, 0.008952976204454899, -0.035191331058740616, -0.10361887514591217, -0.045950666069984436, 0.02393295243382454, -0.03358202427625656, 0.0007578007061965764, 0.0008756053284741938, 0.013812887482345104, -0.06464030593633652, -0.06426559388637543, 0.012209051288664341, -0.027330566197633743, 0.027927258983254433, -0.0024078150745481253, -0.06341149657964706, -0.06756169348955154, -0.022559061646461487, -0.03986725956201553, -0.03937307745218277, -0.04426035284996033, 0.017413929104804993, 0.0003488139482215047, -0.022934984415769577, 0.010148159228265285, -0.07374686747789383, 0.0008532683714292943, 0.03261556476354599, -0.01105986163020134, 0.010101739317178726, 0.014997538179159164, 0.05013788491487503, -0.04998914524912834, -0.04263515770435333, 0.009454489685595036, -0.020674359053373337, 0.002960037440061569, -0.0418364480137825, 0.05591600388288498, 0.043931834399700165, 0.022213075309991837, -0.04055444523692131, 0.049742210656404495, -0.0213505569845438, 0.007055011577904224, 0.06894592940807343, 0.0760578140616417, -0.014400718733668327, -0.02770490013062954, -0.047364238649606705, 0.055112291127443314, 0.03588078171014786, -0.0057883127592504025, -0.0040040710009634495, 0.00915228109806776, -0.02506103739142418, -0.005813712254166603, 0.021476276218891144, -0.005669965874403715, 0.014351092278957367, 0.03244585916399956, -0.051573846489191055, -0.05899803712964058, -0.06024065613746643, 0.005507388152182102, -0.023406242951750755, 0.06247100979089737, 0.051971640437841415, 0.033969756215810776, 0.0743216872215271, 0.020863257348537445, -0.0288174357265234, -0.01571636274456978, 0.09406736493110657, -0.017065223306417465, -0.03313615173101425, 0.039609406143426895, 0.016968395560979843, -0.0009289702866226435, -0.03925706818699837, -0.04252123087644577, 0.0978236123919487, -0.002348110778257251, 0.017536817118525505, 0.03947720676660538, 0.01726241409778595, -0.02826717123389244, -0.0482170432806015, 0.010549564845860004, -0.008786517195403576, 0.003862972604110837, 0.03656352683901787, -0.06645692139863968, 0.04706248641014099, -0.02173599600791931, 0.009810474701225758, -0.011489088647067547, 0.005956620443612337, 0.0681394636631012, 0.020158521831035614, -0.016383379697799683, -0.04761452600359917, 0.02087138034403324, 0.06637196242809296, 0.04751083627343178, 0.04141046479344368, 0.01903395727276802, -0.06722380965948105, -0.02555524930357933, 0.01278507150709629, -0.0157904252409935, -0.029146529734134674, -0.0010202600387856364, 0.028387896716594696, 0.017689218744635582, 0.016147688031196594, -0.008002220652997494, -0.0520755872130394, 0.022931275889277458, -0.03844209760427475, 0.02524610608816147, 0.05269594490528107, 0.05877212435007095, 0.03247220069169998, 0.00553556066006422, -0.032060883939266205, -0.004132044035941362, -0.014049534685909748, 0.018940065056085587, 0.060725871473550797, -0.016422782093286514, 0.08745107054710388, 0.026656316593289375, -0.014769021421670914, -0.0730179026722908, 0.033857785165309906, 0.01149189006537199, 0.0158447977155447, -0.022712770849466324, 0.05239503085613251, 0.027501730248332024, -0.014695724472403526, -0.04962636157870293, 0.009713396430015564, 0.020649604499340057, -0.01029147207736969, 0.07001396268606186, -0.041914865374565125, 0.06445599347352982, 0.018147820606827736, -0.0065298136323690414, -0.029926465824246407, -0.060654617846012115, 0.030268089845776558, -0.03898525610566139, -0.033792536705732346, -0.029006069526076317, -0.06413537263870239, -0.04314052686095238, 0.009544024243950844, -0.009279297664761543, 0.02127978391945362, -0.035723280161619186, -0.014348962344229221, -0.05333009362220764, 0.03149789199233055, 0.009902956895530224, 0.04585050418972969, 0.03332013264298439, 0.018613066524267197, 0.0073134624399244785, 0.05544651299715042, 0.0388018973171711, -0.05510203540325165, -0.028527703136205673, 0.02455885149538517, -0.02025522291660309, 0.007322878576815128, -0.004864207468926907, -5.870833884449138e-33, -0.00020174267410766333, -0.01903396099805832, 0.02800225093960762, -0.0025340470019727945, -0.027515361085534096, 0.006073366850614548, -0.01671193167567253, -0.017461804673075676, -0.00869301613420248, 0.045140381902456284, -0.012813171371817589, -0.024631081148982048, 0.021638987585902214, -0.009432991966605186, 0.05486340448260307, -0.005189474206417799, -0.030203266069293022, 0.01759183406829834, 0.00835929811000824, -0.0360894575715065, 0.03324534744024277, 0.04731230065226555, 0.027936017140746117, -0.06524787843227386, -0.03118824027478695, 0.08218957483768463, 0.02674774080514908, 0.006014873739331961, -0.06246047839522362, 0.03372139483690262, 0.02663922682404518, -0.01449503656476736, 0.04560650885105133, -0.007024632301181555, 0.023824086412787437, -0.0034764795564115047, -0.07016096264123917, -0.05620468780398369, -0.02280315011739731, -0.028711171820759773, -0.024537358433008194, -0.0186176560819149, 0.10185551643371582, 0.017444780096411705, -0.000855579215567559, 0.011117445304989815, 0.03902662545442581, -0.03324899449944496, -0.004110720008611679, -0.027606375515460968, -0.0475747287273407, 0.04985639080405235, 0.031702037900686264, 0.0352778360247612, -0.019334735348820686, 0.015536599792540073, -0.019099395722150803, 0.007311293855309486, -0.034141309559345245, -0.007387121673673391, 0.0010525134857743979, 0.012745773419737816, -0.049310218542814255, 0.006218955386430025, -0.009018182754516602, 0.019729632884263992, 0.02216457761824131, -0.02908775955438614, -0.05319385603070259, 0.02616298571228981, -0.050192318856716156, 0.0937754213809967, 0.031716667115688324, -0.009659480303525925, 0.05324807018041611, -0.04984185844659805, -0.09161099791526794, 0.018950166180729866, 0.027471374720335007, 0.029865313321352005, 0.0030017837416380644, -0.015580037608742714, -0.06801305711269379, 0.012757532298564911, 0.053077053278684616, -0.02834264561533928, -0.009829631075263023, -0.023003289476037025, 0.0008350407006219029, -0.01944470778107643, 0.004833964630961418, 0.007390995044261217, -0.03280121460556984, -0.019551262259483337, 0.07663506269454956, -0.03652772307395935, 0.05312599986791611, -0.0004903908120468259, -0.01672942005097866, -0.009494821541011333, -0.05764501541852951, -0.020338162779808044, -0.01885799877345562, -0.030625127255916595, 0.04098942503333092, 0.02080567553639412, 0.02132396027445793, -0.03854433074593544, -0.003906117519363761, -0.020763074979186058, 0.04476788640022278, -0.030731694772839546, 0.011351536959409714, 0.035940445959568024, -0.00499157328158617, 0.0416463278234005, -0.00138065533246845, 0.015328778885304928, 0.01820867508649826, 0.013680785894393921, -0.04652255401015282, -0.021021652966737747, 0.05378337204456329, 0.013617996126413345, -0.028232453390955925, -0.012578414753079414, -0.024126341566443443, 0.0034983190707862377, -0.021814556792378426, -0.014468434266746044, 0.008365216664969921, 0.024882609024643898, 2.8724986123052076e-07, 0.014572979882359505, 0.008785514160990715, -0.0016640146495774388, -0.01674499176442623, 0.017855575308203697, 0.028277335688471794, -0.012183908373117447, -0.023566756397485733, -0.004762300290167332, -0.004757006652653217, 0.05177507549524307, -0.03435719758272171, 2.5094701413763687e-05, 0.06009221449494362, -0.038698311895132065, -0.07140613347291946, -0.010387880727648735, -0.062471192330121994, -0.012229524552822113, 0.023012347519397736, 0.08533439040184021, 0.06320749223232269, 0.04588084667921066, -0.03796626627445221, 0.02702648937702179, 0.008373196236789227, -0.04108639433979988, 0.017926791682839394, -0.0022293790243566036, 0.022153537720441818, 0.05331358313560486, -0.04244983196258545, 0.008186462335288525, 0.06538720428943634, 0.0009504614281468093, 0.019157927483320236, 0.011679869145154953, 0.07858985662460327, -0.046818554401397705, 0.018571270629763603, 0.024673085659742355, -0.02806415781378746, 0.0436859168112278, -0.009296530857682228, 0.04252328351140022, -0.03160678595304489, -0.04835622385144234, -0.01486616488546133, 0.01220883708447218, -0.004797695204615593, 0.05353385955095291, 0.006724557839334011, -0.00887528620660305, -0.004981137812137604, -0.00165683648083359, -0.01084923092275858, 0.0060872710309922695, -0.050301387906074524, 0.03031410276889801, 0.04896154627203941, 0.003711005672812462, -0.01702498272061348, 0.07145720720291138, 0.01964483968913555, 0.04520171135663986, -0.0473838709294796, -0.0022948365658521652, 2.7808263485332356e-34, -0.018210284411907196, -0.017543382942676544, -0.008208928629755974, 0.013656575232744217, 0.008992067538201809, 0.03041096217930317, -0.0008209174848161638, 0.03708753362298012, -0.034153252840042114, -0.024916423484683037, -0.018491020426154137]

['Arnab Ghosh', 'Viveka Kulharia', 'Vinay Namboodiri']

1612.01294v1

Communicating and sharing intelligence among agents is an important facet of achieving Artificial General Intelligence. As a first step towards this challenge, we introduce a novel framework for image generation: Message Passing Multi-Agent Generative Adversarial Networks (MPM GANs). While GANs have recently been shown to be very effective for image generation and other tasks, these networks have been limited to mostly single generator-discriminator networks. We show that we can obtain multi-agent GANs that communicate through message passing to achieve better image generation. The objectives of the individual agents in this framework are two fold: a co-operation objective and a competing objective. The co-operation objective ensures that the message sharing mechanism guides the other generator to generate better than itself while the competing objective encourages each generator to generate better than its counterpart. We analyze and visualize the messages that these GANs share among themselves in various scenarios. We quantitatively show that the message sharing formulation serves as a regularizer for the adversarial training. Qualitatively, we show that the different generators capture different traits of the underlying data distribution.

Message Passing Multi-Agent GANs

http://arxiv.org/pdf/1612.01294v1

Title Message Passing MultiAgent GANs Summary Communicating sharing intelligence among agent important facet achieving Artificial General Intelligence first step towards challenge introduce novel framework image generation Message Passing MultiAgent Generative Adversarial Networks MPM GANs GANs recently shown effective image generation task network limited mostly single generatordiscriminator network show obtain multiagent GANs communicate message passing achieve better image generation objective individual agent framework two fold cooperation objective competing objective cooperation objective ensures message sharing mechanism guide generator generate better competing objective encourages generator generate better counterpart analyze visualize message GANs share among various scenario quantitatively show message sharing formulation serf regularizer adversarial training Qualitatively show different generator capture different trait underlying data distribution Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.017849059775471687, 0.05504539608955383, 0.0005229501985013485, 0.022542985156178474, -0.021121103316545486, 0.0011106240563094616, 0.05898742750287056, -0.0020006345584988594, -0.0388215146958828, 0.001636327593587339, -0.030131246894598007, -0.0034502067137509584, -0.03480396419763565, 0.010919131338596344, 0.07142531871795654, -0.07112109661102295, -0.01972218230366707, 0.04145536571741104, -0.0006988475215621293, -0.06189609318971634, 0.008664766326546669, -0.015629861503839493, 0.023907490074634552, 0.041186634451150894, -0.07863707095384598, -0.01704394444823265, -0.03816630318760872, 0.006799623370170593, 0.062263019382953644, -0.020321272313594818, 0.012476541101932526, 0.01665080152451992, -0.0026107553858309984, 0.01517548132687807, 2.515009100534371e-06, 0.003200558479875326, 0.004851134959608316, -0.018169591203331947, 0.0262246485799551, 0.003012190107256174, 0.04901689291000366, 0.027543382719159126, -0.0309162475168705, 0.018792198970913887, -0.06295734643936157, -0.03506192937493324, 0.04785538092255592, 0.03998600319027901, 0.029063250869512558, 0.060672685503959656, -0.030176818370819092, -0.035445112735033035, 0.009279021061956882, -0.04201780632138252, 0.00016669125761836767, -0.08906787633895874, 0.003998560830950737, 0.04086211696267128, -0.015963135287165642, -0.012864973396062851, -0.02827160432934761, 0.0327330157160759, 0.046169593930244446, 0.007004829123616219, 0.02165355160832405, 0.06527111679315567, 0.03979460895061493, -0.02636033482849598, -0.029051775112748146, 0.007251904346048832, -0.038032811135053635, 0.048938196152448654, -0.011941678822040558, -0.009813783690333366, 0.0006544669740833342, 0.011187425814568996, -0.043789543211460114, 0.022235708311200142, -0.032272543758153915, 0.015173572115600109, -0.04142799973487854, 0.016453739255666733, 0.0025305068120360374, 0.005779203027486801, -0.02110922522842884, -0.020082635805010796, 0.01669762097299099, 0.04296813905239105, -0.052531898021698, 0.0199902206659317, -0.07647407799959183, -0.04677668586373329, 0.01851068250834942, 0.02570091001689434, -0.022102314978837967, -0.024097176268696785, -0.04982514679431915, -0.05092799291014671, 0.01693831756711006, -0.01293148472905159, 0.05457973852753639, -0.061287716031074524, -0.014289969578385353, 0.015685705468058586, -0.011232931166887283, 0.015045111067593098, -0.03537667542695999, 0.06489545851945877, -0.01941142976284027, -0.04533567652106285, -0.0256314966827631, -0.028687618672847748, -0.006842419039458036, 0.044889405369758606, -0.02155729942023754, -0.0515081062912941, -0.04788227006793022, 0.01214610692113638, -0.050724029541015625, 0.011548253707587719, 0.022442948073148727, 0.0865892618894577, -0.03362775593996048, -0.020201582461595535, 0.001159006031230092, -0.02848374843597412, -0.06338299810886383, 0.02715723030269146, 0.01470533013343811, -0.0343865305185318, 0.002581291599199176, 0.0022330591455101967, 0.008005054667592049, 0.03804550692439079, -0.0002985416795127094, 0.10802377015352249, -0.037732191383838654, 0.027203133329749107, -0.009717673063278198, -0.029225360602140427, 0.03298496827483177, -0.06235013157129288, 0.010273275896906853, -0.025366999208927155, 0.01792156882584095, -0.05260299891233444, -0.021705884486436844, -0.030186692252755165, -0.00213353312574327, -0.019483979791402817, 0.029133422300219536, 0.07934490591287613, 0.014995193108916283, -0.031180867925286293, 0.05542762950062752, 0.03702300786972046, 0.001247555366717279, 0.024733293801546097, 0.05872334912419319, 0.07215910404920578, -0.0011768628610298038, 0.03152312710881233, 0.009557322598993778, -0.0012055074330419302, 0.03375425189733505, 0.01612035371363163, 0.08409087359905243, -0.07173044979572296, -7.62539857532829e-05, 0.03693656995892525, 0.002830957528203726, 0.04970261827111244, -0.03272506967186928, -0.04372240975499153, 0.04763716086745262, 0.031208066269755363, 0.04023599252104759, 0.02947254851460457, 0.008952277712523937, 0.04754810407757759, -0.052546583116054535, 0.0068933493457734585, 0.008051341399550438, 0.10370934009552002, 0.0018144311616197228, -0.03867584094405174, -0.010302537120878696, 0.09882495552301407, -0.04428250342607498, -0.024787748232483864, 0.04383212700486183, -0.006950776558369398, -0.00885977316647768, -0.017659682780504227, 0.03429311886429787, 0.03474104031920433, -0.04797510430216789, -0.08775664865970612, -0.008492548950016499, -0.02782297506928444, 0.01895408146083355, -0.046657782047986984, 0.022053103893995285, -0.021187052130699158, 0.011103037744760513, 0.034147825092077255, -0.015048082917928696, 0.014959488995373249, -0.028215067461133003, -0.0062150112353265285, -0.02336873859167099, -0.01909763365983963, 0.016863305121660233, -0.059166714549064636, -0.04734955355525017, -0.02639392577111721, -0.028621554374694824, 0.05285344645380974, -0.013399826362729073, 0.010309233330190182, 0.017260955646634102, 0.07453542202711105, 0.032846733927726746, 0.023353755474090576, 0.008972681127488613, 0.043158359825611115, 0.02273775450885296, 0.010402366518974304, 0.0479348823428154, -0.005657833069562912, -0.003430594690144062, -0.002959025325253606, 0.0005955748492851853, -0.013662924990057945, -0.06720316410064697, 0.05838050693273544, -0.04338259994983673, -0.05433962121605873, -0.03591744601726532, -0.08507923036813736, 0.03329269215464592, 0.018877191469073296, -0.037855055183172226, -0.030899066478013992, 0.03876380994915962, 0.015208333730697632, -0.03350355476140976, -0.035344578325748444, 0.003631100058555603, 0.032571617513895035, 0.04236874729394913, -0.0003120980109088123, 0.05121515318751335, -0.012758943252265453, -0.06793307512998581, 0.00214122305624187, 0.06878266483545303, 0.03445256128907204, -0.03409068286418915, 0.043092913925647736, 0.02279893308877945, 0.03545090928673744, 0.01213051937520504, 0.010130098089575768, 0.02339472994208336, 0.002181050833314657, 0.002479217015206814, -0.02337605692446232, 0.01474760752171278, 0.006056767888367176, -0.02680118754506111, 0.02766929380595684, -0.010561991482973099, 0.020772991701960564, 0.0097474604845047, -0.06733771413564682, 0.12058472633361816, 0.0278684850782156, -0.04887077584862709, 0.024262450635433197, 0.022939294576644897, 0.04608405753970146, -0.016786443069577217, 0.02932358719408512, 0.015260877087712288, 0.03724170848727226, 0.0912964940071106, -0.04567102715373039, -0.030642123892903328, 0.009176429361104965, -0.02835347130894661, 0.044454824179410934, -0.023179586976766586, -0.05993817746639252, 0.007852431386709213, -0.004610945470631123, 0.010780719108879566, 0.05868803709745407, 0.009193813428282738, 0.03488796949386597, -0.019907522946596146, 0.003561181016266346, -0.07116544991731644, 0.018205322325229645, -0.013067115098237991, 0.007667750585824251, -0.009804848581552505, -0.014668449759483337, 0.0023058857768774033, 0.030478056520223618, 0.04296945780515671, -0.013893517665565014, -0.02634771727025509, 0.06184675544500351, 0.004918006248772144, -0.08814363181591034, -0.007066749967634678, 0.02901453897356987, 0.017236394807696342, -0.05585707351565361, -0.05356069281697273, -0.018691156059503555, 0.03852744773030281, 0.015639226883649826, -0.03112884797155857, 0.012723032385110855, 0.0005618759314529598, 0.019164366647601128, 0.07923923432826996, 0.0006985644577071071, 0.03629488870501518, 0.006946575827896595, -0.00028697305242531, -0.07813220471143723, 0.02338331937789917, 0.05399524047970772, 0.028519945219159126, -0.03169722482562065, -0.03494539111852646, -0.03458792343735695, -0.025287454947829247, -0.03242538869380951, -0.0258034560829401, 0.03321461006999016, 0.04460085555911064, 0.03973928466439247, 0.01725829392671585, -0.02936639077961445, -0.002466730773448944, -0.006728417705744505, -0.00588009599596262, -0.023632502183318138, -0.013976944610476494, -0.0047138407826423645, -0.010043754242360592, 0.04352712631225586, 0.01707703061401844, -0.04622606933116913, -0.03075850009918213, -0.032284460961818695, 0.030922256410121918, 0.08667780458927155, -0.027156542986631393, 0.021750090643763542, -0.05040349066257477, -0.038589779287576675, -0.0330951027572155, 0.043259333819150925, -0.011080832220613956, -0.028223002329468727, 0.06688211858272552, -0.023000089451670647, 0.04770837724208832, -0.0023218386340886354, -0.014846003614366055, -0.029044754803180695, 0.014822261407971382, 0.022016486153006554, -0.029842739924788475, -0.006289882119745016, 0.029160138219594955, -0.05644432455301285, 0.005874553695321083, -0.016835184767842293, -0.03663250803947449, -0.03461134061217308, -0.021797161549329758, -0.016112539917230606, -0.027228135615587234, 0.06521864235401154, 0.008642271161079407, 0.00929374061524868, -0.013267881236970425, 0.041134320199489594, 0.004602309316396713, -0.028191814199090004, -0.020067796111106873, -0.011279348284006119, 0.07411842793226242, -0.009625343605875969, 0.027770867571234703, 0.057693563401699066, -0.019764196127653122, -0.014641128480434418, -0.08143356442451477, 0.0560481883585453, 0.07606992870569229, 0.035135284066200256, 0.021432608366012573, -0.04878168925642967, -0.028938164934515953, 0.03946034982800484, 0.024412311613559723, -0.01976599544286728, 0.06037153676152229, 0.0035608636680990458, -0.0026023644022643566, 0.01249889936298132, 0.05342373624444008, 0.029035255312919617, 0.04423980787396431, 0.06036437675356865, -0.010016490705311298, -0.022190868854522705, -0.030036723241209984, -0.04100717976689339, 0.020314080640673637, 0.03844444453716278, 0.013782737776637077, -0.004140547011047602, 0.01607147417962551, -0.04772327095270157, -0.007200675085186958, 0.00538242282345891, -0.09303385764360428, -0.02448778785765171, 0.005215083248913288, -0.0013971077278256416, -0.03537881746888161, -0.09150226414203644, -0.06957907974720001, 0.036882512271404266, 0.019539855420589447, -0.010681888088583946, -0.028311576694250107, -0.041454896330833435, -0.0010943516390398145, -0.0005330416024662554, -0.0941893607378006, 0.01713106594979763, -0.001680728979408741, 0.013401038944721222, -0.048280972987413406, 0.006654304452240467, -0.03491752967238426, -0.0016712365904822946, 0.007598238065838814, -0.06974238157272339, -0.028091058135032654, -0.02963205985724926, 0.05597252771258354, -0.00995011068880558, 0.0066930558532476425, 0.010151605121791363, -0.020811235532164574, 0.06760681420564651, 0.011833435855805874, 0.02254370041191578, 0.01694149523973465, 0.051122769713401794, 0.02675449475646019, -0.014118997380137444, 0.02379191666841507, -0.00042861432302743196, 0.08154123276472092, 0.0039057873655110598, -0.014927207492291927, -0.03922849893569946, -0.0012571074767038226, 0.01348902564495802, -0.05343577265739441, -0.039606932550668716, -0.008444614708423615, 0.012380185537040234, -0.0436716228723526, 0.0029889787547290325, -0.02827989123761654, 0.01801813393831253, -0.07419683784246445, -0.0025482652708888054, 0.004763660486787558, -0.0035311735700815916, 0.05059463903307915, 0.014055505394935608, 0.05765561759471893, -0.002749919891357422, -0.03218493238091469, 0.013005523942410946, -0.009381353855133057, 0.02667222172021866, -0.04178386554121971, 0.041550058871507645, 0.021275939419865608, -0.028182780370116234, 0.004926253110170364, 0.002526394324377179, 0.013247792609035969, 0.02212182618677616, 0.03011707030236721, -0.025727232918143272, 0.022595899179577827, 0.04366263002157211, -0.03632989898324013, -0.05959055945277214, -0.01583710126578808, 0.07940145581960678, 0.08432167023420334, 0.08536955714225769, 0.011828717775642872, -0.05573370307683945, 0.031217731535434723, -0.01143149845302105, 0.05041263997554779, -0.007197924889624119, -0.04703801870346069, 0.0165540874004364, -0.012009665369987488, 0.021824896335601807, -0.05847001075744629, 0.071995310485363, -0.004620216321200132, 0.014653916470706463, -0.07317448407411575, -0.012955542653799057, -0.027978362515568733, -0.02679780311882496, 0.0447002574801445, -0.04596351832151413, 0.02888677641749382, 0.049644771963357925, 0.016846749931573868, 0.01406127493828535, -0.07452510297298431, 0.017105035483837128, 0.03737471625208855, 0.01214759424328804, 0.025530165061354637, 0.028761209920048714, -0.029333626851439476, -0.04945521429181099, -0.0071106841787695885, -0.028775112703442574, -0.01660076715052128, 0.01901295781135559, -0.0015336184296756983, -7.121263061400469e-33, -0.0182779673486948, -0.04829737916588783, 0.02121254988014698, -0.03642018884420395, -0.02684863470494747, -0.005627091974020004, -0.024309054017066956, -0.0670526996254921, 0.01830483041703701, 0.015301673673093319, -0.00939642172306776, 0.019323501735925674, 0.0016079741762951016, 0.028135759755969048, 0.010872532613575459, 0.016019539907574654, 0.06375933438539505, -0.01060241088271141, 0.011812547221779823, 0.044389836490154266, 0.014326808042824268, 0.04210668429732323, 0.02329081855714321, -0.039012014865875244, -0.037177205085754395, 0.002015394391492009, -0.04116590693593025, -0.04687797278165817, -0.011675591580569744, -0.0206238254904747, 0.023347189649939537, -0.05730803310871124, 0.01122252643108368, -0.04750528559088707, -0.03911495581269264, -0.02025974914431572, -0.026391983032226562, -0.020140687003731728, -0.06494247913360596, -0.009634177200496197, -0.10681148618459702, -0.04270954430103302, 0.006597613915801048, -0.026300620287656784, 0.014437248930335045, -0.038636282086372375, 0.045716043561697006, 0.011833361349999905, -0.003929531201720238, -0.01748189516365528, -0.0386165976524353, -0.004274862818419933, -0.03462745249271393, -0.02083277888596058, 0.012240584008395672, -0.020298680290579796, 0.010048598051071167, -0.026228290051221848, -0.03660304471850395, 0.05022118240594864, -0.009687977842986584, -0.002477560192346573, 0.029291212558746338, 0.04906488209962845, 0.05187895521521568, 0.030215073376893997, 0.02069319784641266, -0.060923557728528976, -0.046856969594955444, -0.017679469659924507, -0.015304122120141983, 0.07025900483131409, 0.04728517681360245, 0.04351751506328583, 0.008809764869511127, -0.052226126194000244, -0.03463219478726387, 0.05910796672105789, 0.017460308969020844, 0.03548015281558037, 0.00803601648658514, 0.035311874002218246, 0.030696433037519455, -0.012191957794129848, 0.03803242743015289, -0.054996516555547714, 0.010120228864252567, -0.07328131049871445, -0.003048275364562869, 0.007601303979754448, -0.014642158523201942, 0.004346461966633797, 0.02203838899731636, -0.06104821711778641, 0.02025979571044445, -0.009879764169454575, 0.005958115216344595, 0.028311872854828835, -0.0068784612230956554, -0.049466244876384735, -0.07052849978208542, -0.010284855030477047, 0.043194424360990524, 0.05152156949043274, -0.010123728774487972, 0.042596325278282166, 0.05483769252896309, 0.018789350986480713, 0.05192314460873604, -0.025690538808703423, -0.04639435559511185, 0.03839358687400818, 0.029388897120952606, -0.048629458993673325, -0.020694086328148842, -0.026805788278579712, -0.036381013691425323, -0.02105468139052391, 0.010824067518115044, -0.0005785780376754701, -0.024371935054659843, 0.0181165412068367, -0.00827772542834282, 0.025230346247553825, -0.04344926029443741, 0.031248752027750015, -0.08580297976732254, -0.034518904983997345, 0.05284767225384712, -0.04657822847366333, -0.05142951011657715, -0.03326636552810669, 3.0695198915964284e-07, -0.03702384606003761, -0.025227319449186325, 0.02083980105817318, 0.025082215666770935, -0.001270241686142981, 0.021335676312446594, 0.01376489456743002, 0.06439363956451416, -0.047847501933574677, 0.028623241931200027, 0.02336575649678707, 0.052947964519262314, -0.002940301550552249, 0.021934939548373222, -0.030973637476563454, 0.023653486743569374, -0.027353735640645027, -0.0071481396444141865, 0.002263440517708659, -0.020041057839989662, 0.030920086428523064, 0.00907246395945549, 0.036235395818948746, -0.00504017248749733, 0.06713179498910904, 0.009918810799717903, 0.03773060068488121, 0.005361791234463453, 0.022321444004774094, 0.007683396805077791, 0.00552133284509182, 0.014699609018862247, -0.015049425885081291, 0.030940623953938484, 0.011316431686282158, -0.04565070942044258, -0.01762879081070423, -0.004764961078763008, -0.004993736743927002, -0.027969757094979286, -0.011420592665672302, 0.006408461835235357, 0.013505901210010052, -0.023288192227482796, 0.02819412387907505, -0.08111529797315598, -0.07179158926010132, 0.010608552955091, 0.0327584333717823, 0.009206611663103104, 0.0020588054321706295, -0.0069323196075856686, -0.003812666516751051, -0.0366070419549942, 0.0062808082439005375, 0.007866636849939823, 0.014597767032682896, -0.028162425383925438, 0.03391855210065842, -0.02981097623705864, -0.0368252657353878, -0.058067094534635544, 0.001060350565239787, -0.02133246324956417, 0.01112794503569603, 0.029083387926220894, -0.04193706810474396, 2.1390284735033446e-34, -0.017273180186748505, 0.016426080837845802, -0.022414682433009148, 0.012271552346646786, 0.005912743508815765, 0.00035986502189189196, -0.013990109786391258, -0.010971516370773315, 0.013750840909779072, 0.04427570477128029, -0.06632475554943085]

['Tong Che', 'Yanran Li', 'Athul Paul Jacob', 'Yoshua Bengio', 'Wenjie Li']

1612.02136v5

Although Generative Adversarial Networks achieve state-of-the-art results on a variety of generative tasks, they are regarded as highly unstable and prone to miss modes. We argue that these bad behaviors of GANs are due to the very particular functional shape of the trained discriminators in high dimensional spaces, which can easily make training stuck or push probability mass in the wrong direction, towards that of higher concentration than that of the data generating distribution. We introduce several ways of regularizing the objective, which can dramatically stabilize the training of GAN models. We also show that our regularizers can help the fair distribution of probability mass across the modes of the data generating distribution, during the early phases of training and thus providing a unified solution to the missing modes problem.

Mode Regularized Generative Adversarial Networks

http://arxiv.org/pdf/1612.02136v5

Title Mode Regularized Generative Adversarial Networks Summary Although Generative Adversarial Networks achieve stateoftheart result variety generative task regarded highly unstable prone miss mode argue bad behavior GANs due particular functional shape trained discriminator high dimensional space easily make training stuck push probability mass wrong direction towards higher concentration data generating distribution introduce several way regularizing objective dramatically stabilize training GAN model also show regularizers help fair distribution probability mass across mode data generating distribution early phase training thus providing unified solution missing mode problem Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.0021598569583147764, 0.08404155820608139, -0.019086865708231926, -0.008449694141745567, 0.03577665239572525, -0.025913136079907417, 0.005626949481666088, 0.00010370239760959521, -0.04340387135744095, 0.051369521766901016, -0.003550903871655464, 0.015018542297184467, -0.02204766683280468, 0.033727481961250305, 0.05946401134133339, -0.08294019103050232, 0.006223800592124462, 0.0439346544444561, -0.02140018157660961, -0.03446054458618164, 0.04525749385356903, -0.02703564055263996, -0.0024718253407627344, 0.041189443320035934, -0.06883712857961655, 0.017239082604646683, -0.0219870712608099, 0.02369675599038601, 0.051904454827308655, -0.025139952078461647, 0.056948449462652206, 0.025695256888866425, 0.007340466137975454, 0.029527882114052773, 2.4432808913843473e-06, -0.021526867523789406, 0.01613183133304119, -0.02444787323474884, 0.05809307098388672, 0.0018883820157498121, 0.017661722376942635, -0.05055505037307739, -0.023384178057312965, -0.00045626520295627415, 0.0031871909741312265, -0.08142401278018951, 0.04271484538912773, 0.07015536725521088, -0.01818697340786457, 0.07057789713144302, -0.034966252744197845, -0.04687994346022606, 0.039302412420511246, -0.0526525154709816, 0.006662013474851847, -0.06474920362234116, 0.014503005892038345, 0.01597847044467926, -0.047058865427970886, -0.014959233812987804, -0.03214533254504204, 0.01922621764242649, 0.044939979910850525, 0.011159759946167469, -0.012251382693648338, 0.06154598668217659, 0.02962169237434864, 0.002327138325199485, -0.010172969661653042, 0.002822945360094309, -0.04639489948749542, -0.016000879928469658, 0.0029937562067061663, -0.011399411596357822, 0.016736336052417755, 0.008146516978740692, -0.026305459439754486, -0.009586380794644356, -0.027055585756897926, 0.02443149872124195, -0.07673712819814682, 0.027325130999088287, 0.011457542888820171, 0.002918396145105362, -0.03806907683610916, -0.053014062345027924, 0.025235634297132492, 0.006338251288980246, -0.07374799996614456, 0.014775724150240421, -0.0438137948513031, -0.01568502001464367, 0.05085310339927673, 0.039522700011730194, 0.027558516710996628, -0.032815951853990555, -0.03783776983618736, -0.02843186818063259, 0.05573906749486923, 0.0030082250013947487, -0.005663733463734388, -0.0347236804664135, -0.08172132074832916, -0.008001599460840225, -0.011454647406935692, 0.01849546656012535, -0.016239117830991745, 0.033720288425683975, -0.016665903851389885, 0.013946488499641418, -0.019577840343117714, 0.007623596582561731, -0.01156911812722683, -0.01102902740240097, 0.035981904715299606, -0.028807876631617546, -0.05764663591980934, -0.025887945666909218, -0.010120119899511337, 0.016429096460342407, 0.004237576387822628, 0.1074037179350853, -0.07126974314451218, -0.03555699437856674, 0.02601860836148262, -0.0007934588356874883, -0.05294439196586609, 0.0672345757484436, 0.034688737243413925, 0.009377090260386467, 0.013886558823287487, -0.015436602756381035, 0.022571086883544922, 0.022975698113441467, -0.004618845414370298, 0.05327852442860603, -0.025806216523051262, 0.035451702773571014, -0.03190120682120323, 0.014439335092902184, -0.02146555297076702, -0.04738384485244751, -0.028580669313669205, -0.019532430917024612, -0.0001687830372247845, -0.0053018564358353615, -0.006782248616218567, -0.04392002150416374, -0.013106889091432095, -0.027111049741506577, 0.02261289209127426, 0.04709867015480995, 0.006995281204581261, -0.038452889770269394, 0.046583227813243866, 0.01744968257844448, 0.038247477263212204, 0.00875225942581892, 0.016234882175922394, 0.061173781752586365, -0.00872779916971922, -0.018097029998898506, 0.03198236972093582, 0.01096587348729372, 0.022369999438524246, 0.007615123875439167, -0.007144811563193798, -0.07462703436613083, -0.05374087020754814, 0.00548013299703598, 0.045799341052770615, 0.051795270293951035, -0.010218062438070774, -0.037746816873550415, 0.044355958700180054, 0.013174309395253658, 0.02448887936770916, 0.051897961646318436, -6.53818788123317e-05, 0.0031203338876366615, -0.008821649476885796, 0.06265966594219208, 0.010211317799985409, 0.027770759537816048, -0.04904339462518692, -0.04811430722475052, -0.03381941840052605, 0.05190184339880943, -0.06048590689897537, -0.06188478320837021, 0.021745992824435234, -0.01786554791033268, -0.034700699150562286, -0.0070913988165557384, 0.06144142150878906, 0.020436648279428482, 0.0038828086107969284, -0.09418437629938126, -0.0044252583757042885, 0.005324791185557842, 0.0029860406648367643, -0.032880451530218124, 0.03663181513547897, -0.04210047423839569, 0.005304751917719841, -0.006050921976566315, -0.02555818296968937, 0.0016111459117382765, -0.06110130995512009, -0.024490082636475563, -0.002954094437882304, -0.012317251414060593, -0.001255636103451252, -0.038328830152750015, -0.0436985157430172, -0.004675024189054966, 0.022125059738755226, 0.027845460921525955, -0.024986224249005318, 0.012583091855049133, 0.004176491405814886, -0.01767430268228054, 0.019118184223771095, 0.02079053595662117, 0.01724473387002945, 0.0032616262324154377, 0.04285041615366936, -0.004643171094357967, -0.02202734537422657, -0.042073968797922134, -0.0016517481999471784, -0.027210045605897903, 0.021088358014822006, -0.040267445147037506, -0.07066407054662704, 0.012192565947771072, -0.032603390514850616, 0.010907948017120361, -0.010503034107387066, -0.02970815636217594, 0.030556656420230865, 0.015423103235661983, -0.03510703891515732, -0.03244258090853691, 0.012522440403699875, 0.022304506972432137, -0.01929750293493271, -0.014331531710922718, -0.012778676114976406, 0.05129456892609596, 0.04950471222400665, -0.03799145668745041, 0.05935743823647499, 0.0016422439366579056, -0.013476847670972347, -0.010154709219932556, -0.012974041514098644, 0.061840351670980453, -0.013279781676828861, 0.005658829119056463, -0.0060435133054852486, -0.03973027691245079, 0.013895216397941113, 0.028783001005649567, -0.007165911607444286, 0.015804952010512352, 0.01574176736176014, -0.05720222368836403, 0.016747964546084404, -0.0018772333860397339, -0.03425874561071396, 0.011227620765566826, 0.01640760339796543, -0.005574721377342939, -0.018064606934785843, -0.06626337021589279, 0.07761941105127335, 0.03735465928912163, -0.05275347828865051, 0.026858847588300705, 0.009191256947815418, 0.04178507253527641, -0.023966196924448013, 0.012231371365487576, 0.014040065929293633, 0.01589059643447399, 0.026720602065324783, -0.021363329142332077, -0.04054556041955948, 0.0641154944896698, -0.03163266181945801, 0.05177296698093414, -0.012149682268500328, -0.06751586496829987, -0.0038019113708287477, -0.0015206328826025128, 0.034581542015075684, 0.06742765754461288, 0.020095640793442726, 0.02159789390861988, -0.03658230975270271, 0.10649595409631729, -0.0563860759139061, 0.003114541759714484, -0.00896862056106329, -0.047822438180446625, -0.01710219494998455, 0.01596340350806713, -0.0016201087273657322, 0.05764968693256378, 0.07627774029970169, 0.003991703037172556, -0.0058981007896363735, 0.0605267770588398, -0.007201352156698704, -0.026348525658249855, -0.014875032007694244, 0.09364053606987, 0.011694046668708324, -0.013932909816503525, -0.02442854456603527, -0.044856052845716476, 0.03182993084192276, 0.06311147660017014, -0.001368119497783482, 0.021643519401550293, -0.04515019431710243, 0.03694513067603111, -0.0071336026303470135, 0.01498111616820097, 0.03172306343913078, 0.029422307386994362, -0.026295818388462067, -0.07044652104377747, 0.007778272032737732, -0.00227526412345469, 0.005676248576492071, 0.029929690062999725, 0.03972090035676956, -0.02768145129084587, -0.03534311428666115, -0.03705872222781181, -0.07403941452503204, -0.0035340895410627127, 0.02671215310692787, 0.016363324597477913, 0.03895776346325874, -0.019147900864481926, -0.0057701850309967995, -0.026100311428308487, -0.033901166170835495, 0.023433586582541466, -0.05599094182252884, -0.01780143566429615, 0.0007908616098575294, 0.11639752984046936, 0.04534657672047615, -0.051143866032361984, -0.04169711098074913, 0.005926427431404591, -0.010139373131096363, 0.05991971120238304, -0.10509281605482101, 0.01226373203098774, -0.06938919425010681, -0.038117896765470505, 0.012019608169794083, 0.04611307382583618, -0.010824100114405155, 0.002810918027535081, 0.08441779762506485, -0.05626837536692619, 0.0037109525874257088, -0.003992742858827114, -0.02416704036295414, -0.05260380357503891, 0.025192122906446457, 0.021152781322598457, 0.036598026752471924, 0.008874601684510708, 0.04094026982784271, -0.03131468594074249, 0.013474306091666222, -0.045257244259119034, -0.01403858419507742, 0.012902656570076942, 0.0009119847672991455, 0.03559255599975586, -0.01709791086614132, 0.055590517818927765, 0.0023009292781352997, -0.03126855939626694, -0.016006655991077423, 0.03519509732723236, 0.027406567707657814, -0.053033921867609024, 0.024995196610689163, -0.009568437933921814, 0.038342639803886414, 0.0036107245832681656, 0.05964614450931549, 0.04456683620810509, -0.0489351786673069, -0.023443613201379776, -0.04463093355298042, 0.018391842022538185, 0.04397273436188698, 0.027459146454930305, -0.0305308997631073, -0.062664695084095, 0.025073861703276634, 0.05608970671892166, 0.00741587346419692, 0.020055431872606277, 0.06926251202821732, 0.03790351003408432, -0.010795940645039082, 0.006399255245923996, 0.07326075434684753, 0.03779231384396553, 0.009397165849804878, 0.024033140391111374, -0.0002097921387758106, -0.01686927303671837, -0.03841120004653931, -0.056195009499788284, -0.021168988198041916, 0.009080881252884865, -0.023113422095775604, -0.006059605162590742, -0.025860067456960678, -0.055529795587062836, -0.09028507024049759, 0.05814163759350777, -0.07855290174484253, -0.027250273153185844, -0.007473351433873177, 0.0735194981098175, -0.03444456309080124, -0.06332448869943619, -0.005709284450858831, -0.0038158008828759193, 0.02097873017191887, -0.004254157654941082, -0.014982125721871853, -0.06892089545726776, -0.028170548379421234, -0.02019546926021576, -0.04426376149058342, 0.03631981089711189, 0.0023744383361190557, -0.03144211694598198, -0.05376509577035904, 0.026750832796096802, -0.049267616122961044, -0.00963439792394638, -0.033608417958021164, -0.049663424491882324, -0.011791197583079338, -0.03141862526535988, 0.06276284158229828, -0.005035861860960722, -0.01990496553480625, -0.009437804110348225, -0.0406852588057518, 0.050478577613830566, 0.04410545527935028, 0.020060306414961815, 0.005283691920340061, 0.05959411710500717, 0.008478633128106594, -0.02676456980407238, -0.0016615582862868905, 0.0241676215082407, 0.09372304379940033, 0.009851587004959583, -0.027810759842395782, -0.008624879643321037, 0.01503605768084526, 0.03902588412165642, -0.07293157279491425, 0.05718376487493515, -0.015042164362967014, -0.009605628438293934, -0.035252079367637634, -0.005354713182896376, 0.02427644096314907, 0.024236293509602547, -0.02715245820581913, -0.010435666888952255, 0.08413606137037277, 0.02766030840575695, 0.008279066532850266, -0.014883297495543957, 0.02425723522901535, 0.04522310197353363, -0.10306494683027267, -0.016362080350518227, 0.0408879853785038, 0.008851071819663048, -0.026659274473786354, 0.0072641209699213505, 0.01647942326962948, 0.032476574182510376, 0.03490450233221054, 0.028665276244282722, -0.02050000987946987, -0.002994439098984003, 0.021450938656926155, 0.02085239812731743, -0.023234644904732704, 0.011883335188031197, -0.01967174932360649, -0.015565097332000732, -0.06915558874607086, 0.040139827877283096, 0.11061470955610275, 0.005999687127768993, -0.00913820881396532, 0.023150581866502762, -0.005111846141517162, -0.017046356573700905, 0.046381812542676926, -0.018921896815299988, -0.02331104315817356, 0.03375820443034172, -0.022597098723053932, 0.028922513127326965, -0.020054979249835014, 0.06666206568479538, 0.04539136216044426, 0.02557721920311451, -0.056104741990566254, -0.006253005005419254, -0.007522387895733118, 0.01653004065155983, 0.0839240700006485, 0.014517032541334629, 0.002130769193172455, 0.018932024016976357, 0.025059815496206284, -0.03541049733757973, -0.03601859137415886, -0.016780700534582138, 0.037379126995801926, -0.033900633454322815, 0.008328014053404331, -0.004621323198080063, -0.06338151544332504, -0.030905473977327347, -0.037620823830366135, -0.03395703062415123, 0.03088720515370369, 0.0032961892429739237, -0.017688540741801262, -6.807169501492815e-33, -0.0005475424695760012, -0.007279145531356335, -0.03312837332487106, -0.09422943741083145, 0.009021171368658543, -0.014964768663048744, -0.04591192305088043, -0.022794209420681, 0.032994575798511505, 0.01760866679251194, -0.023734519258141518, 0.01764546148478985, -0.014853029511868954, 0.03178903087973595, 0.013912246562540531, 0.001542512560263276, 0.06319643557071686, -0.0024848231114447117, 0.04008141905069351, 0.02220728248357773, 0.013416619040071964, 0.033702485263347626, 0.02743261121213436, -0.1092342883348465, -0.06095483526587486, 0.006247710902243853, -0.0506167896091938, -0.07126973569393158, -0.017483120784163475, 0.015743421390652657, 0.02157888375222683, 0.02825520560145378, 0.013035423122346401, 0.002092577051371336, -0.02092110365629196, -0.060520660132169724, -0.013855251483619213, 0.024349771440029144, -0.0561811588704586, 0.002005289774388075, -0.06789112836122513, -0.0026413709856569767, 0.015239939093589783, -0.05113481730222702, -0.043392788618803024, -0.0005467919399961829, 0.06026804819703102, -0.019092176109552383, -0.005983868148177862, -0.04840465635061264, -0.042478203773498535, 0.009054547175765038, -0.00918244756758213, -0.011666462756693363, -0.053094666451215744, -0.0015082162572070956, 0.012167206965386868, -0.013054052367806435, 0.0045386492274701595, -0.0043772486969828606, -0.007761456072330475, 0.05614842101931572, 0.05037280544638634, 0.051805656403303146, -0.0016272898064926267, 0.010300287045538425, 0.02556937001645565, -0.0074150217697024345, -0.03045683540403843, 0.022854425013065338, 0.018556775525212288, 0.04951882362365723, 0.012963504530489445, 0.018607547506690025, 0.060095712542533875, -0.07678211480379105, -0.029916319996118546, 0.0709267258644104, -0.005247440189123154, 0.023746980354189873, -0.03526929393410683, 0.06513120979070663, -0.0061379531398415565, -0.01009201817214489, 0.025487525388598442, -0.10054633766412735, 0.006944752298295498, -0.034434106200933456, 0.01912403106689453, 0.03165217116475105, -0.001528102089650929, -0.01294631790369749, 0.01011055987328291, -0.042929574847221375, -0.001979662338271737, 0.05801653116941452, -0.01680004969239235, 0.024857163429260254, 0.0009313709451816976, -0.035632044076919556, -0.019186347723007202, -0.019266456365585327, 0.03848235681653023, 0.019483331590890884, -0.008089764975011349, 0.032648440450429916, 0.02822306379675865, 0.012581526301801205, 0.015680624172091484, -0.0032712833490222692, -0.036677855998277664, 0.010519067756831646, 0.015413172543048859, 0.029386719688773155, -0.021526720374822617, -0.013380546122789383, -0.006417932454496622, 0.029301369562745094, 0.013310507871210575, -0.02042851224541664, -0.0627242773771286, -0.003369927406311035, -0.005790189374238253, 0.01025185827165842, -0.02551625296473503, -0.008493125438690186, -0.04736980423331261, -0.05158315971493721, 0.03611567243933678, -0.10403813421726227, -0.006551133003085852, -0.037784893065690994, 2.9751143415523984e-07, -0.028455838561058044, -0.01755541004240513, 0.0026512753684073687, -0.034593261778354645, 0.007667179219424725, 0.006369883194565773, -0.029371777549386024, 0.055701419711112976, -0.03460796922445297, 0.0224076509475708, 0.02786361239850521, 0.023283779621124268, -0.015250598080456257, 0.04393051192164421, -0.03806600347161293, 0.03369501233100891, 0.04521006718277931, 0.044686608016490936, -0.017436934635043144, 0.009879134595394135, 0.01685531809926033, 0.07257818430662155, -0.014131883159279823, -0.022456740960478783, 0.12414458394050598, -0.02600894123315811, 0.03737089782953262, 0.04383768513798714, 0.03657140955328941, 0.03689485043287277, 0.04431465268135071, 0.05371173843741417, 0.02897014655172825, -0.049343276768922806, -0.00826292671263218, 0.002097153337672353, 0.019805658608675003, 0.04776526615023613, -0.008222237229347229, -0.0379878468811512, -0.03345580771565437, 0.033111609518527985, 0.03678789734840393, -0.02716626413166523, 0.027889326214790344, -0.019286664202809334, 0.0049899546429514885, -0.005475785117596388, 0.016624294221401215, 0.01804039254784584, 0.018380800262093544, 0.008941182866692543, -0.022241419181227684, -0.015042518265545368, 0.00507091311737895, -0.013325939886271954, -0.03966948017477989, -0.009262415580451488, 0.005484152585268021, 0.012576696462929249, -0.050612494349479675, -0.0014628880890086293, 0.008633257821202278, 0.022221639752388, 0.022109664976596832, 0.048256296664476395, -0.043561000376939774, 2.6022299561462034e-34, -0.020990470424294472, 0.006350270006805658, -0.027435075491666794, -0.029322635382413864, -0.012104558758437634, -0.00996313150972128, 0.03631116449832916, 0.0038259890861809254, 0.013252606615424156, 0.03180624172091484, -0.042472705245018005]

['Bharat Singh', 'Soham De', 'Yangmuzi Zhang', 'Thomas Goldstein', 'Gavin Taylor']

1510.04609v1

The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely large for weights connecting deep layers (layers near the output layer), and extremely small for shallow layers (near the input layer); this results in slow learning in the shallow layers. Additionally, it has also been shown that in highly non-convex problems, such as deep neural networks, there is a proliferation of high-error low curvature saddle points, which slows down learning dramatically. In this paper, we attempt to overcome the two above problems by proposing an optimization method for training deep neural networks which uses learning rates which are both specific to each layer in the network and adaptive to the curvature of the function, increasing the learning rate at low curvature points. This enables us to speed up learning in the shallow layers of the network and quickly escape high-error low curvature saddle points. We test our method on standard image classification datasets such as MNIST, CIFAR10 and ImageNet, and demonstrate that our method increases accuracy as well as reduces the required training time over standard algorithms.

Layer-Specific Adaptive Learning Rates for Deep Networks

http://arxiv.org/pdf/1510.04609v1

Title LayerSpecific Adaptive Learning Rates Deep Networks Summary increasing complexity deep learning architecture resulting training time requiring week even month slow training due part vanishing gradient gradient used backpropagation extremely large weight connecting deep layer layer near output layer extremely small shallow layer near input layer result slow learning shallow layer Additionally also shown highly nonconvex problem deep neural network proliferation higherror low curvature saddle point slows learning dramatically paper attempt overcome two problem proposing optimization method training deep neural network us learning rate specific layer network adaptive curvature function increasing learning rate low curvature point enables u speed learning shallow layer network quickly escape higherror low curvature saddle point test method standard image classification datasets MNIST CIFAR10 ImageNet demonstrate method increase accuracy well reduces required training time standard algorithm Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.004674241412431002, -0.010195175185799599, -0.02250341884791851, 0.06782056391239166, 0.020764455199241638, -0.0065002962946891785, 0.06451480090618134, -0.014551694504916668, -0.024900073185563087, 0.015319187194108963, -0.01956958696246147, 0.039943575859069824, 0.016074420884251595, 0.0381023995578289, 0.006297627929598093, -0.06467315554618835, -0.012885982170701027, 0.042708609253168106, 0.009428775869309902, -0.03586317226290703, 0.03870541974902153, -0.003180324798449874, 0.019629565998911858, 0.026180269196629524, -0.023836525157094002, 0.027461035177111626, -0.0036589903756976128, 0.021740637719631195, 0.0017363331280648708, -0.02470366656780243, 0.06520026922225952, -0.010540910996496677, -0.006403789389878511, 0.05366653949022293, 2.2835865820525214e-06, -0.02625432051718235, 0.030535604804754257, -0.009521661326289177, -0.0073251971043646336, -0.0028896317817270756, 0.049188751727342606, 0.010254663415253162, -0.0023699766024947166, 0.0028187630232423544, -0.01891046017408371, -0.03569620102643967, -0.001354233711026609, 0.07832484692335129, 0.011572574265301228, 0.05419161170721054, 0.0007692657527513802, -0.039665061980485916, 0.02141374722123146, -0.039870087057352066, -0.02984292432665825, -0.06771852821111679, -0.024287458509206772, -0.05565256252884865, -0.06176028400659561, -0.027484413236379623, 0.0160837322473526, 0.050474513322114944, 0.043857231736183167, -0.008870030753314495, 0.0279036033898592, 0.051901135593652725, -0.021045437082648277, -0.051090601831674576, 0.015026260167360306, 0.061404500156641006, -0.07078877836465836, 0.03326486796140671, -0.011751068755984306, -0.01328323595225811, -0.013502570800483227, -0.00809468887746334, -0.02126864530146122, 0.01685515232384205, -0.023501526564359665, 0.0009446606854908168, -0.06054640933871269, 0.024445850402116776, 0.015781309455633163, 0.03332805261015892, 0.03459971770644188, -0.02821655571460724, -0.014905079267919064, 0.021677978336811066, 0.012181157246232033, -0.027162497863173485, 0.017506703734397888, 0.00378564465790987, 0.03080016002058983, -0.007691903039813042, -0.019373781979084015, -0.01767469197511673, -0.02631688304245472, -0.04139197990298271, 0.0376935750246048, -0.07829948514699936, 0.08809233456850052, -0.022745048627257347, -0.017072517424821854, 0.020785901695489883, -0.08974715322256088, 0.051445428282022476, -0.036312349140644073, 0.03960941731929779, -0.03053450770676136, 0.01756487786769867, 0.0030512327793985605, 0.0006254273466765881, -0.05110891908407211, 0.040389109402894974, 0.017373697832226753, -0.029500529170036316, -0.039574217051267624, -0.014583444222807884, -0.013528501614928246, -0.009762212634086609, 0.03523583710193634, 0.08887988328933716, -0.009311233647167683, -0.010447191074490547, 0.008226078003644943, 0.005778298247605562, 0.004615552723407745, 0.04500659927725792, -0.015979427844285965, 0.004209350794553757, 0.01244654506444931, 0.015290509909391403, 0.035788316279649734, 0.03587455675005913, 0.03705310449004173, 0.018620040267705917, -0.0014597990084439516, 0.03063148446381092, -0.026123208925127983, -0.010032608173787594, 0.022567881271243095, -0.00917928759008646, -0.0007568236324004829, -0.04465983808040619, 0.0007291875663213432, -0.02343403548002243, -0.01825881004333496, 0.018210023641586304, 0.0016746405744925141, -0.02921471558511257, -0.07938793301582336, 0.006039280444383621, -0.05631599202752113, -0.041666820645332336, 0.11030173301696777, 0.0055944304913282394, 0.019552532583475113, 0.0011059297248721123, 0.014448420144617558, 0.045950278639793396, -0.0025057168677449226, 0.0006363439606502652, -0.054384201765060425, 0.002197803696617484, -0.015181446447968483, -0.012426674365997314, -0.0174076147377491, -0.03500448912382126, -0.04861734062433243, 0.05154364928603172, 0.024486152455210686, 0.01783599704504013, 0.005319198593497276, -0.05148359388113022, -0.008946199901401997, 0.006007720250636339, 0.061493922024965286, 0.043530240654945374, -0.014114822261035442, -0.0063735307194292545, 0.023494979366660118, -0.045319076627492905, 0.002126441104337573, 0.04223693534731865, -0.01929575577378273, -0.046286676079034805, -0.029796533286571503, -0.025445597246289253, -0.06348644196987152, -0.04359893128275871, 0.035254377871751785, -0.03739865869283676, 0.011646470054984093, 0.010132289491593838, 0.03434872254729271, 0.04234401881694794, -0.035160429775714874, -0.026912914589047432, 0.00504722073674202, 0.012242485769093037, -0.058874547481536865, -0.05276966467499733, 0.017194533720612526, -0.06176134571433067, -0.018189923837780952, -0.0005621947930194438, -0.0771922841668129, 0.009444688446819782, 0.0038245159666985273, 0.015042901039123535, 0.010654838755726814, -0.003137524938210845, 0.028296317905187607, -0.06381522864103317, -0.002102761762216687, 0.04718391224741936, -0.006519006565213203, 0.023062050342559814, -0.011984840966761112, 0.019549105316400528, 0.03496428206562996, 0.015209058299660683, -0.0516170896589756, 0.0014889900339767337, 0.05043164640665054, -0.006781131494790316, 0.0371420755982399, 0.041496530175209045, -0.008404645137488842, -0.004364657681435347, 0.026660002768039703, -0.042785655707120895, 0.03647342324256897, -0.04800034314393997, -0.05861159414052963, -0.007611311040818691, -0.06969808042049408, -0.004680468235164881, 0.028842061758041382, -0.01921216957271099, 0.038137029856443405, -0.003979236353188753, 0.005051881540566683, -0.04929407685995102, 0.02764127030968666, 0.050412263721227646, 0.015633955597877502, -0.006472274195402861, -0.010829627513885498, -0.026623664423823357, 0.02259129099547863, -0.020896099507808685, 0.009505581110715866, 0.015541919507086277, 0.0166518222540617, -0.0652715191245079, 0.008679086342453957, 0.046973034739494324, 0.020139597356319427, -0.025386005640029907, -0.018207266926765442, -0.07332513481378555, 0.005150140263140202, 0.009530199691653252, 0.04917493835091591, 0.030564356595277786, -0.014443117193877697, 0.025731490924954414, 0.009148973971605301, -0.009052285924553871, -0.03790717571973801, -0.01735793985426426, 0.011080163531005383, 0.06473059207201004, -0.055461443960666656, -0.013507059775292873, 0.11566921323537827, -0.008829513564705849, -0.03117588721215725, 0.01971558853983879, 0.027615366503596306, 0.019541418179869652, 0.006721310783177614, -0.04456722363829613, -0.002752126893028617, 0.02418610453605652, 0.06470771878957748, -0.0031593581661581993, 0.01690453104674816, -0.034376125782728195, 0.0063822162337601185, 0.04666277393698692, -0.00012555702414829284, -0.07040871679782867, -0.005045413039624691, -0.015291635878384113, -0.06925510615110397, 0.07476626336574554, 0.015926573425531387, -0.026908298954367638, -0.04488232359290123, 0.1387140303850174, -0.018780797719955444, 0.00920943170785904, -0.0020976760424673557, -0.02029179036617279, -0.0019525059033185244, 0.005707539618015289, -0.04578113555908203, 0.01929369382560253, 0.012004245072603226, 0.027100179344415665, 0.00018465628090780228, -0.017497818917036057, 0.019337903708219528, -0.00893163401633501, -0.03829300031065941, -0.02092321589589119, -0.0004019867046736181, -0.02814272977411747, 0.007494563236832619, -0.008057297207415104, -0.04408680647611618, 0.04581708461046219, -0.014001397415995598, 0.008900185115635395, -0.04057229310274124, 0.00033103019814006984, -0.022094998508691788, 0.03660199046134949, 0.05467412620782852, 0.0032966912258416414, -0.0368749238550663, 0.005083682481199503, -0.009027442894876003, 0.02602502703666687, -0.00864243134856224, 0.000776050437707454, 0.048318345099687576, -0.020680386573076248, -0.0382414273917675, -0.0407174788415432, -0.047336332499980927, 0.01800370216369629, 0.009240125305950642, -0.0011047287844121456, -0.05816778913140297, 0.0034869357477873564, -0.012786549516022205, 0.004142270423471928, -0.022510716691613197, 0.043878812342882156, -0.03529932349920273, 0.009954722598195076, 0.0019187411526218057, 0.030014976859092712, 0.022266291081905365, 0.0078056310303509235, -0.048882775008678436, 0.015210278332233429, 0.05373949185013771, 0.02016286924481392, -0.05437246710062027, 0.04800964891910553, -0.14575143158435822, 0.025966456159949303, -0.0006122863269411027, 0.004636399447917938, -0.03158024698495865, -0.015002327971160412, -0.017426010221242905, -0.0551629438996315, 0.041167035698890686, 0.028312217444181442, 0.0013690820196643472, -0.11624599248170853, -0.04479006677865982, 0.01725953444838524, -0.037672195583581924, 0.014201815240085125, -0.00210180738940835, 0.007162370719015598, -0.010029041208326817, -0.03929181769490242, -0.009162811562418938, -0.01352841779589653, -0.03399166837334633, 0.027751198038458824, 0.0028963496442884207, -0.0012836389942094684, -0.02195219323039055, -0.05429717153310776, -0.014562350697815418, -0.029446065425872803, 0.006259203888475895, -0.015598736703395844, 0.028504565358161926, -0.013964208774268627, 0.03143326938152313, -0.030432898551225662, 0.04979027807712555, -0.07950409501791, 0.025053849443793297, 0.01636638306081295, -0.07874563336372375, -0.029261697083711624, 0.013754392974078655, 0.011980448849499226, -0.05011281371116638, -0.013929963111877441, 0.02901429682970047, 0.02328931912779808, 0.025667784735560417, -0.03461861610412598, 0.04501447454094887, 0.04580305889248848, -0.025876667350530624, 0.01996256224811077, 0.036261186003685, -0.019938822835683823, 0.07730689644813538, 0.02705676108598709, 0.026040377095341682, 0.0006575476145371795, 0.014693341217935085, -0.06264884024858475, -0.0153254559263587, -0.025587525218725204, -0.03656039386987686, -0.028137462213635445, -0.03974126651883125, -0.003199202474206686, -0.003296832786872983, -0.00022180315863806754, -0.06332580745220184, 0.005411130841821432, 0.04954444244503975, 0.008492261171340942, -0.03988021984696388, -0.034496795386075974, 0.019001364707946777, -0.022720547392964363, 0.041168030351400375, 0.03763692453503609, -0.014818484894931316, 0.08041903376579285, 0.014324300922453403, -0.05715741962194443, -0.006988410837948322, 0.059274546802043915, -0.020389549434185028, -0.02766534872353077, 0.036077242344617844, 0.045261282473802567, -0.032404810190200806, 0.018380844965577126, -0.04309750348329544, -0.023287499323487282, -0.004966770764440298, 0.03019835241138935, 0.022615162655711174, -0.005782124120742083, -0.019634416326880455, -0.04672006145119667, -0.06535162031650543, 0.03116937354207039, -0.014095689170062542, 0.045994263142347336, -0.0494752861559391, 0.0572669543325901, -0.049844224005937576, -0.026533303782343864, 0.012639264576137066, 0.005995843559503555, 0.03036467730998993, -0.013787676580250263, -0.055038996040821075, -0.061971526592969894, -0.012883021496236324, 0.003691831836476922, 0.0038728273939341307, 0.05503047630190849, 0.02223839983344078, -0.033177196979522705, -0.03415000066161156, 0.038063231855630875, 0.050520721822977066, 0.00760769285261631, -0.022278865799307823, 0.02109302207827568, 0.046165503561496735, 0.0018157254671677947, 0.009717617183923721, -0.043344177305698395, 0.08446022868156433, -0.036952536553144455, -0.05253373831510544, 0.07309096306562424, -0.01756858080625534, 0.047523364424705505, -0.020932817831635475, 0.0289022047072649, -0.027360154315829277, -0.0009394045919179916, 0.02858630381524563, -0.0191180557012558, -0.05325998365879059, -0.013782682828605175, 0.01534500066190958, 0.0037191887386143208, -0.07547347247600555, 0.0366259403526783, 0.031071532517671585, 0.01428297534584999, -0.0472998172044754, 0.051786236464977264, 0.04512058198451996, -0.031909678131341934, -0.036025915294885635, 0.012658443301916122, 0.004910940304398537, -0.01827932894229889, 0.03638650104403496, -0.0019029902759939432, -0.013784945011138916, 0.07453256845474243, -0.004955310840159655, 0.01498479675501585, 0.028008271008729935, 0.020472846925258636, -0.015050209127366543, -0.032387491315603256, 0.015508261509239674, 0.020650183781981468, -0.03493041545152664, 0.048124633729457855, 0.015514889732003212, 0.03348700702190399, -0.015447397716343403, 0.05104852840304375, 0.07088196277618408, -0.002302815904840827, 0.019927693530917168, -0.03373856097459793, 0.03139917925000191, 0.012906317599117756, 0.029647475108504295, 0.014034491032361984, 0.023136446252465248, -0.04526969790458679, 0.01613469421863556, -0.03500751033425331, -0.02267996221780777, 0.02043388970196247, -0.00011444547271821648, -6.1492350277620115e-33, 0.02026774361729622, 0.002475942252203822, -0.03057990036904812, 0.027393782511353493, -0.03769655153155327, 0.06895851343870163, -0.008116651326417923, 0.002382487989962101, -0.03860423341393471, 0.026396282017230988, -0.027801262214779854, 0.006763305515050888, 0.004838724620640278, 0.046430569142103195, 0.02785736694931984, 0.005812112707644701, 0.024775702506303787, -0.025698119774460793, 0.06051896885037422, 0.01909019984304905, 0.01217720564454794, 0.010773026384413242, 0.040321364998817444, -0.09834468364715576, -0.058530136942863464, 0.009057643823325634, -0.021071571856737137, -0.03432784229516983, -0.004968256689608097, -0.002152822446078062, -0.0070012821815907955, 0.04090553894639015, -0.001823407132178545, -0.021467575803399086, -0.00045124534517526627, -0.04854823648929596, -0.04459768161177635, -0.02341742441058159, -0.0711638405919075, 0.06853983551263809, -0.05943533778190613, 0.004688155371695757, 0.048140041530132294, -0.018317557871341705, -0.03238820284605026, 0.025546293705701828, 0.04865843802690506, -0.007770933210849762, -0.07245118170976639, 0.017982816323637962, -0.010761250741779804, 0.03517734631896019, -0.014230568893253803, 0.0069926464930176735, 0.0168619342148304, -0.02203936129808426, -0.03925732523202896, -0.022331226617097855, -0.07453984022140503, -0.012131295166909695, -0.030552228912711143, 0.032201774418354034, -0.028491688892245293, 0.03629225865006447, -0.008375239558517933, -0.027239888906478882, 0.05678456276655197, 0.014003336429595947, 0.016921423375606537, 0.010233737528324127, 0.02571786195039749, 0.05201015621423721, 0.06158393248915672, -0.017376836389303207, 0.06357839703559875, -0.10428985953330994, -0.003970498684793711, 0.022992148995399475, 0.039621055126190186, 0.02360878325998783, -0.018282575532794, -0.028694309294223785, -0.0062505584210157394, 0.003443978726863861, 0.013946738094091415, -0.02445792220532894, -0.0034358433913439512, -0.000587242073379457, -0.008226254023611546, 0.042947184294462204, 0.049542125314474106, 0.034343358129262924, -0.02558193914592266, -0.01450439728796482, 0.11279792338609695, -0.04863083362579346, 0.055697645992040634, 0.0487208291888237, 0.05503988265991211, 0.0016684276051819324, -0.0023515638895332813, 0.0013428597012534738, -0.0416051410138607, 0.007287563756108284, 0.02789088897407055, 0.0327148400247097, 0.03012135811150074, 0.022462988272309303, 0.024393649771809578, -0.0138364527374506, -0.005691364407539368, -0.026575421914458275, 0.0353829450905323, 0.05187886208295822, -0.0062956418842077255, -0.04178154841065407, 0.011766060255467892, 0.05235195904970169, -0.013196730986237526, -0.003962854854762554, -0.05460115522146225, -0.03611605614423752, 0.01666858047246933, 0.025880545377731323, -0.08123761415481567, -0.006052688229829073, -0.03808489441871643, -0.013506290502846241, -0.002643000800162554, -0.08215777575969696, -0.0018783508567139506, 0.03248944878578186, 2.871539663829026e-07, -0.05155719444155693, 0.03828909993171692, -0.04857032746076584, -0.03522862121462822, -0.010811259970068932, 0.012606102041900158, 0.009106588549911976, 0.021927734836935997, -0.06387770175933838, 0.08431262522935867, 0.0379503034055233, -0.012990524992346764, 0.013379830867052078, 0.005271130707114935, -0.024721922352910042, -0.028542788699269295, -0.0377238392829895, 0.06476927548646927, 0.022822419181466103, 0.0632093995809555, 0.007031142245978117, 0.07766705751419067, -0.001624784548766911, -0.05815468356013298, 0.05769794061779976, -0.03899695351719856, -0.03579777851700783, 0.03900595381855965, 0.06367050111293793, -0.01481699850410223, 0.007175699807703495, 0.08452095091342926, -0.023127086460590363, -0.03180798515677452, -0.021830491721630096, 0.0038689628709107637, 0.01028132252395153, -0.006922644563019276, -0.028649827465415, -0.038421694189310074, 0.0627892017364502, 0.003441194072365761, 0.03902868553996086, -0.03382512927055359, 0.03872073069214821, 0.027791695669293404, -0.0066603715531528, -0.05290520563721657, 0.020428739488124847, 0.04405906796455383, 0.03886597603559494, -0.015887480229139328, 0.017947427928447723, -0.033446528017520905, 0.023296048864722252, -0.09374582022428513, -0.0478665865957737, -0.0786142647266388, 0.029526643455028534, 0.05652211606502533, 0.00479781161993742, 0.02747517265379429, 0.003185175359249115, 0.006531561259180307, 0.10249222069978714, 0.027323035523295403, -0.009295630268752575, 2.5287227587226837e-34, -0.017158741131424904, -0.027514144778251648, 0.028835633769631386, 0.009191161021590233, -0.04069822281599045, -0.006010000593960285, -0.0020825311075896025, -0.005106054712086916, -0.01831813156604767, -0.027964184060692787, -0.04103649780154228]

['Baochen Sun', 'Jiashi Feng', 'Kate Saenko']

1511.05547v2

Unlike human learning, machine learning often fails to handle changes between training (source) and test (target) input distributions. Such domain shifts, common in practical scenarios, severely damage the performance of conventional machine learning methods. Supervised domain adaptation methods have been proposed for the case when the target data have labels, including some that perform very well despite being "frustratingly easy" to implement. However, in practice, the target domain is often unlabeled, requiring unsupervised adaptation. We propose a simple, effective, and efficient method for unsupervised domain adaptation called CORrelation ALignment (CORAL). CORAL minimizes domain shift by aligning the second-order statistics of source and target distributions, without requiring any target labels. Even though it is extraordinarily simple--it can be implemented in four lines of Matlab code--CORAL performs remarkably well in extensive evaluations on standard benchmark datasets.

Return of Frustratingly Easy Domain Adaptation

http://arxiv.org/pdf/1511.05547v2

Title Return Frustratingly Easy Domain Adaptation Summary Unlike human learning machine learning often fails handle change training source test target input distribution domain shift common practical scenario severely damage performance conventional machine learning method Supervised domain adaptation method proposed case target data label including perform well despite frustratingly easy implement However practice target domain often unlabeled requiring unsupervised adaptation propose simple effective efficient method unsupervised domain adaptation called CORrelation ALignment CORAL CORAL minimizes domain shift aligning secondorder statistic source target distribution without requiring target label Even though extraordinarily simpleit implemented four line Matlab codeCORAL performs remarkably well extensive evaluation standard benchmark datasets Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.006140164099633694, 0.03558460250496864, -0.02201683446764946, -0.03230151906609535, -0.02162107452750206, 0.00257741822861135, 0.08435023576021194, -0.0018613454885780811, -0.05232500284910202, -0.008091026917099953, -0.0293829794973135, 0.00776475016027689, 0.02512151189148426, 0.05079600214958191, -0.029154613614082336, -0.041176844388246536, 0.014088429510593414, 0.02447054162621498, -0.02826547622680664, 0.017201879993081093, 0.005851883441209793, -0.03735912963747978, -0.01292407140135765, 0.014594157226383686, -0.03501676023006439, -0.012355076149106026, -0.002682045567780733, 0.004366915673017502, 0.029482346028089523, -0.005055130459368229, 0.0647263154387474, 0.019543401896953583, -0.004375329241156578, 0.0485537089407444, 2.1384544197644573e-06, -0.06431400030851364, -0.06077353283762932, -0.020555775612592697, 0.027213657274842262, -0.022560210898518562, 0.010602251626551151, -0.053017985075712204, 0.0005178744322620332, 0.006047394126653671, -0.022452041506767273, -0.012020976282656193, 0.09999576210975647, 0.040929652750492096, 0.01964745856821537, 0.06741898506879807, -0.018949950113892555, -0.023210352286696434, -0.046228162944316864, -0.017442505806684494, 0.006083196960389614, -0.05416985973715782, 0.04988322779536247, 0.003236128017306328, -0.04484054446220398, -0.0334894172847271, -0.055958811193704605, 0.009479220025241375, -0.028119856491684914, 0.0018043372547253966, 0.0358378142118454, 0.017670975998044014, -0.028295716270804405, -0.017349855974316597, -0.0003821722639258951, 0.04957973584532738, -0.017914162948727608, 0.007460009306669235, 0.01477845013141632, -0.014689909294247627, 0.0008245657081715763, 0.036129653453826904, -0.00993774738162756, -0.05682838335633278, 0.0029026134870946407, -0.01622280292212963, -0.04789205268025398, 0.07623541355133057, -0.011322892270982265, -0.025510258972644806, -0.04950675368309021, 0.048482563346624374, -0.020302699878811836, -0.013665623962879181, 0.009518626146018505, -0.00825478509068489, 0.015411046333611012, -0.017789306119084358, 0.010929955169558525, -0.017424924299120903, -0.035129088908433914, -0.010645096190273762, -0.07299365103244781, -0.07616059482097626, 0.02640669047832489, -0.022364972159266472, 0.054608579725027084, -0.0061000618152320385, -0.03367619588971138, 0.02866397239267826, -0.0032565826550126076, 0.05078887939453125, -0.051237765699625015, 0.022822318598628044, -0.009019228629767895, 0.013525458052754402, -0.07477493584156036, 0.01870109513401985, 0.0014010632876306772, 0.022786004468798637, -0.014603680931031704, 0.010654600337147713, -0.07302930951118469, 0.020368993282318115, -0.014432654716074467, -0.04482787102460861, -0.0001483419182477519, 0.056254707276821136, 0.011859569698572159, 0.017532706260681152, -0.0028433124534785748, 0.07895989716053009, -0.014389295130968094, 0.06702081859111786, 0.007958165369927883, 0.02966468781232834, 0.016697585582733154, 0.03738362342119217, -0.005181738641113043, -0.018790068104863167, 0.015671541914343834, 0.1254126876592636, 0.027537362650036812, 0.004767030943185091, -0.017666984349489212, 0.004774349741637707, -0.04385397210717201, -0.011108756065368652, 0.024425728246569633, -0.030739979818463326, 0.014302922412753105, 0.004787478130310774, -0.03766527399420738, -0.07589635252952576, -0.022188987582921982, -0.0348513238132, -0.02390681393444538, 0.09989584982395172, -0.008030639961361885, -0.0028200780507177114, 0.07212300598621368, -0.028269696980714798, -0.028540749102830887, 0.049485012888908386, 0.014990286901593208, -0.01872580125927925, 0.012593746185302734, -0.028217513114213943, 0.005444045178592205, -0.0031302091665565968, -0.036960311233997345, -0.018295710906386375, 0.007528549991548061, 0.005102889612317085, 0.012603300623595715, 0.04260649159550667, 0.0676800087094307, -0.04388035461306572, 0.05942465364933014, -0.05294021591544151, 0.061779413372278214, 0.0035118861123919487, 0.010137591511011124, 0.01477297767996788, -0.022656232118606567, -0.021757861599326134, -0.023869743570685387, -0.027623025700449944, -0.01929917372763157, 0.038807108998298645, -0.03198348358273506, -0.01642758958041668, -0.06113812327384949, 0.02624674327671528, -0.011182976886630058, -0.04345107823610306, -0.007696977350860834, -0.02211032621562481, -0.020379509776830673, -0.02343926765024662, 0.07120218127965927, -0.004742063116282225, 0.0016289665363729, -0.007295734714716673, -0.009725048206746578, -0.007829241454601288, -0.05966911464929581, -0.024208547547459602, -0.03131173551082611, -0.047258663922548294, -0.043068643659353256, -0.05846378952264786, -0.04867761582136154, -0.00885466206818819, 0.053843993693590164, -0.002479397691786289, 0.020991122350096703, 0.03626782447099686, 0.0038280996959656477, -0.036238301545381546, -0.03416798263788223, 0.02967197261750698, 0.00045954357483424246, 0.019779212772846222, -0.006754222791641951, -0.01320037990808487, -0.004273077938705683, -0.03143637254834175, 0.01094105839729309, 0.030969001352787018, -0.022714735940098763, 0.0037669073790311813, 0.0446387454867363, 0.04538322612643242, 0.02955731749534607, -0.008130964823067188, 0.03682253509759903, -0.022411417216062546, 0.02364090271294117, 0.005715633742511272, -0.0536896288394928, 0.01806388795375824, 0.011541592888534069, 0.017832348123192787, 0.04571183770895004, -0.03015853278338909, -0.0008545028977096081, 0.014450718648731709, -0.0554976612329483, -0.023162012919783592, 0.015537533909082413, -0.028053877875208855, -0.042794693261384964, 0.035511311143636703, 0.06152934581041336, -0.004546537064015865, 0.03694046661257744, -0.06205059960484505, 0.037440575659275055, 0.048898953944444656, -0.04000944644212723, -0.01733703911304474, -0.023845793679356575, 0.032562728971242905, 0.0026191521901637316, 0.045526087284088135, -0.010666635818779469, -0.03786960616707802, 0.032867223024368286, -0.004299248103052378, -0.013434170745313168, -0.020986106246709824, 0.03583591431379318, 0.02444281429052353, 0.022120989859104156, 0.032060932368040085, 0.02108905464410782, 0.028597522526979446, -0.0031241902615875006, -0.021716279909014702, -0.021695468574762344, -0.03082553669810295, 0.01871388591825962, -0.020736491307616234, -0.026320526376366615, 0.0431143157184124, -0.005031343083828688, -0.027932200580835342, -0.024397799745202065, 0.010647130198776722, -0.025465000420808792, 0.059471674263477325, 0.03554029390215874, -0.04003129526972771, -0.07848992198705673, 0.044493138790130615, -0.02605408802628517, -0.0018700360087677836, 0.012326141819357872, -0.0036523458547890186, -0.08248110860586166, 0.04174647107720375, -0.004592479672282934, 0.05511455610394478, -0.0013451380655169487, 0.027734242379665375, 0.03343281149864197, 0.059399738907814026, -0.003030461259186268, -0.017478659749031067, -0.027487339451909065, -0.02022061124444008, 0.01716526225209236, 0.006791343912482262, 0.0256520863622427, 0.054757777601480484, 0.025274092331528664, 0.0043381014838814735, 0.007676110602915287, 0.03683723136782646, 0.007136084139347076, 0.017231039702892303, -0.05652790144085884, -0.010970436967909336, -0.014407310634851456, 0.04739401116967201, -0.018033867701888084, -0.04356152191758156, 0.05715971440076828, 0.03270416706800461, 0.028905538842082024, -0.06963464617729187, -0.05184286832809448, -0.0065460107289254665, -0.030226733535528183, -0.01823032647371292, 0.021273577585816383, 0.061288587749004364, -0.02706991694867611, -0.028604205697774887, 0.021381841972470284, 0.022009113803505898, -0.025800609961152077, 0.040320102125406265, -0.014499162323772907, 0.012186738662421703, 0.004490300547331572, -0.030722888186573982, -0.04939023032784462, 0.007516614161431789, 0.0311120692640543, -0.020396433770656586, -0.02611939050257206, -0.020266657695174217, -0.08304845541715622, 0.01619952730834484, 0.0006928443326614797, 0.03341901674866676, -0.03646790236234665, -0.019021477550268173, 0.010786502622067928, 0.03318462148308754, 0.019413460046052933, 0.02172558195888996, -0.04775514826178551, -0.003187071066349745, -0.01811215654015541, 0.02800832688808441, -0.030576949939131737, -0.021650070324540138, -0.08753010630607605, 0.03288789838552475, -0.0023562705609947443, -0.044925544410943985, -0.01828080415725708, -0.022065194323658943, 0.03731062635779381, -0.022494401782751083, 0.010425707325339317, 0.05111292004585266, 0.03660530596971512, -0.04260807856917381, -0.019925041124224663, -0.04088880866765976, 0.002792541403323412, 0.020726831629872322, 0.011528822593390942, -0.013650568202137947, -0.020398152992129326, -0.007588422391563654, 0.04464248940348625, -0.004592375364154577, -0.047782644629478455, 0.031459175050258636, -0.0701378732919693, 0.004374946933239698, 0.013109509833157063, -0.07758314162492752, -0.06998395919799805, -0.054389942437410355, 0.027942579239606857, -0.04372287914156914, -0.013791404664516449, 0.010477333329617977, -0.0023545394651591778, -0.03366240859031677, 0.06817743182182312, -0.0622650571167469, -0.026174921542406082, -0.0077041988261044025, -0.06315959990024567, 0.02056027017533779, 0.10099904984235764, 0.021450495347380638, -0.013140699826180935, 0.004125941079109907, 0.03332485258579254, 0.0011347208637744188, 0.029952414333820343, 0.0135674849152565, 0.11474684625864029, 0.0027730234432965517, 0.021894901990890503, -0.0014051710022613406, 0.03690529614686966, -0.04237733036279678, 0.004689333960413933, 0.05054677277803421, 0.05196908116340637, -0.008885717950761318, 0.017404118552803993, -0.06357280910015106, 0.012099063023924828, -0.013829785399138927, -0.005541274324059486, 0.02331640012562275, -0.05021199956536293, 0.011809620074927807, 0.0075858659110963345, -0.001107688876800239, 0.00696621323004365, -0.00017424518591724336, 0.04198208823800087, -0.03877801075577736, -0.08242346346378326, -0.06990034878253937, -0.0009047800558619201, 0.01013200730085373, 0.025457827374339104, 0.04308243840932846, -0.013304827734827995, -0.032472915947437286, -0.00705330353230238, -0.07789921760559082, 0.006229076534509659, 0.04739980399608612, 0.013504321686923504, -0.06607677042484283, 0.028517987579107285, 0.0471213273704052, -0.03715791553258896, -0.01563217304646969, -0.014386159367859364, -0.026309020817279816, -0.056589771062135696, -8.719481411390007e-05, 0.03972579538822174, 0.027226600795984268, 0.00916539691388607, -0.022795865312218666, 0.0006134493160061538, -0.0002516301756259054, 0.07530033588409424, -0.004610784351825714, 0.018433501943945885, 0.012916846200823784, -0.06676515936851501, -0.0187368206679821, -0.02896304428577423, -0.039538562297821045, 0.07846786826848984, 0.022273333743214607, -0.05777004361152649, -0.008442675694823265, -0.01628267392516136, 0.010177253745496273, -0.017718510702252388, 0.13204936683177948, -0.011283180676400661, -0.05185769498348236, -0.00396630447357893, 0.015625305473804474, 0.008172081783413887, -0.009485621936619282, 0.011548829264938831, -0.05477449297904968, 0.031394828110933304, 0.0502961203455925, -0.02071046084165573, 0.009513313882052898, 0.013684572651982307, -0.006693833973258734, -0.016239579766988754, 0.03784612938761711, -0.04555286467075348, 0.0777667909860611, -0.021278230473399162, 0.03525172546505928, 0.030602382495999336, -0.008243996649980545, 0.04939249902963638, 0.040420591831207275, 0.008525490760803223, 0.018346259370446205, 0.02792600356042385, 0.03735886141657829, -0.039642758667469025, 0.03616853803396225, -0.022489117458462715, 0.027064504101872444, -0.05024188756942749, -0.008242489770054817, 0.0485868975520134, -0.0594889260828495, 0.019108429551124573, 0.02233036980032921, -0.001778931706212461, -0.035178154706954956, 0.068216972053051, 0.0055291918106377125, 0.046943459659814835, 0.02329876832664013, -0.020893463864922523, -0.021507086232304573, -0.009348219260573387, 0.025413721799850464, 0.04899279773235321, -0.012772021815180779, -0.0409514456987381, -0.03910590708255768, 0.0015016597462818027, 0.06771819293498993, 0.009859599173069, -0.041212115436792374, -0.019744884222745895, -0.05884850025177002, -0.05838128179311752, -0.04048364609479904, 0.04804738238453865, -0.02929884009063244, 0.058562662452459335, -0.0010108264395967126, 0.011265551671385765, 0.036164626479148865, -0.019283903762698174, -0.0048020812682807446, -0.006658404599875212, -0.02045576088130474, 0.010079341940581799, -0.014392657205462456, -0.028731193393468857, -5.275100694292095e-33, -0.013546918518841267, -0.043236929923295975, -0.0298144593834877, 0.010240970179438591, -0.02063732221722603, -0.0022614148911088705, -0.007254980970174074, 0.020503900945186615, 0.04123185575008392, -0.022666145116090775, 0.011586297303438187, -0.02019810862839222, 0.021952826529741287, -0.01675688661634922, 0.034502528607845306, -0.015661189332604408, 0.005486130714416504, -0.03619023412466049, -0.02410053461790085, -0.04160415008664131, 0.005415827035903931, 0.054220519959926605, 0.02985254116356373, -0.12766055762767792, -0.05156166851520538, 0.061945389956235886, 0.01785321533679962, -0.06046028807759285, 0.008707012049853802, 0.04466073960065842, 0.05533706024289131, 0.04133100435137749, 0.008556148037314415, -0.025559142231941223, -0.019417496398091316, 0.00695424247533083, -0.07500990480184555, -0.0010655837832018733, -0.036391690373420715, 0.046010009944438934, 0.011716587468981743, -0.026902200654149055, 0.08913920074701309, 0.014017948880791664, -0.04457408934831619, -0.031129956245422363, 0.08962766081094742, -0.06842699646949768, -0.008232660591602325, -0.020649192854762077, -0.0804356262087822, 0.018704764544963837, -0.00019174379121977836, 0.004764451179653406, 0.01988927833735943, 0.04382297769188881, 0.00519641675055027, 0.019275663420557976, -0.05738004669547081, 0.03290710970759392, -0.006418468430638313, 0.040575794875621796, 0.05542583018541336, 0.05869865044951439, -0.015148954465985298, 0.038784753531217575, 0.04275015741586685, -0.02977084554731846, 0.03360448032617569, -0.028196783736348152, -0.012506796978414059, 0.036281339824199677, 0.023025915026664734, 0.032126352190971375, 0.054076965898275375, -0.0533875934779644, -0.08289175480604172, 0.07528714090585709, -0.06876102089881897, -0.07032422721385956, -0.03737367317080498, 0.013703889213502407, -0.04148373007774353, 0.015009286813437939, 0.048719070851802826, 0.03410101681947708, -0.019071897491812706, -0.03922251611948013, 0.033290185034275055, -0.040030691772699356, 0.0006653846357949078, 0.0461457334458828, -0.014454261399805546, -0.038463350385427475, 0.023693380877375603, -0.01866956241428852, -0.007841323502361774, 0.030575912445783615, 0.009954746812582016, -0.02523258700966835, 0.007539251819252968, -0.04444708302617073, 0.002691729227080941, 0.04925626516342163, 0.0716581791639328, -0.03491067886352539, 0.044255685061216354, -0.007109183352440596, -0.07445269078016281, 0.001814352348446846, 0.017309054732322693, -0.024959789589047432, -0.00390302250161767, 0.05709277465939522, 0.005096678156405687, -0.014666377566754818, -0.0002095107629429549, 0.05203937366604805, 0.042169515043497086, -0.06571797281503677, -0.056414201855659485, 0.013903218321502209, -0.010822671465575695, 0.007803692948073149, -0.0482364222407341, -0.0022659304086118937, 0.011915389448404312, -0.009458898566663265, 0.002135196002200246, -0.06934595108032227, -0.035619691014289856, -0.05246908217668533, 2.789000745906378e-07, 0.06552678346633911, 0.059676479548215866, 0.02407139725983143, -0.02664978988468647, -0.006289859768003225, 0.032151125371456146, -0.03888173773884773, 0.02919861674308777, 0.01059389766305685, 0.013747325167059898, 0.03665122389793396, -0.056123219430446625, 0.005485933274030685, 0.0076321084052324295, -0.037691567093133926, -0.016263101249933243, 0.046655163168907166, 0.03132263571023941, -0.04269079864025116, 0.0270505640655756, 0.0448652021586895, 0.06741006672382355, 0.013034812174737453, -0.04093128442764282, 0.028703495860099792, 0.008701134473085403, 0.016677506268024445, -0.004717695526778698, 0.058712225407361984, -0.018760861828923225, -0.02537180669605732, -0.03467554599046707, -0.04372422769665718, 0.046411238610744476, -0.027644453570246696, 0.04252813383936882, 0.016814108937978745, 0.037116292864084244, -0.03238518536090851, 0.01793813705444336, 0.008612769655883312, 0.05456988885998726, 0.04581588879227638, -0.0009076946880668402, 0.02104872837662697, -0.061680521816015244, -0.03142013028264046, 0.010893496684730053, -0.05050455778837204, 0.009647993370890617, 0.04589824005961418, 0.02942056581377983, 0.0012989721726626158, 0.013890988193452358, 0.011680945754051208, -0.004282039124518633, -0.008212846703827381, -0.02944270893931389, 0.0008328451658599079, 0.024845954030752182, -0.016722816973924637, 0.009294652380049229, 0.02376556769013405, 0.012848426587879658, 0.07780788838863373, -0.03101964294910431, -0.02215980552136898, 2.980639725186389e-34, -0.03692182898521423, 0.006633492186665535, 0.016800377517938614, 0.0030492558144032955, -0.049782611429691315, -0.009007947519421577, 0.014902477152645588, 0.04658010974526405, 0.009333898313343525, 0.020329248160123825, 0.004813607782125473]

['Lukas Cavigelli', 'Luca Benini']

1512.04295v2

An ever increasing number of computer vision and image/video processing challenges are being approached using deep convolutional neural networks, obtaining state-of-the-art results in object recognition and detection, semantic segmentation, action recognition, optical flow and superresolution. Hardware acceleration of these algorithms is essential to adopt these improvements in embedded and mobile computer vision systems. We present a new architecture, design and implementation as well as the first reported silicon measurements of such an accelerator, outperforming previous work in terms of power-, area- and I/O-efficiency. The manufactured device provides up to 196 GOp/s on 3.09 mm^2 of silicon in UMC 65nm technology and can achieve a power efficiency of 803 GOp/s/W. The massively reduced bandwidth requirements make it the first architecture scalable to TOp/s performance.

Origami: A 803 GOp/s/W Convolutional Network Accelerator

http://arxiv.org/pdf/1512.04295v2

Title Origami 803 GOpsW Convolutional Network Accelerator Summary ever increasing number computer vision imagevideo processing challenge approached using deep convolutional neural network obtaining stateoftheart result object recognition detection semantic segmentation action recognition optical flow superresolution Hardware acceleration algorithm essential adopt improvement embedded mobile computer vision system present new architecture design implementation well first reported silicon measurement accelerator outperforming previous work term power area IOefficiency manufactured device provides 196 GOps 309 mm2 silicon UMC 65nm technology achieve power efficiency 803 GOpsW massively reduced bandwidth requirement make first architecture scalable TOps performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.03533274680376053, 0.014776026830077171, -0.0014125180896371603, 0.11635368317365646, 0.015131840482354164, -0.014659779146313667, 0.02819630317389965, 0.006116359960287809, -0.02864663116633892, -0.03482743725180626, 0.019600851461291313, 0.012567292898893356, 0.017588449642062187, 0.06970798969268799, 0.04495895653963089, -0.01297629252076149, -0.004507011733949184, 0.049323905259370804, -0.013211949728429317, 0.04642842337489128, 0.05445459112524986, -0.06959071755409241, -0.004389822483062744, 0.006997215561568737, -0.04692085087299347, 0.01662250980734825, -0.015179661102592945, -0.026079967617988586, 0.024248329922556877, -0.023127609863877296, -0.027884401381015778, -0.020991411060094833, 0.031283725053071976, 0.043831996619701385, 2.4455478069285164e-06, -0.01845245249569416, 0.013775497674942017, -0.016132283955812454, -0.02490820735692978, -0.02831166423857212, 0.013731022365391254, -0.028309166431427002, -0.04065314307808876, 0.03326151520013809, 0.002941455226391554, -0.02602139301598072, 0.03727085515856743, 0.0015617329627275467, -0.04011664539575577, 0.0581594742834568, -0.016078483313322067, -0.05536247417330742, 0.014661649242043495, -0.0015047646593302488, -0.005633600056171417, -0.0007820883765816689, -0.015334776602685452, -0.028963323682546616, 0.007112647872418165, -0.04845903068780899, -0.029216842725872993, 0.03689490258693695, 0.03650512546300888, 0.0034405977930873632, 0.0388558991253376, 0.00609131483361125, -0.06231554225087166, -0.015706026926636696, -0.031340375542640686, 0.015366028994321823, -0.05549156293272972, 0.03736155852675438, -0.0007623301935382187, 0.008240515366196632, -0.0604187473654747, -0.05227116122841835, 0.013104361481964588, 0.011324123479425907, -0.01505451649427414, -0.024533724412322044, -0.06370847672224045, 0.005461822729557753, 0.024236442521214485, 0.03225650265812874, 0.0005269435350783169, -0.009471246972680092, 0.03523518890142441, 0.09593498706817627, 0.0019567080307751894, 0.029971344396471977, -0.0013170000165700912, -0.049535270780324936, 0.037948787212371826, 0.0057413093745708466, -0.01847921311855316, -0.021139860153198242, -0.0532229021191597, -0.038605451583862305, -0.03746527433395386, -0.09287166595458984, 0.0028496580198407173, -0.013376753777265549, 0.025522593408823013, 0.06803978234529495, -0.011587835848331451, 0.04734833166003227, -0.07699321210384369, 0.04713139310479164, -0.03828421235084534, 0.012963591143488884, 0.046980347484350204, -0.009478943422436714, 0.007192709948867559, 0.013808077201247215, -0.04543300345540047, -0.0487670823931694, -0.03675459325313568, -0.0003701591049320996, 0.0007573288748972118, -0.026391692459583282, -0.05319376289844513, 0.027132464572787285, 0.02526412531733513, -0.0662039965391159, -0.005577012896537781, -0.003920970484614372, 0.025159532204270363, 0.006485220976173878, -0.006254630628973246, -0.049335189163684845, 0.043866198509931564, 0.033407289534807205, 0.0046747345477342606, 0.04670907184481621, 0.004058499354869127, 0.0391920767724514, -0.021129533648490906, -0.02537204511463642, -0.03672400861978531, 0.08928695321083069, 0.01641719415783882, 0.010245890356600285, 0.01767887733876705, -0.054203543812036514, 0.05431501194834709, -0.0237482488155365, 0.013027691282331944, 0.00371607206761837, 0.02676045149564743, 0.016651632264256477, -0.02828316204249859, 0.02290317974984646, -0.011157892644405365, -0.039644625037908554, 0.032930273562669754, -0.013158864341676235, 0.05765761062502861, 0.020580707117915154, 0.04725594446063042, -0.007493241224437952, 0.02668091468513012, 0.005029056221246719, 0.01071921642869711, 0.019086411222815514, -0.04819773510098457, -0.03399711102247238, -0.017856236547231674, -0.017130844295024872, -0.01678978092968464, 0.061811018735170364, 0.029798412695527077, 0.0062944903038442135, 0.030524974688887596, -0.006381063722074032, -0.0005546097527258098, 0.0062528192065656185, 0.007419276051223278, -0.006023889407515526, -0.04747737944126129, -0.021763958036899567, 0.008549947291612625, -0.05765609070658684, 0.029853440821170807, 0.06881622970104218, -0.013527234084904194, -0.04957536607980728, -0.04000480845570564, -0.008079972118139267, -0.07236793637275696, -0.0323251374065876, -0.02259918861091137, -0.020549997687339783, -0.020233154296875, 0.03551006317138672, 0.045312754809856415, -0.0369151309132576, 0.025049541145563126, -0.049104973673820496, -0.0207124724984169, -0.010096299462020397, -0.010348806157708168, -0.10869348794221878, 0.039435021579265594, 0.004238446708768606, 0.020015239715576172, -0.007222909014672041, 0.0011343664955347776, 0.02841566503047943, -0.0009087984799407423, -0.03325387090444565, 0.017487552016973495, -0.006888800300657749, 0.04904979094862938, -0.009108442813158035, 0.009699137881398201, 0.022391458973288536, -0.0041907550767064095, 0.009753660298883915, -0.005516017321497202, 0.010331422090530396, 0.003891815198585391, 0.08444765955209732, 0.005011024884879589, 0.03207025304436684, 0.02925480715930462, 0.02873491309583187, 0.04686930775642395, 0.034184280782938004, -0.012440085411071777, 0.00829797238111496, 0.029558157548308372, -0.051719795912504196, 0.02773897349834442, -0.020072396844625473, 0.07321981340646744, 0.0019280406413599849, -0.016192661598324776, 0.022385336458683014, 0.025866959244012833, -0.025333484634757042, 0.014716699719429016, 0.029527004808187485, -0.013550967909395695, -0.041787367314100266, -0.008296064101159573, -0.0004155100614298135, 0.025986583903431892, -0.01979583501815796, 0.06766468286514282, 0.033001262694597244, -0.026270415633916855, -0.02742014080286026, 0.031007688492536545, 0.027636956423521042, 0.02253270521759987, 0.03932309150695801, 0.028427552431821823, 0.01151235867291689, 0.02464195340871811, -0.02963077835738659, -0.041843436658382416, -0.007334169466048479, -0.02136835642158985, 0.01110308151692152, 0.004870285280048847, -0.01867719180881977, 0.030619757249951363, -0.03528913855552673, 0.033280614763498306, -0.01948842592537403, -0.041767437011003494, 0.004339019767940044, 0.049310989677906036, 0.030153637751936913, -0.012908621691167355, -0.0347038209438324, 0.05218841880559921, -0.00919327512383461, -0.049903739243745804, -0.0034041793551295996, 0.06138484925031662, 0.018554914742708206, -0.01533073466271162, 7.985443517100066e-05, 0.02879858762025833, 0.0023733789566904306, 0.03960948437452316, -0.0291910357773304, 0.024101903662085533, -0.06557659804821014, -0.0133909797295928, 0.0012686061672866344, -0.0019329522037878633, -0.01891167275607586, -0.011730476282536983, 0.0004631372867152095, -0.0455053485929966, 0.08885341882705688, 0.035747312009334564, 0.014796875417232513, -0.012478284537792206, 0.011041463352739811, 0.027962708845734596, -0.013868624344468117, 0.029339563101530075, -0.01631019450724125, -0.02886531502008438, 0.05450650677084923, -0.08654486387968063, -0.003971131052821875, -0.0656728446483612, 0.05437392368912697, 0.001275084912776947, -0.05571368336677551, -0.004388083703815937, -0.03104468062520027, -0.027520693838596344, 0.03257393464446068, -0.020206179469823837, -0.01577850803732872, -0.021700570359826088, -0.03447480872273445, -0.051411136984825134, 0.0338333435356617, -0.02842184714972973, 0.02409311942756176, -0.006373150739818811, -0.014341992326080799, 0.06857311725616455, 0.059949036687612534, 0.051332008093595505, -0.046056412160396576, 0.014778518117964268, 0.04025571048259735, 0.011869501322507858, -0.0590364933013916, -0.05216393992304802, 0.012497826479375362, -0.06179391220211983, -0.003150895005092025, -0.055710166692733765, -0.019874775782227516, -0.030546868219971657, 0.03392732888460159, -0.02875482849776745, -0.03080371581017971, -0.013498291373252869, -0.05912390351295471, 0.030037768185138702, 0.00222078338265419, 0.02838090807199478, 0.01816757209599018, 0.056265804916620255, -0.010903382673859596, -0.048922907561063766, 0.04533388838171959, 0.020177531987428665, 0.005966573487967253, -0.005908680614084005, 0.037362053990364075, 0.04940315708518028, 0.07436614483594894, -0.01409314014017582, -0.011823445558547974, -0.14128823578357697, 0.048557087779045105, 0.005793475545942783, 0.016771240159869194, -0.027129631489515305, 0.014046031050384045, 0.03302519768476486, -0.048471830785274506, 0.02610556222498417, -0.03853708133101463, -0.010295945219695568, -0.0780143290758133, -0.0013807095820084214, 0.09054321050643921, -0.049072265625, 0.009952392429113388, -0.0031162844970822334, -0.04196975752711296, -0.040373433381319046, 0.007232270669192076, -0.058095600455999374, -0.02181289903819561, 0.018159417435526848, -0.017541348934173584, -0.012625856325030327, 0.05524051934480667, -0.005202615633606911, 0.007102932780981064, -0.019468454644083977, 0.0009701927192509174, 0.04251442849636078, -0.038971953094005585, 0.020642951130867004, -0.025440270081162453, 0.020835721865296364, -0.023701686412096024, -0.01315393764525652, -0.052004020661115646, 0.036880429834127426, 0.04665578529238701, -0.05076339840888977, -0.05555086210370064, 0.020885536447167397, -0.004754561465233564, -0.02641083486378193, -0.017112456262111664, 0.010714014992117882, -0.035833653062582016, 0.018352756276726723, -0.007329104468226433, 0.019230090081691742, -0.01809435710310936, -0.060596488416194916, 0.014996329322457314, 0.04253600537776947, -0.014998381957411766, 0.045712776482105255, -0.012027557007968426, -0.0023903008550405502, 0.01527857780456543, 0.04541192948818207, -0.04902999475598335, -0.07195347547531128, -0.039842233061790466, -0.03920300677418709, -0.058862943202257156, 0.0036463169381022453, -0.007453721482306719, -0.0011374590685591102, 0.010319259017705917, 0.002047071699053049, 0.011450542137026787, 0.0018369487952440977, 0.02754463441669941, -0.0822458565235138, 0.010711591690778732, -0.012337800115346909, 0.03918343037366867, 0.023233389481902122, 0.020511547103524208, -0.060693204402923584, 0.04174289107322693, 0.04622330144047737, -0.08375173062086105, 0.0026700899470597506, -0.009239195846021175, 0.07070247828960419, -0.07156255841255188, 0.07889239490032196, 0.037458181381225586, 0.025598034262657166, 0.019443828612565994, 0.05158691853284836, -0.07670865952968597, -0.04754731059074402, -0.0037443554028868675, 0.060746386647224426, 0.00016055614105425775, 0.030066484585404396, -0.010516617447137833, 0.054536476731300354, -0.05409675091505051, -0.035290904343128204, -0.019213659688830376, 0.019390856847167015, 0.01507481187582016, -0.04111165553331375, -0.0253757257014513, -0.003681766102090478, 0.006018972024321556, 0.015850095078349113, -0.01625024527311325, -0.034674305468797684, -0.065699502825737, -0.05866841971874237, 0.00944098923355341, -0.03504212573170662, 0.05751996859908104, 0.04968240484595299, 0.04694507643580437, -0.0007511660223826766, 0.04125186428427696, 0.026210132986307144, 0.039043862372636795, -0.07139026373624802, -0.04094347357749939, 0.004002165514975786, -0.016872961074113846, 0.034659236669540405, 0.025434376671910286, 0.04913407564163208, -0.07310107350349426, -0.005998643115162849, 0.021664315834641457, -0.026368746533989906, 0.030500631779432297, -0.09396930783987045, -0.005999690853059292, 0.028304528445005417, 0.004578195512294769, -0.0037414298858493567, 0.022471843287348747, -0.016428589820861816, -0.011399631388485432, 0.016032977029681206, 0.005384248681366444, -0.028780516237020493, 0.027615614235401154, 0.03651144355535507, -0.0046407850459218025, -0.07003810256719589, 0.0410999096930027, 0.07100385427474976, -0.04165751859545708, -0.01841312274336815, -0.002611178904771805, -0.000667853164486587, -0.060056671500205994, 0.02829926460981369, -0.03880874067544937, -0.0006578390020877123, 0.03176804259419441, 0.020009784027934074, 0.030263295397162437, 0.016412604600191116, -0.001056077191606164, 0.0046859849244356155, -0.01730349101126194, 0.016770921647548676, -0.004330730531364679, -0.03197206184267998, 0.00786574836820364, 0.005217835307121277, 0.008038030005991459, 0.022526904940605164, -0.005691893398761749, -0.00343911605887115, -0.004590079188346863, -0.018224917352199554, -0.0170071329921484, 0.050617288798093796, -0.05153628811240196, 0.016193220391869545, -0.021440213546156883, 0.006291201803833246, -0.041619960218667984, -0.004072236362844706, -0.021115083247423172, -0.03147663548588753, 0.03178318217396736, -0.024695422500371933, -5.39836303191932e-33, 0.014614101499319077, 0.012246860191226006, 0.0448266938328743, -0.013469490222632885, -0.017601553350687027, 0.047692254185676575, 0.03830181062221527, 0.00505661778151989, -0.061286117881536484, -0.036409445106983185, -0.04291224852204323, 0.02875165082514286, 0.01207853201776743, 0.022130373865365982, 0.0036156466230750084, -0.0024488873314112425, 0.03074624203145504, -0.04398353397846222, 0.02161327749490738, -0.03911304101347923, 0.022364096716046333, -0.0027817371301352978, 0.042475536465644836, -0.0430048443377018, -0.0657365694642067, 0.011181795038282871, 0.00257593160495162, -0.08609148114919662, 0.008618475869297981, -0.0241184551268816, -0.02744009718298912, -0.02584940940141678, 0.004002123139798641, -0.010455192066729069, 0.004958559293299913, 0.022849000990390778, -0.04039947688579559, -0.005925937555730343, -0.04437034949660301, 0.07526466995477676, -0.06099776551127434, 0.028976505622267723, 0.0014439348597079515, 0.027220485731959343, -0.06856762617826462, 0.0020871220622211695, -0.017152803018689156, -0.047778207808732986, -0.048596594482660294, -0.015239082276821136, 0.02845718339085579, 0.025257589295506477, 0.026328058913350105, -0.020743491128087044, 0.03437533602118492, -0.04060956835746765, -0.05847620591521263, -0.021115215495228767, -0.010685241781175137, 0.02258186601102352, -0.037472158670425415, 0.021923672407865524, 0.04972824826836586, 0.05015995725989342, 0.03885118290781975, 0.04992207884788513, -0.013458844274282455, -0.08096542954444885, 0.01976975053548813, 0.043790753930807114, 0.01843433454632759, 0.036492906510829926, 0.027900414541363716, 0.006221309304237366, 0.0864306092262268, -0.03020326793193817, -0.008233888074755669, 0.016257047653198242, -0.004816936794668436, 0.015675319358706474, -0.02831374667584896, -0.004306693561375141, -0.06214635446667671, 0.01589750126004219, 0.034635309129953384, 0.021186361089348793, -0.004122574348002672, -0.024475237354636192, 0.020186681300401688, 0.0449516735970974, -0.027616774663329124, 0.03421015292406082, -0.0032699189614504576, -0.013806124217808247, 0.08257823437452316, 0.015590899623930454, 0.06493160128593445, 0.025157691910862923, 0.0662618950009346, -0.0061705769039690495, -0.04909403994679451, -0.017850391566753387, -0.04189183935523033, 0.05126055330038071, -0.03252461180090904, 0.03493902087211609, -0.0076531460508704185, 0.0643925592303276, 0.03493062034249306, -0.002663084538653493, -0.0069573200307786465, 0.01947886310517788, -0.0021422854624688625, 0.018787870183587074, 0.019208228215575218, -0.025783440098166466, 0.02182711660861969, 0.07737559080123901, -0.05039283633232117, -0.044534832239151, -0.027970099821686745, -0.031231941655278206, -0.007207369897514582, 0.04135001823306084, -0.06391947716474533, -0.015028059482574463, -0.0566435307264328, 0.021848630160093307, 0.02212393283843994, -0.05859558284282684, -0.0013319933786988258, 0.019265685230493546, 3.0207485224309494e-07, -0.062408119440078735, -0.04290562868118286, -0.010844938457012177, -0.021625569090247154, -0.026341566815972328, -0.0010195242939516902, 0.06824811547994614, 0.042418237775564194, 0.018358206376433372, -0.015583241358399391, 0.03585050255060196, -0.027194097638130188, 0.02950282208621502, -0.018842220306396484, 0.043717022985219955, -0.008029156364500523, 0.038686688989400864, 0.0742926374077797, -0.00729737151414156, 0.029427146539092064, 0.04543402045965195, 0.11990151554346085, 0.04353956878185272, -0.0008664513588882983, 0.05269800126552582, -0.008539961650967598, -0.0030588628724217415, 0.016164787113666534, 0.0053642503917217255, -0.03592793270945549, -0.02572220005095005, 0.09887406975030899, -0.01931731216609478, 0.04007875546813011, -0.011368310078978539, -0.020003562793135643, 0.04247032105922699, 0.03557194769382477, -0.05857863649725914, -0.002053548116236925, -0.006766103208065033, -0.02331523969769478, -0.01209250558167696, -0.016309326514601707, 0.034683458507061005, 0.05656109377741814, -0.005750272423028946, -0.07212266325950623, 0.0037093001883476973, 0.00874464213848114, 0.0015660477802157402, 0.04972812533378601, 0.030654646456241608, -0.013061856850981712, 0.017900219187140465, -0.07299310714006424, -0.04805760085582733, -0.058179426938295364, 0.022308306768536568, -0.05690200626850128, -0.010640748776495457, 0.025918837636709213, -0.027048006653785706, 0.017143113538622856, 0.018168792128562927, 0.034662868827581406, -0.1077314242720604, 2.423459076316471e-34, -0.006661442574113607, -0.00377524271607399, -0.003275898052379489, -0.010686121881008148, -0.024198321625590324, 0.013581952080130577, 0.035188790410757065, 0.008484060876071453, -0.04935859143733978, -0.009772292338311672, 0.0005751450662501156]

['Aravind S. Lakshminarayanan', 'Ramnandan Krishnamurthy', 'Peeyush Kumar', 'Balaraman Ravindran']

1605.05359v2

This paper introduces an automated skill acquisition framework in reinforcement learning which involves identifying a hierarchical description of the given task in terms of abstract states and extended actions between abstract states. Identifying such structures present in the task provides ways to simplify and speed up reinforcement learning algorithms. These structures also help to generalize such algorithms over multiple tasks without relearning policies from scratch. We use ideas from dynamical systems to find metastable regions in the state space and associate them with abstract states. The spectral clustering algorithm PCCA+ is used to identify suitable abstractions aligned to the underlying structure. Skills are defined in terms of the sequence of actions that lead to transitions between such abstract states. The connectivity information from PCCA+ is used to generate these skills or options. These skills are independent of the learning task and can be efficiently reused across a variety of tasks defined over the same model. This approach works well even without the exact model of the environment by using sample trajectories to construct an approximate estimate. We also present our approach to scaling the skill acquisition framework to complex tasks with large state spaces for which we perform state aggregation using the representation learned from an action conditional video prediction network and use the skill acquisition framework on the aggregated state space.

Option Discovery in Hierarchical Reinforcement Learning using Spatio-Temporal Clustering

http://arxiv.org/pdf/1605.05359v2

Title Option Discovery Hierarchical Reinforcement Learning using SpatioTemporal Clustering Summary paper introduces automated skill acquisition framework reinforcement learning involves identifying hierarchical description given task term abstract state extended action abstract state Identifying structure present task provides way simplify speed reinforcement learning algorithm structure also help generalize algorithm multiple task without relearning policy scratch use idea dynamical system find metastable region state space associate abstract state spectral clustering algorithm PCCA used identify suitable abstraction aligned underlying structure Skills defined term sequence action lead transition abstract state connectivity information PCCA used generate skill option skill independent learning task efficiently reused across variety task defined model approach work well even without exact model environment using sample trajectory construct approximate estimate also present approach scaling skill acquisition framework complex task large state space perform state aggregation using representation learned action conditional video prediction network use skill acquisition framework aggregated state space Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.030196843668818474, 0.0006299293017946184, -0.02648656629025936, -0.008701860904693604, 0.003459151368588209, -0.027547433972358704, 0.014461868442595005, -0.00015311477181967348, -0.03315132483839989, -0.013102319091558456, 0.00047338573494926095, 0.0448630228638649, 0.0005496739177033305, 0.07918047159910202, 0.017431600019335747, -0.13359111547470093, 0.005008559208363295, -0.02324722148478031, -0.015489696525037289, 0.012805952690541744, 0.04165058210492134, -0.02880788967013359, -0.005832887254655361, 0.052832432091236115, -0.04915976896882057, 0.010786890983581543, -0.05479636788368225, -0.03760756924748421, 0.06069695204496384, -0.08385128527879715, 0.021788908168673515, -0.0020269828382879496, 0.07968982309103012, 0.026941535994410515, 2.3852080630604178e-06, -0.01469670981168747, -0.02748830057680607, -0.04408491775393486, 0.06428921967744827, -0.0370684489607811, 0.019491488113999367, 0.004281505476683378, 0.00690474221482873, 0.006803871598094702, -0.01161938440054655, -0.009764372371137142, 0.039130210876464844, -0.013865211978554726, 0.011859087273478508, 0.01986272633075714, -0.009998085908591747, -0.011737672612071037, -0.0050127385184168816, -0.007604799699038267, -0.03410632163286209, -0.0016887731617316604, 0.020687712356448174, 0.06046130880713463, 0.05135709419846535, -0.02275308594107628, -0.06230076029896736, -0.019229011610150337, 0.01338814664632082, -0.01986422948539257, 0.026807039976119995, 0.035604849457740784, 0.07900021970272064, 0.01382935419678688, -0.009345179423689842, 0.0031816528644412756, -0.050987474620342255, 0.02189330942928791, 0.0014615191612392664, -0.008457518182694912, -0.002131932182237506, 0.06580517441034317, -0.029446152970194817, 0.02369464375078678, -0.0044997562654316425, -0.015170086175203323, -0.03097836673259735, 0.06817831844091415, -0.03838319331407547, -0.002371130743995309, 0.016134191304445267, 0.039895251393318176, -0.01643695868551731, 0.0008017915533855557, -0.03369826078414917, -0.006086819805204868, 0.045976363122463226, -0.07100453972816467, 0.023581450805068016, 0.03729803115129471, -0.05870500206947327, -0.017402702942490578, 0.01650032214820385, 0.03721953183412552, -0.028614968061447144, -0.0020331304986029863, 0.05786723643541336, 0.0075215622782707214, 0.041166920214891434, -0.0014921827241778374, 0.02487894706428051, 0.03802435100078583, -0.07206997275352478, 0.008591038174927235, -0.038265977054834366, 0.03674396872520447, -0.0933041125535965, 0.01619374379515648, -0.01032766979187727, 0.034712087363004684, 0.011081840842962265, 0.003950882237404585, -0.03321012109518051, 0.026231199502944946, -0.06573380529880524, 0.010585700161755085, -0.04176005721092224, 0.04579434171319008, 0.014895258471369743, 0.007571632042527199, -0.0650254562497139, 0.017597418278455734, -0.04318476840853691, 0.04788818210363388, -0.006582650821655989, 0.08090363442897797, 0.02036152593791485, 0.027266893535852432, 0.015606882981956005, 0.02800831012427807, 0.007546436507254839, 0.04698340594768524, -0.02424618788063526, 0.032196518033742905, -0.04011426120996475, -0.03462019935250282, 0.0025831134989857674, 0.006484384648501873, -0.017965832725167274, -0.0724170058965683, -0.021740032359957695, -0.08288256824016571, -0.0349540188908577, 0.046446822583675385, -0.03980913385748863, -0.011910482309758663, -0.02629082277417183, 0.02778865583240986, -0.01321407500654459, 0.013388827443122864, 0.06849515438079834, -0.01607278548181057, -0.0650736466050148, 0.021391524001955986, 0.03832390159368515, 0.0808253139257431, 0.006499897222965956, 0.02864130213856697, 0.03205273300409317, -0.007909570820629597, -0.045773375779390335, 0.005129470024257898, -0.045491691678762436, -0.02223624475300312, -0.006787261925637722, 0.023582791909575462, 0.021839773282408714, -0.052797652781009674, -0.04037544131278992, 0.031568530946969986, 0.008174658752977848, 0.05834943801164627, -0.01841605454683304, -0.05634857341647148, 0.04540696367621422, 0.0497172586619854, -0.0297728031873703, -0.013593703508377075, 0.007455585524439812, 0.06945298612117767, -0.015541056171059608, -0.02995884232223034, -0.04419183358550072, 0.030703265219926834, -0.039894167333841324, -0.05712800845503807, 0.030262013897299767, 0.00944211333990097, 0.01895555667579174, 0.017265431582927704, 0.06277456134557724, -0.017443252727389336, -0.013225559145212173, -0.03214648365974426, 0.02460813894867897, 0.05059313401579857, 0.005412151571363211, -0.03511510789394379, 0.03718459978699684, -0.004418306052684784, -0.009969008155167103, -0.0354519858956337, -0.057403575628995895, -0.008099685423076153, 0.005960701033473015, -0.05997149273753166, -0.03618846461176872, -0.07470045238733292, -0.0022483549546450377, -0.009725875221192837, -0.06878875195980072, 0.02699059434235096, 0.01154764462262392, 0.008035887032747269, -0.02485562674701214, -0.0020406930707395077, -0.021326692774891853, 0.038262203335762024, -0.03275188058614731, 0.019793665036559105, 0.015638114884495735, 0.012395365163683891, 0.05265531688928604, 0.02240273915231228, 0.012019852176308632, -0.03483825549483299, 0.02630969136953354, -0.020187491551041603, 0.025485550984740257, 0.018392229452729225, -0.0012350844917818904, 0.031090304255485535, -0.0009037911077030003, -0.03064770996570587, 0.009067485108971596, -0.012396865524351597, 0.014433490112423897, -0.004181426018476486, -0.04497856646776199, -0.049239225685596466, -0.010545976459980011, 0.01117277704179287, -0.007872993126511574, 0.02652139402925968, 0.02097773551940918, 0.0007457039318978786, -0.007179079577326775, -0.017306780442595482, 0.05205286294221878, 0.006196210626512766, -0.03152979910373688, -0.04274008423089981, 0.06456981599330902, 0.017052896320819855, -0.08119836449623108, 0.02397400140762329, -0.011684931814670563, -0.0499153807759285, -0.01415194571018219, 0.017934197559952736, 0.07146112620830536, -0.005825774744153023, -0.009892858564853668, 0.0029834858141839504, -0.020462429150938988, 0.0018316874047741294, -0.024373795837163925, 0.007052103988826275, -0.05524136871099472, -0.00285663572140038, -0.02982335537672043, -0.006503556855022907, 0.04985317960381508, -0.00909509975463152, -0.0313631035387516, 0.001036932342685759, 0.015934698283672333, -0.03361688554286957, -0.006799247115850449, 0.009837784804403782, -0.016277138143777847, 0.020467329770326614, 0.03559217229485512, -0.003313755616545677, -0.021604832261800766, -0.006692261900752783, 0.011438680812716484, 0.024281321093440056, -0.006120812613517046, -0.03948155790567398, 0.015665827319025993, -0.005107820965349674, -0.03787742182612419, 0.06211216375231743, 0.01482552383095026, 0.011726874858140945, 0.037456214427948, 0.010992373339831829, -0.006377412471920252, 0.036731261759996414, -0.04789545014500618, -0.02374613843858242, -0.004913111682981253, 0.015869222581386566, 0.019242174923419952, 0.013429568149149418, 0.02506360411643982, 0.022201253101229668, -0.05132215470075607, -0.053893912583589554, -0.009577308781445026, -0.000496870547067374, -0.056809838861227036, -0.003511848160997033, -0.022472044453024864, -0.013879818841814995, -0.04865057021379471, -0.042093392461538315, 0.023035716265439987, 0.03892088308930397, 0.009114638902246952, 0.0026161412242799997, -0.06503131240606308, 0.031042661517858505, 0.024487566202878952, 0.032234277576208115, 0.018684368580579758, -0.03747277706861496, -0.009711607359349728, -0.048414845019578934, -0.03554210811853409, 0.0007422015769407153, 0.005315457936376333, -0.022209618240594864, -0.045287467539310455, -0.004043692257255316, 0.023294730111956596, -0.01485175546258688, -0.05884535238146782, 0.0770624428987503, 0.0036704486701637506, 0.004057187121361494, -0.015396167524158955, -0.016702555119991302, 0.012334402650594711, 0.0006735339411534369, 0.022674931213259697, 0.04974304139614105, -0.03166218474507332, -0.027964327484369278, 0.005508129484951496, 0.04191034287214279, 0.044453203678131104, 0.04340219125151634, -0.07960067689418793, -0.040156539529561996, 0.017797289416193962, 0.06312554329633713, 0.036981865763664246, -0.04284050688147545, -0.08447202295064926, 0.041543103754520416, -0.007961759343743324, -0.041128627955913544, -0.0061324648559093475, 0.059850357472896576, 0.019187523052096367, -0.058165598660707474, 0.012271314859390259, 0.01749061793088913, -0.0028867225628346205, -0.08277247846126556, 0.011926914565265179, 0.036295998841524124, -0.01573116146028042, 0.014155264012515545, 0.03237773850560188, 0.032525718212127686, 0.04058528319001198, -0.04436212405562401, 0.014763331972062588, 0.015535944141447544, 0.002878702711313963, 0.050801847130060196, -0.06041862815618515, 0.10814419388771057, 0.01012114156037569, -0.08618586510419846, -0.03247421234846115, 0.0021068465430289507, 0.0037416741251945496, -0.0537690743803978, -0.039981674402952194, 0.0054097590036690235, 0.0033013562206178904, -0.0060439566150307655, 0.0533219613134861, -0.049999598413705826, -0.014120650477707386, 0.026039354503154755, -0.07941632717847824, 0.010000482201576233, 0.0372951366007328, 0.020369671285152435, -0.01994427852332592, -0.007430423982441425, -0.0401298925280571, 0.06025421619415283, 0.033047497272491455, -0.04515499994158745, 0.03937283158302307, 0.02447432279586792, 0.04449619725346565, 0.020239202305674553, 0.06949061155319214, 0.06251594424247742, -0.03846040368080139, 0.06868838518857956, 0.0767248198390007, -0.017304543405771255, 0.02594522014260292, -0.02938348986208439, -0.005586354993283749, 0.04717404395341873, -0.042006656527519226, -0.07472186535596848, -0.0018070678925141692, 0.0008030623430386186, 0.01567220129072666, -0.012643435038626194, -0.015551675111055374, -0.01997126266360283, -0.024700263515114784, 0.008594629354774952, 0.02211582101881504, -0.04788971692323685, 0.01879613660275936, 0.042581189423799515, 0.08258795738220215, -0.024678349494934082, 0.027027534320950508, 0.04950748011469841, 5.4951942729530856e-05, -0.05591919273138046, -0.009380037896335125, 0.04537477716803551, -0.02696371078491211, -0.04040403664112091, -0.03146631270647049, 0.008106202818453312, -0.05168580636382103, -0.022563427686691284, -0.10112220048904419, -0.004907086957246065, -0.015535976737737656, -0.015145898796617985, 0.0717715248465538, 0.002372817136347294, 0.06191622465848923, -0.026064381003379822, 0.013072860427200794, 0.06180906668305397, -0.07646474987268448, 0.019658274948596954, -0.025634733960032463, 0.005635878071188927, 0.03777382895350456, -0.029209693893790245, 0.0056170872412621975, -0.019635161384940147, 0.05760867893695831, -0.006009557284414768, -0.03772515431046486, -0.04504590854048729, 0.03699704259634018, -0.004003522451967001, -0.06447241455316544, 0.10667609423398972, 0.00774738471955061, -0.02331492491066456, -0.03558221086859703, -0.024946089833974838, 0.0028662558179348707, -0.007532679475843906, -0.0289081372320652, 0.031282663345336914, 0.01665317639708519, 0.026283109560608864, 0.03844735771417618, -0.03622959926724434, 0.07221265137195587, -0.0926533117890358, -0.022093068808317184, 0.004277775529772043, 0.013508584350347519, 0.025092406198382378, -0.04403059557080269, 0.0479077510535717, 0.049508288502693176, -0.015696968883275986, 0.010699818842113018, 0.025138629600405693, 0.023619450628757477, 0.017186013981699944, 0.031153960153460503, 0.014162699691951275, -0.030270099639892578, 0.0208317618817091, -0.0048331390134990215, -0.016632800921797752, -0.03264179453253746, 0.018850266933441162, 0.10343226045370102, -0.09724624454975128, -0.026426216587424278, -0.008669146336615086, 0.03404683992266655, 0.002035829471424222, 0.035808809101581573, -0.024565501138567924, -0.019688399508595467, 0.04553920775651932, 0.0016725133173167706, -0.01752208173274994, 0.013945863582193851, 0.049469079822301865, 0.03613132983446121, -0.006081270519644022, -0.009768292307853699, -0.00934763252735138, -0.021087992936372757, 0.017306821420788765, 0.0330679826438427, 0.03222126141190529, -0.032270319759845734, 0.010510380379855633, -0.018443292006850243, -0.0012663825182244182, -0.021550528705120087, -0.0022968766279518604, -0.0032768435776233673, -0.003453706158325076, 0.032507769763469696, -0.025787025690078735, -0.011726337485015392, 0.028233246877789497, -0.037277065217494965, -0.08862783759832382, 0.044266194105148315, -0.012332634069025517, -0.04470251128077507, -6.059426157333235e-33, -0.0005329287378117442, -0.059822145849466324, 0.011279724538326263, -0.026620497927069664, -0.008151344023644924, -0.004646840505301952, 0.00250599579885602, -0.058504629880189896, 0.02784637361764908, 0.01988563872873783, 0.009483912028372288, -0.01930996961891651, -0.004053442273288965, 0.013688609935343266, 0.08245212584733963, 0.008488497696816921, 0.021617881953716278, -0.0053910561837255955, 0.01724911481142044, 0.005016583949327469, 0.05144987255334854, -0.0012647842522710562, 0.02312758006155491, -0.04330278933048248, -0.07335071265697479, 0.044995348900556564, -0.04849070683121681, 0.02039121277630329, -0.04053935036063194, 0.025084679946303368, 0.00437830900773406, -0.05371065065264702, -0.00942298024892807, -0.027795718982815742, -0.04489414393901825, -0.03869416564702988, -0.0067281657829880714, -0.039025019854307175, -0.07620290666818619, 0.0007633641944266856, -0.057892851531505585, -0.004462873563170433, 0.03584864363074303, 0.01993272267282009, -0.010174650698900223, 0.01501600444316864, 0.07245738059282303, -0.013211343437433243, 0.017082924023270607, 0.016712047159671783, -0.01459415815770626, 0.028704719617962837, 0.0034775661770254374, -0.014708890579640865, 0.020614970475435257, -0.013063454069197178, 0.04185866191983223, -0.044708993285894394, -0.05429660901427269, 0.04063256084918976, 0.00479273172095418, 0.04454946517944336, 0.018043575808405876, 0.05819113180041313, 0.0716516375541687, 0.026909569278359413, -0.014471195638179779, -0.015526781789958477, 0.01477603055536747, 0.0136246457695961, 0.0017427598359063268, 0.07393607497215271, -0.013651438988745213, -0.013877348974347115, 0.038667261600494385, -0.010833799839019775, -0.016740532591938972, 0.056174784898757935, -0.025389723479747772, 0.07812059670686722, -0.07131846994161606, 0.00905778631567955, -0.05029617249965668, -0.018192172050476074, 0.03791908547282219, 0.007423417177051306, 0.02696230635046959, -0.04005071520805359, 0.0277705080807209, 0.013052149675786495, 0.032029323279857635, -0.009449570439755917, -0.007421406917273998, -0.02134576439857483, 0.05935383960604668, -0.02483833208680153, -0.024988671764731407, 0.028184697031974792, 0.037987228482961655, -0.01081069651991129, -0.05069555342197418, -0.06915684044361115, -0.007159785833209753, -0.028262628242373466, -0.030421042814850807, 0.03317167982459068, -0.04053507745265961, 0.0750022605061531, 0.025243936106562614, 0.030786745250225067, 0.03899696469306946, -0.06163354218006134, 0.03875585272908211, 0.00013845936337020248, 0.04542818292975426, -0.0373196117579937, -0.014880329370498657, 0.08080754429101944, -0.00975457951426506, -0.05410216748714447, 0.0015815390506759286, 0.02258615754544735, -0.01643127202987671, 0.02519533783197403, -0.023656154051423073, 0.014744522050023079, -0.062171224504709244, -0.04917207360267639, -0.01863420195877552, -0.013026062399148941, -0.001001861528493464, 0.01795690879225731, 3.034695623682637e-07, -0.057010602205991745, 0.03221680596470833, -0.01698743924498558, -0.04026990383863449, -0.012330951169133186, 0.01777803897857666, -0.025764960795640945, -0.007131514605134726, -0.024031739681959152, 0.03952554240822792, 0.05967395380139351, 0.011759367771446705, 0.019152594730257988, -0.00034312825300730765, -0.0174083448946476, -0.035171546041965485, 0.012465047650039196, 0.05988467112183571, -0.04768254980444908, -0.022689983248710632, 0.014003160409629345, 0.061190616339445114, 0.08225744217634201, 0.020189478993415833, 0.05573016777634621, 0.020877422764897346, -0.0044012293219566345, 0.05199379101395607, -0.004622240085154772, 0.004042693413794041, -0.07752258330583572, 0.03958699479699135, -0.052256662398576736, -0.001595943933352828, -0.07190994173288345, 0.036007385700941086, -0.02797328308224678, 0.027430135756731033, -0.02513728477060795, 0.028440464287996292, 0.02312474325299263, 0.035869866609573364, 0.04282081872224808, -0.02333248406648636, 0.012342682108283043, -0.046977534890174866, 0.028453795239329338, 0.012242993339896202, -0.005673482548445463, 0.03704952821135521, -0.019971543923020363, 0.044406600296497345, -0.035613007843494415, -0.011363048106431961, -0.013137209229171276, 0.001645536394789815, 0.00018263586389366537, -0.027681024745106697, 0.046737201511859894, 0.020535044372081757, -0.007500815205276012, -0.00477880472317338, 0.016018182039260864, 0.016809653490781784, 0.0241997130215168, 0.02249629981815815, -0.030670059844851494, 3.1936032561231455e-34, -0.036528512835502625, 0.013772674836218357, -0.036995779722929, -0.034860167652368546, -0.03322345390915871, 0.010683107189834118, -0.02162366360425949, 0.010562088340520859, 0.03620874136686325, 0.014638055115938187, -0.03912908211350441]

['Andreas Veit', 'Michael Wilber', 'Serge Belongie']

1605.06431v2

In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short paths during training. To support this observation, we rewrite residual networks as an explicit collection of paths. Unlike traditional models, paths through residual networks vary in length. Further, a lesion study reveals that these paths show ensemble-like behavior in the sense that they do not strongly depend on each other. Finally, and most surprising, most paths are shorter than one might expect, and only the short paths are needed during training, as longer paths do not contribute any gradient. For example, most of the gradient in a residual network with 110 layers comes from paths that are only 10-34 layers deep. Our results reveal one of the key characteristics that seem to enable the training of very deep networks: Residual networks avoid the vanishing gradient problem by introducing short paths which can carry gradient throughout the extent of very deep networks.

Residual Networks Behave Like Ensembles of Relatively Shallow Networks

http://arxiv.org/pdf/1605.06431v2

Title Residual Networks Behave Like Ensembles Relatively Shallow Networks Summary work propose novel interpretation residual network showing seen collection many path differing length Moreover residual network seem enable deep network leveraging short path training support observation rewrite residual network explicit collection path Unlike traditional model path residual network vary length lesion study reveals path show ensemblelike behavior sense strongly depend Finally surprising path shorter one might expect short path needed training longer path contribute gradient example gradient residual network 110 layer come path 1034 layer deep result reveal one key characteristic seem enable training deep network Residual network avoid vanishing gradient problem introducing short path carry gradient throughout extent deep network Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.008388273417949677, 0.02791118435561657, -0.022707780823111534, 0.055501021444797516, 0.01037044171243906, -0.02185480110347271, 9.231572767021134e-05, -0.010486502200365067, -0.06265868246555328, 0.028354881331324577, 0.01657799817621708, 0.024325605481863022, -0.008000190369784832, -0.006819234229624271, 0.01959122158586979, -0.07343939691781998, -0.009343461133539677, 0.01773822493851185, -0.034124817699193954, -0.0362493135035038, 0.01382500771433115, -0.03972244635224342, 0.0036932711955159903, 0.050468809902668, -0.061557210981845856, 0.01134428009390831, -0.01695866324007511, 0.00169911899138242, 0.008563541807234287, -0.025914715602993965, 0.049179740250110626, -0.012486571446061134, 0.03826344385743141, 0.03407907858490944, 2.168548235204071e-06, -0.023598365485668182, -0.008643323555588722, -0.010449699126183987, 0.0007655803929083049, -0.034962136298418045, -0.08052441477775574, 0.044604625552892685, -0.016510237008333206, -0.026770444586873055, -0.013473207131028175, 0.04690224304795265, 0.039344239979982376, 0.04660964757204056, 0.021403800696134567, 0.026894723996520042, 0.0001285570178879425, -0.05715092271566391, 0.037850916385650635, -0.0433778315782547, 0.05666205286979675, -0.00556874880567193, -0.0031846596393734217, -0.0065687308087944984, -0.059136584401130676, -0.05455190688371658, -0.03318612650036812, 0.005849612411111593, 0.07077788561582565, 0.022158337756991386, 0.031720805913209915, 0.04262625426054001, 0.025022534653544426, -0.021790768951177597, 0.011731650680303574, 0.055937159806489944, -0.026165040209889412, 0.014297207817435265, -0.004360214341431856, -0.005609801504760981, 0.002119594719260931, -0.03570493683218956, -0.024565478786826134, 0.03968333080410957, -0.006816456560045481, -0.00211670296266675, -0.07651099562644958, 0.04654416814446449, 0.034487590193748474, 0.005537081975489855, -0.030720824375748634, -0.013667723163962364, -0.014483889564871788, 0.03590402007102966, -0.05528445541858673, -0.024846957996487617, -0.016280585899949074, -0.0029160520061850548, -0.0045752800069749355, 0.026945950463414192, -0.012371190823614597, -0.03280116617679596, 0.025695819407701492, -0.05581262707710266, 0.03055669367313385, 0.022147951647639275, 0.03089003451168537, -0.009773642756044865, -0.05000586435198784, -0.0013502208748832345, -0.06350096315145493, 0.019367920234799385, -0.0660381093621254, 0.020040124654769897, 0.013995902612805367, -0.021393239498138428, -0.04334360733628273, -0.03205793350934982, -0.033482298254966736, 0.06672100722789764, -0.010980995371937752, -0.0321832075715065, -0.037709832191467285, -0.004205573350191116, -0.040175795555114746, -0.0056680613197386265, 0.03394230082631111, 0.09557215124368668, -0.00840168260037899, 0.00022551823349203914, -0.008380518294870853, -0.009027685970067978, -0.047565117478370667, 0.03567442297935486, 0.0335409976541996, 0.01960735023021698, 0.021339183673262596, -0.013705488294363022, 0.013173896819353104, 0.027800077572464943, 0.01747305504977703, 0.056418728083372116, 0.0322149284183979, 0.022475043311715126, -0.09197238832712173, 0.0066011399030685425, -0.0008049619500525296, -0.06126971170306206, -0.0035371228586882353, -0.11657198518514633, -0.01033129170536995, -0.014712907373905182, 0.021219948306679726, -0.018913166597485542, 0.01752360910177231, -0.03340303897857666, -0.0359344445168972, 0.02734590694308281, -0.0006026161136105657, -0.03175147995352745, 0.07208127528429031, 0.001959516666829586, 0.02308688871562481, 0.011441248469054699, 0.04981366917490959, 0.06643866747617722, 0.0008322129724547267, 0.0073301889933645725, 0.013796787708997726, -0.010975937359035015, 0.0071855466812849045, -0.028963493183255196, -0.06996127963066101, -0.06888328492641449, -0.07807352393865585, 0.03061904013156891, 0.002270116237923503, 0.029125548899173737, -0.019324127584695816, -0.06904258579015732, -0.006482062395662069, 0.06751879304647446, 0.02289634197950363, 0.07697295397520065, 0.05263322591781616, -0.05528084561228752, -0.02180539444088936, 0.03296371549367905, -0.003835425479337573, 0.061038389801979065, 0.019952265545725822, -0.04928385466337204, -0.0431460402905941, 0.00113002210855484, -0.07053614407777786, -0.0600871816277504, 0.019433382898569107, -0.01698620431125164, -0.005723537877202034, -0.050893064588308334, 0.06108352541923523, -0.015872012823820114, -0.028986390680074692, -0.004430055618286133, 0.020679231733083725, -0.008405767381191254, -0.07234090566635132, -0.03931962698698044, 0.039688944816589355, -0.020654235035181046, -0.0332297757267952, -0.03919617831707001, -0.022573838010430336, -0.012600629590451717, -0.020585699006915092, -0.044516030699014664, 0.021759631112217903, 0.020776476711034775, 0.02597740851342678, -0.040302760899066925, -0.022022293880581856, 0.03699278458952904, 0.025082368403673172, 0.04546564072370529, -0.02511894516646862, -0.015423857606947422, 0.01887141354382038, 0.0021712842863053083, -0.03339163959026337, 0.01887143775820732, -0.0587443932890892, 0.031306277960538864, 0.0279795303940773, 0.040799953043460846, -0.031373634934425354, -0.009773701429367065, 0.014063470996916294, -0.02573193982243538, 0.04256192594766617, -0.021094992756843567, -0.07055603712797165, -0.020101342350244522, -0.03601901978254318, -0.0012222876539453864, -0.000580405059736222, -0.005473535042256117, 0.016393247991800308, 0.05074380338191986, -0.001690613222308457, -0.03995434194803238, 0.03183187544345856, 0.000753209344111383, 0.010478852316737175, -0.00923922285437584, 0.001229648943990469, 0.005899862386286259, 0.0390043780207634, 0.001541338162496686, -0.0007745886105112731, -0.016248418018221855, 0.009046318009495735, -0.03657953813672066, 0.01039425190538168, 0.04955250397324562, -0.023450180888175964, -0.02789113111793995, -0.02033345401287079, -0.03338185325264931, 0.007184828631579876, 0.02027788758277893, -0.04051337391138077, -0.008831411600112915, 0.005979585461318493, -0.023621924221515656, 0.01848858967423439, -0.009618586860597134, -0.038144905120134354, -0.0312562994658947, 0.001934082480147481, 0.024068521335721016, -0.020092405378818512, -0.004377527628093958, 0.11066951602697372, 0.03243979439139366, -0.055878378450870514, 0.03758702799677849, 0.0022951180581003428, -0.038678258657455444, -0.022858668118715286, -0.04000689461827278, 0.0047749406658113, 0.03565506637096405, -0.00674576498568058, -0.08601444959640503, -0.009820870123803616, -0.0488240048289299, -0.017376553267240524, 0.020518334582448006, -0.01655225269496441, -0.10139644145965576, -0.04665570706129074, -0.023923387750983238, 0.02211577259004116, 0.06805907189846039, 0.021098069846630096, 0.055803749710321426, -0.02537725307047367, 0.06434784829616547, -0.03374126926064491, 0.012149250134825706, -0.029983479529619217, -0.017102735117077827, -8.684144268045202e-05, 0.001511870650574565, -0.029622957110404968, 0.016214633360505104, 0.029991185292601585, 0.010018205270171165, 0.014399023726582527, -0.020610500127077103, 0.027165217325091362, -0.01242025662213564, -0.016567809507250786, 0.008674625307321548, 0.0065813008695840836, -0.023427965119481087, -0.007525961846113205, -0.03861662372946739, 0.0007206656155176461, 0.03488607332110405, 0.009138019755482674, 0.03742530196905136, -0.055421676486730576, 0.008730405010282993, 0.065370112657547, 0.03934283182024956, 0.012005146592855453, 0.006940215360373259, -0.028470033779740334, -0.02530798688530922, -0.035412777215242386, -0.01274082064628601, -0.010643758811056614, -0.0010633368510752916, -0.012981359846889973, 0.001617578323930502, -0.009251846931874752, 0.004479902796447277, -0.044758714735507965, -0.004607103765010834, 0.013493763282895088, 0.045181117951869965, -0.03561042994260788, -0.05006847158074379, -0.00454397639259696, 0.01662861369550228, 0.02402130886912346, 0.06625166535377502, -0.030932018533349037, 9.508056245977059e-05, 0.010026611387729645, 0.044712942093610764, -0.008111213333904743, -0.002657137345522642, 0.03591873124241829, -0.029417123645544052, 0.07431986927986145, 0.029721753671765327, -0.04736408591270447, 0.03013627976179123, -0.12921753525733948, -0.005016399547457695, -0.06231231614947319, 0.020764723420143127, -0.03971901535987854, -0.008067533373832703, 0.0509488619863987, -0.09129003435373306, 0.04018491879105568, 0.009633109904825687, -0.013974885456264019, -0.09901633858680725, 0.014090461656451225, 0.03490395471453667, 0.015322539024055004, 0.015549824573099613, -0.004858792293816805, -0.006602587178349495, 0.004451053217053413, -0.0055632940493524075, -0.021338343620300293, -0.014636951498687267, -0.02351834997534752, 0.01051909476518631, -0.02095646969974041, 0.07032343745231628, -0.0016566216945648193, -0.030964307487010956, 0.006998803000897169, -0.011538708582520485, 0.011583231389522552, -0.004222959280014038, -0.0027916321996599436, 0.00761275552213192, 0.04361262917518616, -0.05641721934080124, 0.05828713998198509, -0.05653674900531769, 0.006210881285369396, 0.021496467292308807, -0.07086774706840515, -0.0188770592212677, -0.005041108001023531, 0.03787517547607422, -0.047863613814115524, -0.004076083190739155, 0.04021069034934044, -0.011442145332694054, 0.04738561436533928, 0.025983674451708794, 0.08506118506193161, 0.07275853306055069, -0.002253905637189746, 0.03471863642334938, 0.07004377245903015, -0.027870336547493935, 0.0402674563229084, -0.005435480736196041, 0.042300086468458176, -0.019843677058815956, 0.005659667309373617, -0.050214577466249466, -0.07073283195495605, 0.005720583721995354, -0.022910963743925095, 0.006366147194057703, -0.005557035095989704, -0.06926056742668152, -0.018100706860423088, -0.020655211061239243, -0.025568602606654167, -0.008314437232911587, 0.010119963437318802, 0.013452701270580292, -0.06008703261613846, -0.05696239694952965, 0.013923559337854385, -0.019244689494371414, 0.07515856623649597, -0.003518690587952733, 0.004066742490977049, -0.04121924191713333, 0.010306896641850471, -0.068257637321949, 0.01333020068705082, 0.05282749608159065, 0.0429854653775692, -0.01667962782084942, 0.02706475928425789, 0.04120011255145073, -0.011224117130041122, -0.010956385172903538, -0.07548699527978897, -0.08892159909009933, -0.025648774579167366, -0.008539969101548195, 0.03309762850403786, 0.009291520342230797, 0.009627582505345345, -0.02509537898004055, -0.03431134670972824, 0.022381655871868134, 0.019533807411789894, 0.02889636531472206, -0.0010474688606336713, 0.06036915257573128, -0.04625159502029419, -0.03043539449572563, 0.030751140788197517, -0.006853953935205936, 0.08801965415477753, 0.005856654141098261, -0.03800618276000023, 0.0025739308912307024, 0.04746733605861664, 0.030977513641119003, -0.05253428593277931, 0.05120834335684776, 0.0432722382247448, -0.011482072994112968, -0.0108650429174304, 0.03551726043224335, 0.0317830927670002, -0.004436807706952095, -0.0239958968013525, 0.02552086114883423, 0.027336494997143745, 0.02519327960908413, 0.010840028524398804, -0.03361627086997032, 0.11719285696744919, -0.000268333125859499, -0.0662061795592308, 0.04391507804393768, 0.010892241261899471, -0.00274028186686337, -0.00903749093413353, 0.04728604108095169, -0.01941031590104103, -0.015409675426781178, 0.004431257955729961, 0.008936948142945766, 0.009862855076789856, -0.015935484319925308, 0.015809835866093636, 0.041163261979818344, -0.07544038444757462, -0.008714287541806698, -0.05555419623851776, -0.03231556713581085, -0.04247472062706947, 0.07287517189979553, 0.09324449300765991, -0.027214838191866875, -0.02718384563922882, 0.018437014892697334, 0.02888757735490799, -0.03292914479970932, 0.008554262109100819, -0.04920785874128342, 0.04556919261813164, 0.04306497052311897, -0.0025803118478506804, 0.0007307760533876717, 0.003631114261224866, 0.039354003965854645, 0.019485535100102425, 0.030826538801193237, -0.033879201859235764, 0.04410060867667198, -0.033673010766506195, 0.04419787600636482, 0.029958289116621017, -0.01047346368432045, 0.021618278697133064, 0.035181622952222824, 0.043682172894477844, -0.0349603146314621, 0.012804620899260044, 0.005928629543632269, 0.04100118204951286, -0.017982332035899162, 0.013754538260400295, 0.04127013310790062, -0.0002352665615035221, 0.02574462816119194, -0.015486743301153183, -0.015044606290757656, -0.04276472330093384, 0.012881295755505562, -0.02738376148045063, -5.771927789770951e-33, 0.021141545847058296, -0.0332019105553627, -0.007287805899977684, -0.005115922074764967, -0.04214101284742355, 0.02663475088775158, -0.0307999849319458, -0.013894205912947655, -0.020991047844290733, 0.03576280176639557, -0.038308534771203995, 0.02833797037601471, -0.003934480249881744, 0.030369484797120094, 0.01471832673996687, 0.02614610642194748, 0.01676050014793873, 0.01799599826335907, 0.031697869300842285, 0.008702754974365234, 0.06239328160881996, 0.03748706355690956, 0.06376441568136215, -0.02491862326860428, -0.0874810740351677, -0.0173466969281435, -0.019495269283652306, 0.0013508640695363283, -0.020703354850411415, 0.03352678567171097, 0.022478440776467323, -0.008234978653490543, 0.023331835865974426, -0.014956150203943253, -0.04555877670645714, -0.03510674089193344, -0.04548630490899086, -0.01617409661412239, -0.08325684070587158, 0.010696287266910076, -0.05286822095513344, 0.029484620317816734, 0.06385073810815811, -0.02008015103638172, 0.014055364765226841, 0.018462922424077988, 0.06780148297548294, -0.03623627871274948, -0.02113073319196701, -0.010708842426538467, 0.007426626980304718, 0.03872990980744362, -0.034440409392118454, -0.01844380423426628, 0.01702204905450344, -0.008101115934550762, -0.026195721700787544, 0.03221512585878372, -0.03227200731635094, -0.008959167636930943, -0.02378006838262081, 0.055684223771095276, -0.019301429390907288, 0.04221328720450401, 0.048614613711833954, 0.055207427591085434, 0.028997447341680527, -0.007447985000908375, -0.06073432043194771, -0.015912862494587898, 0.002348650246858597, 0.0648960992693901, 0.031147396191954613, 0.013417831622064114, 0.0776580199599266, -0.06239521875977516, -0.06544933468103409, 0.015749825164675713, -0.010794932022690773, 0.03975944221019745, 0.0011425118427723646, 0.029777634888887405, 0.022517725825309753, 0.009891125373542309, 0.010795259848237038, -0.06769654154777527, 0.011597694829106331, -0.0026428713463246822, 0.0149897625669837, 0.0007751033408567309, 0.02004975639283657, 0.0001701371802482754, 0.012694795615971088, -0.03502998501062393, 0.014934824779629707, 0.055386949330568314, 0.018961580470204353, 0.05228162556886673, 0.054294291883707047, -0.011841963045299053, -0.021270399913191795, -0.011950855143368244, -0.05009236931800842, 0.03890633583068848, 0.007904019206762314, 0.05177586153149605, 0.04091186821460724, 0.015606504864990711, 0.01842796802520752, -0.0442667119204998, -0.020014027133584023, -0.02056807279586792, -0.0197280440479517, 0.077606700360775, 0.027404909953475, -0.021740177646279335, -0.016520213335752487, 0.09376247227191925, -0.031142832711338997, 0.013517157174646854, -0.032677024602890015, 0.027370547875761986, 0.006373132579028606, 0.04543223977088928, -0.06670555472373962, -0.041146766394376755, -0.048991862684488297, 0.002104399725794792, 0.038335882127285004, -0.06811417639255524, -8.28399060992524e-05, 0.02741136960685253, 2.811911485878227e-07, -0.05257077515125275, -0.03515206277370453, 0.023178527131676674, -0.04043314605951309, 0.04736242815852165, -0.017061803489923477, -0.013702786527574062, 0.0009410188649781048, -0.04583076760172844, -0.04769718274474144, 0.03227076306939125, 0.02097502537071705, 0.017295675352215767, -0.0005452301120385528, -0.0463702529668808, 0.012364277616143227, -0.035507868975400925, 0.023628516122698784, 0.0027587844524532557, 0.01165253296494484, 0.025606365874409676, 0.09453676640987396, 0.033142026513814926, -0.02593098394572735, 0.03405908867716789, 0.042669620364904404, -0.0007332430686801672, 0.02761710248887539, 0.06273889541625977, -0.01822025515139103, 0.014278381131589413, 0.008710754103958607, 0.0036104172468185425, 0.0077296956442296505, -0.004199335351586342, 0.06355183571577072, -0.008427934721112251, 0.025195550173521042, -0.06056765466928482, -0.018296942114830017, 0.03978079929947853, 0.05391775444149971, 0.04745401814579964, -0.024403581395745277, 0.0064191329292953014, -0.010431346483528614, 0.0010580335510894656, -0.04322630167007446, 0.005798866972327232, 0.05956103280186653, 0.04266210272908211, 0.011423997581005096, -0.0049083540216088295, -0.011325969360768795, 0.006817100569605827, -0.03500539809465408, -0.0029906192794442177, -0.06201563775539398, 0.0035262713208794594, 0.019419243559241295, -0.04471242055296898, -0.023096466436982155, -0.020509470254182816, -0.05553599074482918, 0.06322336196899414, 0.015950540080666542, -0.06732209771871567, 2.2239512822767834e-34, 0.017762180417776108, 0.0026764394715428352, -0.02837313897907734, 0.036043472588062286, -0.02900688536465168, -0.01657174341380596, 0.0760021060705185, 0.00730102276429534, -0.0003663035458885133, 0.009720029309391975, -0.06120508164167404]

['Anh Nguyen', 'Alexey Dosovitskiy', 'Jason Yosinski', 'Thomas Brox', 'Jeff Clune']

1605.09304v5

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right - similar to why we study the human brain - and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

Synthesizing the preferred inputs for neurons in neural networks via deep generator networks

http://arxiv.org/pdf/1605.09304v5

Title Synthesizing preferred input neuron neural network via deep generator network Summary Deep neural network DNNs demonstrated stateoftheart result many pattern recognition task especially vision classification problem Understanding inner working computational brain fascinating basic science interesting right similar study human brain enable researcher improve DNNs One path understanding neural network function internally study neuron learned detect One method called activation maximization synthesizes input eg image highly activates neuron dramatically improve qualitative state art activation maximization harnessing powerful learned prior deep generator network DGN algorithm 1 generates qualitatively stateoftheart synthetic image look almost real 2 reveals feature learned neuron interpretable way 3 generalizes well new datasets somewhat well different network architecture without requiring prior relearned 4 considered highquality generative method case generating novel creative interesting recognizable image Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.01585194654762745, 0.07251649349927902, -0.01084416825324297, 0.02141485922038555, 0.002123874379321933, -0.0032464833930134773, 0.025581488385796547, 0.011971809901297092, -0.01633543334901333, 0.035361990332603455, -0.015380226075649261, 0.004455838818103075, -0.009208879433572292, 0.06377391517162323, 0.06678320467472076, -0.027917034924030304, -0.002827609656378627, 0.0588771253824234, -0.04144006595015526, -0.03528841957449913, -0.029582468792796135, -0.0295436829328537, -0.01354826707392931, 0.020372584462165833, -0.02278113178908825, 0.027756359428167343, -0.008153930306434631, 0.029040662571787834, 0.026481064036488533, -0.025446616113185883, -0.013252466917037964, 0.008545508608222008, -0.008741660043597221, 0.03826569765806198, 2.569582420619554e-06, -0.0070153940469026566, 0.042960695922374725, -0.029672369360923767, -0.009755006060004234, -0.045509953051805496, 0.01421501487493515, 0.0339449904859066, -0.05300358682870865, -0.041381146758794785, -0.05931113287806511, -0.0591612346470356, 0.04413161054253578, 0.07287931442260742, -0.010483451187610626, 0.06085648760199547, -0.02771984413266182, -0.05626368522644043, 0.05625409632921219, -0.03570840135216713, 0.01758117787539959, 0.016314901411533356, 0.007285315077751875, 0.018400942906737328, -0.006318919826298952, -0.04447280615568161, -0.007563535589724779, 0.028384264558553696, 0.06034298241138458, -0.005710373166948557, 0.06230461969971657, 0.0695844516158104, 0.02791457064449787, -0.011924728751182556, 0.009911909699440002, 0.05634678900241852, -0.08453594893217087, 0.018856698647141457, 0.01706789992749691, -0.015156704932451248, -0.004840570501983166, -0.05580006539821625, 0.00232794601470232, -0.006866673473268747, -0.0206085704267025, 0.058062855154275894, -0.03173684701323509, 0.014355280436575413, 0.015790069475769997, -0.017234552651643753, 0.007106588687747717, -0.03499557077884674, 0.013039018958806992, 0.04689102619886398, -0.01878255046904087, -0.012096510268747807, -0.050308044999837875, -0.02550305612385273, 0.03448988497257233, -0.013141337782144547, -0.007338696159422398, -0.028252262622117996, -0.01052682101726532, -0.07408457249403, 0.005749935749918222, -0.02188250608742237, 0.027463652193546295, 0.005377720110118389, -0.05004679784178734, -0.022943979129195213, -0.03245197609066963, 0.03246646746993065, -0.07359281182289124, 0.030655447393655777, -0.035013314336538315, 0.0205326359719038, -0.040724534541368484, -0.004587837029248476, 0.009187922812998295, 0.02608766034245491, -0.007278773467987776, -0.05344357714056969, -0.08806294947862625, -0.0038812614511698484, -0.021421246230602264, -0.036968909204006195, -0.015931978821754456, 0.10579885542392731, -0.06287787109613419, -0.014818515628576279, -0.01208819542080164, -0.0148452864959836, -0.031742580235004425, 0.04803376644849777, 0.03813370689749718, -0.05292487516999245, 0.03313106670975685, 0.005093340761959553, 0.01461969967931509, 0.031128903850913048, 0.017281807959079742, 0.061582062393426895, -0.022555431351065636, 0.05091840773820877, -0.06395025551319122, 0.015380723401904106, 0.03508402779698372, -0.008315585553646088, 0.05765803903341293, -0.05923617631196976, 0.030734267085790634, -0.04597397893667221, -0.024038784205913544, -0.05360604450106621, -0.008332408964633942, -0.02513563632965088, 0.018851492553949356, 0.047284383326768875, -0.06009327620267868, -0.03292924910783768, 0.06335178017616272, 0.004505346063524485, 0.02828473411500454, -0.0048827179707586765, 0.04658150672912598, 0.06287276744842529, -0.03181196749210358, -0.01570160686969757, 0.030522458255290985, 0.012092741206288338, -0.007140421308577061, -0.043958958238363266, -0.029288385063409805, -0.08661387115716934, -0.04003604128956795, 0.056263089179992676, 0.03269747644662857, 0.013096237555146217, -0.04185416176915169, 0.023211751133203506, 0.04509713873267174, 0.018619270995259285, 0.0850379541516304, 0.07092553377151489, -0.008879432454705238, -0.02556023746728897, -0.014049640856683254, 0.028574468567967415, 0.006695460062474012, 0.08763450384140015, 0.007329669315367937, -0.014679946936666965, -0.03447581082582474, 0.03669559210538864, -0.03257681801915169, -0.05049675703048706, 0.06162659078836441, -0.0482671894133091, -0.01146730687469244, -0.009542162530124187, 0.06252104789018631, 0.037934109568595886, -0.03147214651107788, -0.03778589516878128, 0.00788592454046011, 0.04956776648759842, -0.008556599728763103, -0.0505947582423687, -0.012623194605112076, -0.024630486965179443, 0.013856103643774986, -0.0317285992205143, 0.004260442219674587, -0.005256716161966324, -0.05567927286028862, 0.02984544262290001, -0.043801724910736084, 0.022355182096362114, 0.03490437939763069, -0.05177437886595726, -0.020291900262236595, -0.013932749629020691, 0.0003931939136236906, 0.07610925287008286, -0.034454189240932465, 0.014577854424715042, -0.0024140626192092896, 0.04881548509001732, -0.020219456404447556, 0.01051755528897047, -0.035133372992277145, -0.03185345605015755, 0.042102571576833725, 0.008642090484499931, -0.0044481391087174416, -0.015323657542467117, -0.0038307716604322195, -0.011245159432291985, -0.0003210082068108022, -0.055537909269332886, -0.04622144252061844, -0.04621155932545662, -0.06591172516345978, -0.019533950835466385, -0.02117924392223358, -0.05736205726861954, 0.034894924610853195, 0.020430579781532288, -0.01964663341641426, -0.03646017611026764, 0.015909789130091667, 0.016321785748004913, -0.026553969830274582, -0.03851090744137764, -0.035705436021089554, 0.005614737048745155, 0.03376317396759987, -0.003071726532652974, 0.04544311761856079, 0.02395538240671158, -0.02385248988866806, -0.0064644948579370975, 0.00715921726077795, 0.03642338141798973, -0.029654409736394882, -0.004404005594551563, 0.033131491392850876, -0.033168431371450424, -0.02091650851070881, 0.0011616329429671168, 0.023951705545186996, -0.03881566971540451, -0.005773006938397884, -0.018081340938806534, 0.03785841539502144, -0.009791762568056583, -0.027004992589354515, 0.005462619476020336, 0.012692769058048725, 0.01661977916955948, 0.007397317793220282, -0.06525160372257233, 0.06965664029121399, 0.030025947839021683, -0.04944472759962082, 0.05170757696032524, 0.03872346132993698, 0.04207715019583702, -0.010761722922325134, -0.01582769863307476, 0.014919396489858627, 0.040812890976667404, 0.05163359269499779, -0.010308751836419106, 0.005322074051946402, 0.028338978067040443, -0.005407595541328192, 0.041598234325647354, -0.008782886900007725, -0.06659035384654999, -7.987736171344295e-05, -0.002695983275771141, -0.008294603787362576, 0.0891103744506836, 0.017107337713241577, -0.052227914333343506, -0.030110763385891914, 0.06193101406097412, -0.020127499476075172, 0.010256650857627392, -0.01734846644103527, 0.03678188472986221, 0.012259379029273987, 0.006017724517732859, -0.03599702939391136, -0.001400029519572854, 0.060569487512111664, 0.02011825516819954, 0.014003278687596321, 0.05657732114195824, 0.02028810977935791, -0.02061721682548523, -0.026714002713561058, 0.0024867390748113394, -0.02012547105550766, 0.017096802592277527, -0.014392992481589317, -0.04288413003087044, 0.03440836817026138, 0.04386364296078682, -0.014227651990950108, 0.0017789008561521769, -0.007123333401978016, 0.026862312108278275, -0.02400827780365944, 0.027144990861415863, 0.031035033985972404, 0.021806176751852036, -0.008298441767692566, -0.042970433831214905, 0.017647746950387955, -0.014715747907757759, -0.03028136119246483, -0.009965607896447182, 0.011108100414276123, -0.025813914835453033, -0.015672577545046806, -0.035038601607084274, -0.09145518392324448, 0.053463444113731384, 0.003861228469759226, 0.02012806013226509, 0.021642988547682762, -0.0026214406825602055, 0.048416536301374435, -0.044778209179639816, -0.0018385775620117784, 0.04133383184671402, -0.024037353694438934, -0.015448075719177723, -0.012193971313536167, 0.09754776954650879, 0.014847101643681526, -0.0388873815536499, -0.005219522397965193, 0.07777276635169983, 0.010013248771429062, 0.023205319419503212, -0.021466689184308052, 0.031062234193086624, -0.11849026381969452, 0.009614705108106136, -0.028898146003484726, 0.05290528014302254, -0.021873246878385544, -0.023386623710393906, -0.03458571806550026, -0.030533555895090103, 0.03811585158109665, 0.005644928198307753, -0.028207246214151382, -0.06366119533777237, 0.011081257835030556, 0.023255491629242897, -0.028393413871526718, 0.003216611919924617, 0.04273321107029915, -0.033242832869291306, -0.0027423729188740253, -0.03410293161869049, -0.001890359679237008, -0.00867484137415886, -0.014458542689681053, 0.009282469749450684, -0.027468619868159294, 0.06155173480510712, 0.02889304794371128, 0.00902770459651947, 0.001860737451352179, 0.04530471935868263, 0.005231859162449837, 0.01026763953268528, -0.04270069673657417, 0.024601325392723083, 0.05505373701453209, -0.027891727164387703, 0.0266116950660944, 0.04286903142929077, -0.018403738737106323, -0.007230257615447044, -0.03790732100605965, 0.02085726335644722, 0.08323612809181213, 0.04295720160007477, -0.041814666241407394, -0.05231113359332085, 0.009276877157390118, 0.039092693477869034, 0.03805459663271904, -0.00827490072697401, 0.05262498930096626, 0.0634322538971901, -0.014930540695786476, -0.0012210365384817123, 0.09516946226358414, -0.018587375059723854, 0.03948337212204933, -0.009800966829061508, -0.01815151795744896, 0.012955366633832455, -0.003842493984848261, -0.04819705709815025, -5.117821274325252e-06, 0.05864093080163002, -0.053769055753946304, 0.0319964736700058, -0.050039492547512054, -0.020947065204381943, -0.022961793467402458, 0.06263838708400726, -0.09182946383953094, -0.03585253283381462, -0.012855848297476768, 0.0359073244035244, -0.030725717544555664, -0.05597522109746933, 0.004540620371699333, -0.053212765604257584, 0.07768235355615616, 0.0009648994309827685, -0.02210446633398533, 0.028398185968399048, -0.026764821261167526, 0.0013917004689574242, 0.003148318501189351, 0.023496393114328384, -0.02458660863339901, -0.021009990945458412, -0.032156601548194885, 0.052559781819581985, -0.04148733243346214, -0.016883108764886856, 0.012902352027595043, 0.0111271683126688, -0.008144766092300415, 0.02028358168900013, 0.03632357716560364, 0.009253144264221191, -0.022901343181729317, 0.0009051748784258962, -0.04000251740217209, 0.06317334622144699, 0.05586924031376839, 0.03112499788403511, -0.023503761738538742, 0.02251347526907921, -0.007199686486274004, -0.01890314370393753, -0.004998000804334879, -0.009523322805762291, 0.1008782833814621, 0.007049954496324062, -0.029949462041258812, 0.021803822368383408, -0.0023456488270312548, 0.01985977590084076, -0.011485938914120197, 0.023390812799334526, -0.012826650403439999, 0.08009107410907745, -0.06547123938798904, -0.008239882066845894, 0.04250825196504593, 0.05462172254920006, -0.07717685401439667, -0.02126411534845829, 0.030760256573557854, 0.031976159662008286, 0.0004307667550165206, -0.04472308233380318, 0.04304206371307373, -0.014112098142504692, -0.023938439786434174, -0.005098414141684771, 0.01679994724690914, 0.0032990763429552317, -0.036495864391326904, 0.022306319326162338, 0.0026862502563744783, 0.01017905492335558, 0.02419433742761612, 0.03119685873389244, -0.04676363617181778, 0.03179025277495384, 0.023967768996953964, -0.04915748909115791, -0.04711323231458664, 0.030065886676311493, -0.005264465231448412, -0.0515805222094059, -0.05028079077601433, 0.05263231694698334, 0.10511662811040878, 0.02905847318470478, -0.02452186308801174, -0.0069084311835467815, 0.02237688936293125, -0.0409625880420208, 0.011661119759082794, -0.013700589537620544, -0.020901836454868317, -0.017812129110097885, 0.0008277582819573581, 0.014596930705010891, -0.05064070597290993, 0.049360159784555435, 0.024709351360797882, -0.009504655376076698, -0.024632306769490242, 0.03572823107242584, -0.01874619908630848, 0.028949907049536705, -0.010396163910627365, -0.00396001199260354, 0.0006547605153173208, 0.026011928915977478, 0.014736813493072987, -0.03643445670604706, 0.0343303345143795, 0.006665369495749474, 0.022997578606009483, -0.013549091294407845, 0.041671209037303925, -0.022097669541835785, -0.015316787175834179, -0.0394219234585762, 0.03964430093765259, 0.026393208652734756, -0.008830918930470943, -0.017784101888537407, -0.026760239154100418, -6.706898363999736e-33, 0.004307564347982407, -0.011611382476985455, -0.01863267831504345, -0.04528394713997841, -0.033516839146614075, 0.0015585286309942603, -0.01767568662762642, -0.03329714760184288, -0.009424688294529915, -0.0005650307284668088, -0.07265303283929825, 0.007746568415313959, 0.009663625620305538, 0.039647236466407776, -0.003936734516173601, 0.00623852526769042, 0.019464053213596344, -0.014590416103601456, 0.04569952189922333, 0.03165894001722336, 0.0023256412241607904, 0.0372098870575428, 0.057562559843063354, -0.08127834647893906, -0.08792524039745331, -0.007527059875428677, -0.034418735653162, -0.030355634167790413, -0.018917005509138107, -0.01363343559205532, -0.018508685752749443, 0.037708379328250885, 0.010595015250146389, -0.06089387089014053, -0.003763055894523859, -0.059423282742500305, -0.02138340286910534, 0.005573023110628128, -0.06821681559085846, -0.018786538392305374, -0.09828078746795654, -0.005263078026473522, 0.04571809992194176, -0.028882766142487526, -0.029056696221232414, 0.042369671165943146, 0.03348134458065033, -0.030267219990491867, -0.024624478071928024, -0.053211651742458344, -0.045925650745630264, -0.009190228767693043, 0.0010692045325413346, -0.013470872305333614, 0.010377117432653904, -0.014769085682928562, -0.047896068543195724, 0.009440852329134941, -0.08945933729410172, 0.010289083234965801, 0.037908077239990234, 0.02911851368844509, 0.004200361203402281, 0.04757743328809738, 0.07957539707422256, 0.009230583906173706, 0.0689532533288002, -0.030842121690511703, -0.05699938163161278, -0.004558562766760588, 0.01894383504986763, 0.05012178048491478, 0.02656598389148712, 0.03227485343813896, 0.0985967367887497, -0.09865418076515198, -0.05160136893391609, 0.02953227236866951, -0.007395975291728973, -0.005687251221388578, 0.00921543501317501, 0.042773447930812836, 0.014174459502100945, -0.02910546213388443, 0.0286397822201252, -0.05624387785792351, -0.01976737566292286, -0.031907327473163605, 0.007732391357421875, -0.01311691664159298, -0.02455149032175541, -0.03745860978960991, 0.007424522191286087, -0.05671440437436104, 0.07209355384111404, 0.008109619840979576, 0.004656120203435421, 0.043373242020606995, 0.03360647335648537, -0.053020574152469635, -0.008539756760001183, -0.03445378690958023, 0.01664481684565544, 0.0577303022146225, 0.03152034059166908, 0.025738557800650597, -0.004918060731142759, 0.027506887912750244, 0.038773056119680405, 0.001717421691864729, -0.023954477161169052, -0.0025911375414580107, 0.04840115085244179, -0.00882173702120781, -0.035386428236961365, -0.06620708853006363, -0.009574242867529392, -0.021921470761299133, 0.01599411852657795, 0.0490303598344326, -0.04003593698143959, 0.013187751173973083, 0.002312934724614024, 0.050933077931404114, -0.051509156823158264, 0.026402326300740242, -0.06286660581827164, 0.018232598900794983, 0.015071052126586437, -0.04812509939074516, -0.02216356061398983, 0.005812154151499271, 3.23332102425411e-07, -0.03791302070021629, -0.011093155480921268, 0.019290486350655556, -0.030402805656194687, 0.04335241764783859, 0.024635687470436096, 0.022482845932245255, 0.02170098014175892, -0.01964227668941021, -0.03859240934252739, 0.036284103989601135, 0.005325283855199814, -0.017682697623968124, 0.017780480906367302, -0.06373967230319977, 0.02381039597094059, 0.006682285573333502, 0.07523614168167114, 0.01849137619137764, -0.013458909466862679, 0.003978325519710779, 0.047732479870319366, -0.016903601586818695, -0.0475960299372673, 0.10206454992294312, -0.009312497451901436, 0.03325358033180237, 0.03930358216166496, 0.05313486233353615, 0.0210449006408453, 0.05999939516186714, 0.039571549743413925, -0.005897339899092913, -0.033594369888305664, 0.005995970219373703, -0.0020583064761012793, 0.020777389407157898, 0.007866723462939262, -0.01790309138596058, -0.04455842822790146, -0.0022375117987394333, 0.020855793729424477, 0.042571231722831726, -0.015127521008253098, 0.016048673540353775, -0.05594111979007721, -0.03557189926505089, -0.02894001640379429, -0.011910640634596348, -0.011067578569054604, 0.03486403822898865, -0.03154139593243599, -0.008450173772871494, -0.015397449024021626, -0.012469114735722542, -0.030570808798074722, -0.010079675354063511, 0.0021236117463558912, 0.021863272413611412, -0.003586219158023596, -0.060894884169101715, 0.01229985523968935, -0.03324748948216438, 0.010194008238613605, 0.05612577125430107, 0.056150320917367935, -0.0326216034591198, 2.3431569705322215e-34, -0.02333056926727295, 0.022723205387592316, 0.013251385651528835, -0.012254655361175537, -0.008612499572336674, 0.0201733261346817, 0.00661021051928401, -0.01602299138903618, -0.011567637324333191, -0.007725302595645189, -0.07219776511192322]

['Rathinakumar Appuswamy', 'Tapan Nayak', 'John Arthur', 'Steven Esser', 'Paul Merolla', 'Jeffrey Mckinstry', 'Timothy Melano', 'Myron Flickner', 'Dharmendra Modha']

1606.02407v1

We derive a relationship between network representation in energy-efficient neuromorphic architectures and block Toplitz convolutional matrices. Inspired by this connection, we develop deep convolutional networks using a family of structured convolutional matrices and achieve state-of-the-art trade-off between energy efficiency and classification accuracy for well-known image recognition tasks. We also put forward a novel method to train binary convolutional networks by utilising an existing connection between noisy-rectified linear units and binary activations.

Structured Convolution Matrices for Energy-efficient Deep learning

http://arxiv.org/pdf/1606.02407v1

Title Structured Convolution Matrices Energyefficient Deep learning Summary derive relationship network representation energyefficient neuromorphic architecture block Toplitz convolutional matrix Inspired connection develop deep convolutional network using family structured convolutional matrix achieve stateoftheart tradeoff energy efficiency classification accuracy wellknown image recognition task also put forward novel method train binary convolutional network utilising existing connection noisyrectified linear unit binary activation Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.016599668189883232, 0.04337156191468239, -0.00867722649127245, 0.11679377406835556, 0.0019713821820914745, -0.0058877295814454556, 0.016658274456858635, 0.01525559090077877, -0.006829366087913513, -0.032412685453891754, -0.042291976511478424, 0.010505524463951588, -0.004430582281202078, 0.04620462656021118, 0.028348928317427635, -0.030440382659435272, 0.0301455520093441, 0.025812046602368355, -0.016427529975771904, -0.015048199333250523, 0.00782067235559225, -0.015614147298038006, 0.012175868265330791, 0.023458190262317657, -0.07279177755117416, 0.012164019048213959, -0.021240098401904106, 0.03256068751215935, 0.030468042939901352, -0.029631691053509712, 0.022619744762778282, 0.010048550553619862, 0.018055599182844162, 0.00953214056789875, 2.431712346151471e-06, 0.019628839567303658, -0.008125725202262402, -0.020729118958115578, 0.007462976034730673, -0.013644563965499401, 0.00938432477414608, -0.01042348425835371, 2.55712238868e-05, -0.0010156900389119983, -0.012340011075139046, -0.014695463702082634, 0.06569191068410873, 0.055038608610630035, -0.023765770718455315, 0.045943379402160645, -0.026169557124376297, -0.04703248664736748, 0.07112206518650055, -0.014760803431272507, 0.005713315214961767, 0.01338678877800703, -0.01772194355726242, 0.01628364995121956, -0.057619184255599976, -0.004979720804840326, -0.03486078232526779, 0.020249057561159134, 0.04097661375999451, -0.027690110728144646, 0.071197509765625, 0.05177924782037735, -0.01881803385913372, -0.0004286168550606817, -0.003735792124643922, 0.07649315148591995, -0.03308124840259552, 0.03359029069542885, 0.011363263241946697, 0.0015716982306912541, -0.06451091915369034, -0.04241150617599487, 0.032550662755966187, -0.010436869226396084, -0.007877062074840069, 0.01754414662718773, -0.048818279057741165, 0.03896990045905113, 0.02506208047270775, 0.05211235582828522, 0.011505916714668274, 0.023261936381459236, -0.004753527697175741, 0.02647980861365795, 0.008811142295598984, -0.009319423697888851, 0.015468061901628971, -0.038837019354104996, 0.028643237426877022, -0.01968657597899437, 0.02076251059770584, -0.017481215298175812, -0.045030638575553894, -0.05059380829334259, -0.008944622240960598, -0.05874107405543327, 0.034051235765218735, -0.0006139660254120827, 0.007902031764388084, 0.0397329181432724, -0.05474615469574928, 0.0182998888194561, -0.05940147861838341, 0.015778178349137306, -0.04192223399877548, 0.02492348849773407, 0.0005831334856338799, 0.022757258266210556, -0.023052947595715523, 0.03997467830777168, -0.034049201756715775, -0.04763457179069519, -0.03698660805821419, 0.008101633749902248, -0.03545001149177551, 0.0013358814176172018, -0.044170353561639786, 0.059404488652944565, 0.03908945620059967, -0.012788675725460052, -0.018622493371367455, 0.02551604062318802, 0.029855666682124138, -0.016171250492334366, -0.012802273966372013, -0.007301140110939741, 0.03946024551987648, 0.017681319266557693, 0.009111403487622738, -0.0019707896281033754, 0.0383966788649559, 0.05037437006831169, 0.027547767385840416, -0.06342735886573792, -0.059864819049835205, 0.015918783843517303, 0.04979737848043442, -0.02413139119744301, 0.055860426276922226, -0.05726613476872444, 0.017219558358192444, -0.04108056053519249, -0.01731066219508648, -0.008873088285326958, 0.035958413034677505, -0.01933201402425766, -0.03217608109116554, 0.07113197445869446, -0.0213040579110384, -0.023683007806539536, 0.050766631960868835, -0.007631565444171429, 0.05243410915136337, 0.038417574018239975, 0.10649044066667557, 0.007557510863989592, 0.012171544134616852, -0.009500469081103802, -0.05033644661307335, -0.029883015900850296, 0.04144396632909775, -0.02797839790582657, -0.040417782962322235, -0.025292538106441498, -0.0311297494918108, 0.010536005720496178, 0.03323160856962204, 0.03824426233768463, -0.015948021784424782, 0.0012236302718520164, -0.0032041778322309256, -0.014359502121806145, 0.008741220459342003, 0.06232167407870293, -0.04144930839538574, -0.03429342806339264, 0.0025393671821802855, -0.038137663155794144, -0.04172753542661667, 0.10937783122062683, 0.006785763893276453, -0.07147903740406036, -0.017659839242696762, 0.003663453971967101, -0.043550264090299606, -0.03534464165568352, 0.042284246534109116, -0.02679537422955036, 0.03114461526274681, 0.00034493691055104136, 0.015823906287550926, 0.0009545402717776597, -0.036394957453012466, 0.030766453593969345, 0.0004788386868312955, 0.012918950989842415, -0.05813946947455406, -0.04173063486814499, -0.010127903893589973, 0.004290955141186714, -0.01763402856886387, 0.020574407652020454, -0.012169591151177883, 0.021535079926252365, -0.02241235226392746, -0.055405449122190475, -0.010279282927513123, -0.008824341930449009, 0.04811882600188255, -0.06458000093698502, -0.03639039024710655, -0.013234644196927547, -0.009188108146190643, 0.020152077078819275, -0.023750856518745422, -0.006796186324208975, 0.030378593131899834, 0.07501359283924103, 0.03765440732240677, -0.0020058222580701113, 0.047944214195013046, 0.008867979049682617, 0.06465718150138855, 0.039675273001194, 0.03667799383401871, 0.012717300094664097, 0.019508015364408493, -0.03466281667351723, 0.04406609758734703, -0.06707567721605301, -0.001930360565893352, -0.04224536567926407, -0.06326460093259811, 0.00893044751137495, -0.007838606834411621, 0.023932581767439842, 0.03453266620635986, 0.03046906366944313, -0.028330938890576363, -0.04752785339951515, 0.009708689525723457, -0.011387193575501442, 0.03905705735087395, -0.00647793710231781, -0.002688380191102624, 0.02957581728696823, 0.009826567955315113, -0.007023284211754799, 0.03404149413108826, -0.01888246089220047, 0.013938136398792267, -0.038886334747076035, 0.01246159803122282, 0.03943374752998352, -0.020915646106004715, -0.002761811949312687, 0.004939465317875147, -0.04143451899290085, 0.0012297084322199225, -0.0038211094215512276, 0.012151068076491356, 0.012657437473535538, 0.04627581313252449, -0.04969935119152069, 0.03780561313033104, -0.014140576124191284, -0.0022811582311987877, 0.005360778886824846, -0.004211428575217724, 0.04735903441905975, -0.016345025971531868, -0.02662336826324463, 0.08339786529541016, -0.06517943739891052, -0.01798601634800434, 0.01743539422750473, 0.015323683619499207, -0.03175445646047592, -0.015848712995648384, -0.06411582976579666, 0.0003062295727431774, 0.03751692175865173, 0.02246112935245037, -0.06152194365859032, 0.015111091546714306, 0.008939629420638084, 0.010565163567662239, 0.014420073479413986, -0.014746767468750477, -0.035951610654592514, -0.030516931787133217, 0.0042222230695188046, 0.007648984901607037, 0.05949550122022629, 0.005787550937384367, 0.0006101507460698485, 0.02986065484583378, 0.03435955196619034, 0.03622308745980263, 0.047706328332424164, 0.025174353271722794, 0.043450064957141876, 0.03510645404458046, 0.01031528040766716, -0.08185673505067825, -0.007273056078702211, -0.023555556312203407, 0.042618703097105026, 0.02160356566309929, -0.05527946725487709, 0.023806137964129448, -0.022110305726528168, -0.049673911184072495, -0.012316543608903885, 0.027337225154042244, -0.01990378089249134, -0.018543319776654243, -0.03301383554935455, -0.018191050738096237, 0.022760938853025436, -0.009036937728524208, -0.006313268560916185, -0.04900381714105606, 0.024138808250427246, 0.08172953873872757, 0.07525365054607391, 0.06672144681215286, -0.003689609467983246, -0.0002181256131734699, -0.035175956785678864, -0.03695809096097946, -0.025021567940711975, -0.011704482138156891, 0.038119345903396606, -0.0005490595358423889, 0.006849339231848717, -0.03416956588625908, -0.0501762330532074, -0.04293975606560707, 0.07512006908655167, -0.02887020818889141, 0.014383608475327492, 0.0063655199483036995, -0.059982165694236755, 0.02423926070332527, -0.006026467774063349, 0.027334608137607574, 0.018547765910625458, 0.018251756206154823, -0.007701375521719456, -0.015857378020882607, 0.08136735111474991, 0.0363120511174202, -0.01511524710804224, 0.002010130090638995, 0.045087505131959915, 0.007731692399829626, 0.06452180445194244, -0.05299073085188866, 0.04864481836557388, -0.13058948516845703, 0.010544983670115471, -0.016974441707134247, 0.06291136890649796, -0.06076546758413315, -0.023867793381214142, 0.022315682843327522, -0.04740167036652565, 0.02879837527871132, 0.0003603390359785408, -0.019587131217122078, -0.08522354066371918, -0.006794557441025972, 0.022617340087890625, 0.015004193410277367, 0.00024393103376496583, 0.010772067122161388, -0.05068950355052948, -0.038003772497177124, 0.0013102866942062974, -0.03294989466667175, 0.0007483243243768811, -0.02230164222419262, -0.0059069362469017506, -0.012111181393265724, -0.01987873576581478, -0.006143045611679554, -0.009051768109202385, -0.05017172545194626, -0.04385892301797867, -0.012394241988658905, -0.016447611153125763, -0.03239087760448456, -0.004082818049937487, 0.011793653480708599, -0.04474161937832832, -0.000848697149194777, -0.003731279633939266, 0.048725757747888565, -0.0017027888679876924, -0.05019601061940193, -0.01979982852935791, 0.06635334342718124, 0.014450394548475742, -0.017794497311115265, -0.04680309444665909, 0.016379794105887413, -0.01274058036506176, -0.019058074802160263, -0.07021337002515793, 0.04065687954425812, 0.03844520449638367, -0.04476218670606613, -0.018222123384475708, 0.03725128248333931, -0.038164686411619186, 0.013530425727367401, -0.02924979291856289, 0.02894691564142704, 0.0035903644748032093, 0.013275900855660439, -0.04265616089105606, -0.03785507753491402, 0.022030869498848915, 0.018181635066866875, -0.015245087444782257, 0.010412064380943775, -0.07953783869743347, 0.03763209655880928, 0.022306343540549278, -0.0336633026599884, 0.015698162838816643, 0.011462576687335968, -0.022447051480412483, -0.02543366327881813, -0.017070405185222626, 0.001908873557113111, -0.012619261629879475, 0.04180694371461868, -0.03184295818209648, -0.08184031397104263, 0.0374719575047493, 0.017584048211574554, -0.05380646884441376, 0.0037479230668395758, 0.024120312184095383, 0.036339275538921356, -0.04099445790052414, -0.026346003636717796, 0.04102497547864914, 0.0286547988653183, -0.005878684110939503, -0.05983554199337959, -0.09969129413366318, -0.007405940443277359, -0.045744698494672775, 0.05770562216639519, -0.00125943124294281, -0.006929187569767237, 0.053471747785806656, 0.013714658096432686, -0.05542583391070366, 0.053009167313575745, -0.030579032376408577, 0.023311536759138107, 0.02342253178358078, -0.02005237713456154, -0.025059038773179054, 0.051509324461221695, -0.014992447569966316, 0.06192797049880028, -0.0347134955227375, 0.017951184883713722, -0.05537508428096771, -0.015692325308918953, -0.0022719567641615868, -0.020786313340067863, 0.04666600003838539, 0.03990612551569939, 0.01302018016576767, -0.017167910933494568, 0.03951973468065262, 0.018394075334072113, 0.05222111940383911, -0.08848439902067184, -0.013410876505076885, 0.0034645581617951393, 0.016483301296830177, 0.017238039523363113, -0.0628717690706253, 0.09796543419361115, -0.042272791266441345, 0.046624913811683655, 0.0166647806763649, -0.00101015018299222, 0.05586676672101021, -0.03461414575576782, 0.04921886697411537, -0.024191780015826225, 0.017866527661681175, 0.05647429823875427, 0.025539670139551163, -0.02390509471297264, -0.02099117636680603, 0.01652780920267105, -0.024969711899757385, -0.10005464404821396, 0.027855873107910156, 0.01860920898616314, -0.024672184139490128, -0.01448504813015461, -0.0037888858933001757, 0.0384979210793972, -0.009814932942390442, -0.009509969502687454, -0.03180913254618645, 0.007989460602402687, -0.01477732416242361, 0.03385269641876221, -0.04469800367951393, 0.02232028730213642, 0.06424682587385178, 0.027632737532258034, 0.0006776596419513226, 0.02450546622276306, 0.007619607727974653, 0.02061907760798931, 0.004576861392706633, 0.005595474503934383, 0.011570119298994541, -0.00780393835157156, 0.030658064410090446, -0.023715298622846603, -0.004610864911228418, 0.0036566765047609806, 0.013033095747232437, 0.008205641061067581, -0.020588602870702744, 0.007143229246139526, -0.026272492483258247, 0.0769096240401268, -0.008705390617251396, 0.05662820115685463, -0.01628015749156475, 0.044481582939624786, -0.08380924165248871, 0.01601685956120491, -0.0343317911028862, 0.008857852779328823, -0.03643389418721199, -0.04776156321167946, -6.665728143730124e-33, 0.03073403798043728, -0.028995929285883904, -0.006072133779525757, 0.0019245559815317392, -0.03199726715683937, 0.0699787512421608, -0.014524027705192566, -0.015191790647804737, -0.0811714231967926, -0.006728260777890682, -0.027344010770320892, -0.006366321817040443, 0.01753416657447815, 0.03170090168714523, 0.005158301908522844, -0.018054546788334846, 0.022774092853069305, -0.014589283615350723, 0.07733460515737534, 0.04754241555929184, 0.04571067914366722, 0.011081493459641933, 0.012644675560295582, -0.09039288759231567, -0.09514128416776657, -0.0005696716834791005, -0.024799780920147896, -0.006477854214608669, -0.00434292946010828, -0.004874315112829208, -0.053004585206508636, -0.00945669412612915, 0.018408332020044327, 0.04401060566306114, 0.017986303195357323, 0.009768911637365818, -0.10916166007518768, -0.0021523195318877697, -0.08200700581073761, 0.012251081876456738, -0.05539705604314804, -0.0009201392531394958, 0.044899482280015945, 0.02120128646492958, -0.003276247764006257, -0.017099758610129356, -0.006157726515084505, -0.01651507429778576, -0.048066213726997375, -0.008312447927892208, -0.02616225928068161, 0.014356897212564945, 0.03413568437099457, 0.010437652468681335, 0.0118675222620368, -0.0457233227789402, -0.032994210720062256, 0.003693402511999011, -0.07394704967737198, -0.03535189852118492, -0.0031712036579847336, 0.06601782143115997, 0.003837356809526682, 0.02958764135837555, 0.03868652880191803, 0.01006369199603796, 0.05155019462108612, -0.0011627032654359937, -0.03913644701242447, 0.017015241086483, 0.0026867256965488195, 0.07214817404747009, 0.030719110742211342, -0.019789133220911026, 0.08641394227743149, -0.05907057225704193, -0.09158643335103989, -0.024530714377760887, 0.04759649187326431, 0.04448145627975464, -0.05257800221443176, 0.02398589439690113, -0.006886482238769531, -0.003796459874138236, 0.03766056150197983, 5.628622602671385e-05, -0.026938723400235176, -0.0534113310277462, -0.017105402424931526, -0.0043137031607329845, -0.009437955915927887, 0.014745923690497875, -0.005046119913458824, -0.026579437777400017, 0.05714190751314163, 0.026305127888917923, 0.0377693846821785, 0.04731925204396248, 0.051185138523578644, 0.0002347757836105302, -0.040321964770555496, -0.043698471039533615, -0.0406837984919548, 0.0031010648235678673, 0.00868814904242754, 0.025873543694615364, 0.06099141389131546, 0.0532168447971344, 0.005875258706510067, -0.039163339883089066, -0.0360981784760952, -0.03986704349517822, 0.0512828454375267, 0.001973179867491126, -0.020681321620941162, -0.011241435073316097, 0.01466847863048315, 0.0972684845328331, -0.021755456924438477, 0.02462497167289257, -0.02646220661699772, -0.00501616345718503, 0.0013569819275289774, 0.058880992233753204, -0.007156826555728912, -0.030062925070524216, -0.08041274547576904, 0.002365425694733858, 0.007984191179275513, -0.08542467653751373, -0.026569105684757233, 0.0029624521266669035, 3.090961229190725e-07, -0.05736655741930008, -0.012116900645196438, -0.015576986595988274, -0.02669629268348217, -0.01165804360061884, 0.03301926329731941, 0.0781557485461235, 0.021567683666944504, -0.046752724796533585, -0.03748033195734024, 0.02250043675303459, -0.00843882653862238, 0.0053601861000061035, 0.00760095939040184, -0.006347282323986292, 0.007149314973503351, -0.01977396197617054, 0.00854968186467886, 0.011235221289098263, -0.007134701125323772, 0.03685455024242401, 0.07617335021495819, 0.046688273549079895, -0.024223294109106064, 0.0608162097632885, 0.007258689496666193, 0.02611534111201763, -0.0057534691877663136, 0.07959338277578354, -0.03981190174818039, -0.02515402063727379, -0.012274385429918766, -0.012502726167440414, 0.03444070741534233, 0.000522565736901015, -0.005730512086302042, 0.001064080628566444, 0.013769854791462421, -0.02761600725352764, -0.028941158205270767, 0.014221403747797012, 0.01735571026802063, -0.006182648241519928, -0.016687680035829544, 0.06463783979415894, 0.015588237904012203, -0.0005863986443728209, -0.012082040309906006, 0.01889953576028347, 0.03197614103555679, 0.009419156238436699, 0.04137340188026428, -0.01039415504783392, -0.012743102386593819, -0.007383516523987055, -0.07020750641822815, -0.0016944146482273936, -0.03927524760365486, 0.07464348524808884, 0.04401389881968498, 0.01474603172391653, 0.02985280007123947, -0.030591139569878578, -0.029749469831585884, 0.07516602426767349, 0.057465266436338425, -0.06102299317717552, 2.975560533482631e-34, -0.034421760588884354, -0.034524720162153244, 0.007016011513769627, 0.03665473684668541, -0.04021843522787094, -0.009349768981337547, -0.03712989762425423, -0.03866320103406906, -0.022032739594578743, -0.04204917699098587, -0.04952504113316536]

['Baochen Sun', 'Kate Saenko']

1607.01719v1

Deep neural networks are able to learn powerful representations from large quantities of labeled input data, however they cannot always generalize well across changes in input distributions. Domain adaptation algorithms have been proposed to compensate for the degradation in performance due to domain shift. In this paper, we address the case when the target domain is unlabeled, requiring unsupervised adaptation. CORAL is a "frustratingly easy" unsupervised domain adaptation method that aligns the second-order statistics of the source and target distributions with a linear transformation. Here, we extend CORAL to learn a nonlinear transformation that aligns correlations of layer activations in deep neural networks (Deep CORAL). Experiments on standard benchmark datasets show state-of-the-art performance.

Deep CORAL: Correlation Alignment for Deep Domain Adaptation

http://arxiv.org/pdf/1607.01719v1

Title Deep CORAL Correlation Alignment Deep Domain Adaptation Summary Deep neural network able learn powerful representation large quantity labeled input data however cannot always generalize well across change input distribution Domain adaptation algorithm proposed compensate degradation performance due domain shift paper address case target domain unlabeled requiring unsupervised adaptation CORAL frustratingly easy unsupervised domain adaptation method aligns secondorder statistic source target distribution linear transformation extend CORAL learn nonlinear transformation aligns correlation layer activation deep neural network Deep CORAL Experiments standard benchmark datasets show stateoftheart performance Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.010725886560976505, 0.05521048605442047, -0.019344104453921318, -0.018435906618833542, -0.012039180845022202, 0.00935688428580761, 0.04981807991862297, -0.024802017956972122, -0.026348521932959557, 0.03277937322854996, -0.07072371989488602, 0.019499894231557846, 0.031083934009075165, 0.04162105545401573, -0.02454502135515213, -0.018770771101117134, 0.012018374167382717, 0.04072757810354233, -0.026726724579930305, -0.004687092732638121, 0.012630772776901722, -0.041092462837696075, -0.0026356384623795748, 0.02847999334335327, -0.033983681350946426, -0.021166527643799782, -0.027043486014008522, 0.02431921288371086, 0.03158382326364517, 0.011285081505775452, 0.062494318932294846, 0.014378132298588753, 0.028340665623545647, 0.03002757392823696, 2.1466537418746157e-06, -0.042189132422208786, -0.023112207651138306, -0.02175309881567955, 0.021490050479769707, -0.025503916665911674, -0.03756682202219963, -0.056092310696840286, -0.012785560451447964, -0.024690603837370872, -0.01849692314863205, -0.016178898513317108, 0.09344170242547989, 0.010955271311104298, 0.04413214698433876, 0.06920258700847626, -0.004727465566247702, -0.0013141034869477153, 0.0006340174586512148, -0.026477936655282974, 0.007309273350983858, -0.05945331230759621, 0.026715151965618134, 0.01553591899573803, -0.065545953810215, -0.04324622079730034, -0.03366347774863243, 0.048818811774253845, 0.0059193638153374195, -0.005695233587175608, 0.0229968074709177, 0.010019544512033463, -0.025194520130753517, -0.02240845188498497, 0.020136479288339615, 0.06133660674095154, -0.04989872872829437, 0.010817226953804493, -0.0055163223296403885, 0.0034937679301947355, 0.025645509362220764, 0.011137635447084904, -0.01635565795004368, -0.037108924239873886, 0.008679249323904514, -0.016928043216466904, -0.05157921090722084, 0.050386637449264526, -0.0031455038115382195, -0.016482099890708923, -0.06650688499212265, 0.043224189430475235, -0.01043388806283474, 0.01737913489341736, -0.06828056275844574, -0.020051924511790276, 0.04030897840857506, -0.009600860998034477, 0.008098235353827477, 0.003887491300702095, -0.049857936799526215, -0.014767435379326344, -0.06577984243631363, -0.09649550169706345, 0.005310853943228722, -0.05008091777563095, 0.014125343412160873, 0.011026335880160332, -0.07606842368841171, 0.05707051232457161, -0.021567389369010925, 0.10457657277584076, -0.0935187041759491, 0.05445513501763344, 0.009506404399871826, -0.01204671710729599, -0.05676589906215668, -0.02146456576883793, 0.0002588190545793623, 0.02206878550350666, 0.026101695373654366, -0.027075989171862602, -0.042288683354854584, 0.000501113070640713, -0.007853735238313675, -0.0351727157831192, -0.0064691114239394665, 0.08724816143512726, -0.010268925689160824, 0.017299555242061615, -0.017958318814635277, 0.0710800364613533, -0.014119233936071396, 0.05901437625288963, 0.01881164126098156, 0.0067788963206112385, 0.02852667309343815, 0.05305110663175583, 0.016367996111512184, -0.022307829931378365, 0.021946506574749947, 0.11362449079751968, 0.016433292999863625, 0.008704780600965023, 0.006565275602042675, 0.02797771617770195, -0.025876235216856003, -0.005222059786319733, 0.019528385251760483, -0.045945946127176285, 0.04139432683587074, -0.010553248226642609, -0.0361541248857975, -0.04711879417300224, -0.007538790348917246, -0.03736405819654465, -0.011373196728527546, 0.07369343191385269, -0.005944443866610527, -0.029532592743635178, 0.07404439896345139, -0.033796533942222595, 0.029834846034646034, 0.03169466182589531, 0.03948059305548668, -0.0009549233363941312, -0.004176005721092224, -0.034500911831855774, -0.003030507592484355, 0.015302902087569237, -0.03262541815638542, -0.041369352489709854, -0.021586626768112183, -0.00621343869715929, 0.014541121199727058, 0.08076806366443634, 0.04103101044893265, -0.033299770206213, 0.019939865916967392, -0.07795178890228271, 0.032342564314603806, 0.0003014824178535491, 0.037034597247838974, 0.021616250276565552, 0.004635329358279705, -0.04744550585746765, -0.00525858998298645, -0.03305191919207573, -0.0441037192940712, 0.06125383824110031, -0.003306644968688488, -0.011822222732007504, -0.09148436039686203, 0.027395563200116158, -0.041054174304008484, -0.042842697352170944, 0.02344820834696293, -0.022320585325360298, -0.06569594889879227, -0.045907162129879, 0.054288581013679504, 0.005372204352170229, -0.0020782246720045805, -0.01246190071105957, -0.02058723010122776, -0.014452284201979637, -0.017292069271206856, -0.02662862092256546, -0.005474356934428215, -0.02803962491452694, -0.04058311879634857, -0.036907922476530075, -0.08994678407907486, 0.009039335884153843, 0.03655709698796272, 0.022504599764943123, -0.016840647906064987, 0.03294200077652931, -0.016695160418748856, -0.05368475243449211, -0.029222438111901283, 0.01870238222181797, -0.029890617355704308, 0.02437354065477848, -0.023459363728761673, -0.00226087449118495, 0.034490812569856644, 0.012932629324495792, 0.0038029239512979984, 0.0261578056961298, 0.007035059854388237, 0.00859617069363594, 0.0032694460824131966, 0.05558560788631439, 0.036980971693992615, 0.0018780891550704837, 0.03790612518787384, -0.03036835603415966, 0.026701772585511208, -0.0019867457449436188, -0.028056422248482704, 0.010748427361249924, -0.014673890545964241, 0.01813419722020626, 0.05688151344656944, -0.04768748581409454, 0.017305653542280197, 0.032598596066236496, -0.015717647969722748, -0.021549955010414124, 0.03717709705233574, 0.02320016361773014, -0.03911667317152023, 0.036192893981933594, 0.04995822533965111, 0.0007845023646950722, 0.045138925313949585, -0.014082338660955429, 0.02988649718463421, 0.04499137029051781, -0.04489365220069885, 0.023335641250014305, -0.0024168333038687706, 0.01352873258292675, -0.04047182574868202, 0.01560715027153492, -0.04872510954737663, -0.019830606877803802, 0.0036868576426059008, -0.007074497640132904, 0.002998152282088995, -0.013644631020724773, 0.02592049539089203, 0.024329155683517456, 0.0220014788210392, 0.008202734403312206, -0.01263523567467928, 0.020421603694558144, -0.025913450866937637, 0.021811265498399734, -0.022637246176600456, -0.0463753379881382, 0.07023745775222778, -0.020270375534892082, -0.01906249299645424, 0.04149412363767624, -0.004074702039361, -0.027277223765850067, -0.051403872668743134, -0.005001045297831297, -0.019265513867139816, 0.05419820547103882, 0.03763486072421074, -0.11164150387048721, -0.03681143745779991, 0.006241660099476576, -0.0539461225271225, -0.016494648531079292, 0.007115189451724291, -0.013472127728164196, -0.042671408504247665, -0.00879973080009222, -0.035040974617004395, 0.06043523550033569, 0.014898824505507946, 0.005192652810364962, -0.014324123039841652, 0.04822414368391037, -0.046987541019916534, 0.0014853752218186855, -0.03485265374183655, -0.00284773507155478, 0.010261799208819866, 0.03776269033551216, -0.021998073905706406, 0.04917836934328079, -0.014615408144891262, 0.024106724187731743, 0.0024504950270056725, 0.01413597259670496, 0.028403179720044136, -0.0034681360702961683, -0.06582727283239365, 0.004982050973922014, -0.007823252119123936, -0.020450111478567123, -0.03530623018741608, -0.053433358669281006, 0.022808395326137543, 0.05070875957608223, 0.007689329329878092, -0.0381757989525795, -0.02387591265141964, 0.004609241615980864, 0.004469316452741623, 0.018866393715143204, 0.013086347840726376, 0.055042050778865814, -0.06520792841911316, -0.04604697972536087, -0.0026434140745550394, -0.021427376195788383, -0.032303933054208755, 0.02271338179707527, -0.012464223429560661, 0.011803839355707169, -0.010801916010677814, -0.013477161526679993, -0.06687009334564209, 0.0185113325715065, 0.007673109415918589, 0.010091091506183147, -0.025156965479254723, -0.03598173335194588, -0.05664895102381706, -0.003462899709120393, 0.019324826076626778, 0.020567607134580612, -0.017114702612161636, 0.004982604179531336, -0.0077995979227125645, 0.04131963104009628, 0.014843557961285114, 0.049069710075855255, -0.037586599588394165, 0.008790340274572372, -0.009219227358698845, -0.004139460623264313, -0.04511813819408417, -0.0272221602499485, -0.10244721919298172, 0.018650908023118973, -0.01083905715495348, 0.021700561046600342, 0.0030932207591831684, -0.050599321722984314, 0.016398964449763298, -0.03174871951341629, 0.024758946150541306, 0.033844657242298126, 0.021907279267907143, -0.0673728957772255, -0.032068297266960144, -0.0046876585111021996, -0.01681908778846264, 0.0333637073636055, -0.010065287351608276, -0.00844553206115961, -0.01820676214993, 0.008155252784490585, -0.027837373316287994, 0.042055800557136536, -0.022546768188476562, 0.005079592112451792, -0.02549542300403118, -0.04267346113920212, 0.006836920045316219, -0.038160569965839386, -0.053983423858881, -0.02532895840704441, 0.016865933313965797, -0.03904455527663231, 0.03331268951296806, 0.043154142796993256, 0.05747194215655327, -0.05349880829453468, 0.059443797916173935, -0.022181738168001175, 0.03670096397399902, -0.04714066907763481, -0.08194292336702347, 0.026570724323391914, 0.05811318755149841, 0.02535679191350937, -0.03228898346424103, 0.0004402350459713489, 0.025147581472992897, 0.010526761412620544, 0.04707242548465729, 0.04652538150548935, 0.06832149624824524, 0.033525895327329636, -0.03342907503247261, -0.001720129163004458, 0.04669434577226639, -0.03614071011543274, 0.05665724352002144, 0.032318923622369766, 0.04615690931677818, 0.024677833542227745, 0.047572650015354156, -0.06225893273949623, -0.0057524400763213634, -0.04247257485985756, -0.022968534380197525, 0.024960482493042946, -0.027524510398507118, 0.022943058982491493, 0.0033230138942599297, -0.01171101350337267, -0.013254805468022823, -0.022467494010925293, 0.000229234152357094, -0.002982259960845113, -0.0612793006002903, -0.06518738716840744, 0.02734229527413845, 0.005209977738559246, 0.04506600648164749, 0.04532262682914734, -0.07190345227718353, -0.027813458815217018, -0.015527798794209957, -0.024514105170965195, 0.031936291605234146, 0.014054778032004833, 0.02775072678923607, -0.08595098555088043, 0.027900921180844307, 0.05521804839372635, -0.06241030991077423, -0.0018073843093588948, -0.016821935772895813, -0.033555496484041214, -0.0410597026348114, -0.00011285323125775903, 0.024089375510811806, 0.014862602576613426, -0.0006922268075868487, -0.02638874761760235, -0.007494587916880846, -0.04484771192073822, 0.12102140486240387, -0.03445946052670479, 0.03087255358695984, 0.02178928814828396, -0.05963222682476044, -0.013988842256367207, -0.007086639758199453, -0.05556000769138336, 0.03267206624150276, -0.0010142455575987697, -0.01092295441776514, -0.007395068649202585, -0.04156970977783203, 0.022971294820308685, -0.03780412673950195, 0.12300178408622742, 0.03472422808408737, -0.020903581753373146, -0.024562211707234383, 0.013597100973129272, 0.018064230680465698, 0.008129936642944813, 0.012373014353215694, -0.018553461879491806, 0.03383345156908035, 0.05581839382648468, -0.02278292551636696, 0.010221480391919613, 0.08252184838056564, -0.019554898142814636, -0.010331549681723118, 0.016765344887971878, -0.04968315735459328, 0.06871671974658966, -0.03474902734160423, 0.016850370913743973, 0.013983531855046749, 0.012479490600526333, 0.03460665047168732, 0.026947079226374626, 0.009821286424994469, -0.0212772898375988, 0.03005366399884224, 0.028196407482028008, -0.061638399958610535, 0.009076257236301899, 4.415631337906234e-05, -0.017321854829788208, -0.033560506999492645, 0.03902601823210716, 0.05142205208539963, -0.034777045249938965, 0.006345726549625397, 0.04031180962920189, -0.02459249459207058, -0.04026764631271362, 0.01697380840778351, -0.005653182975947857, 0.02184547483921051, 0.06833257526159286, -0.006361634936183691, -0.02559259533882141, -0.024594388902187347, 0.022889718413352966, 0.04016486555337906, 0.013149955309927464, -0.04894615337252617, 0.014283745549619198, 0.01457167137414217, 0.05788944661617279, 0.01867244578897953, -0.006706285756081343, -0.02228689379990101, -0.059752900153398514, 0.00680365227162838, -0.05678429454565048, 0.06827522814273834, 0.014952347613871098, 0.0315120667219162, 0.03225871920585632, 0.007156564388424158, 0.012497411109507084, -0.012366246432065964, 0.0017748152604326606, 0.021504849195480347, -0.03464529290795326, 0.03205867484211922, -0.0001902492222143337, -0.012693120166659355, -5.302962481800476e-33, -0.03138940408825874, -0.025859661400318146, -0.0030632324051111937, 0.024832623079419136, -0.0031064997892826796, 0.034574106335639954, 0.01161744724959135, 0.01531690452247858, -0.007004745304584503, -0.020420068874955177, 0.019006751477718353, 0.008479769341647625, 0.012926684692502022, -0.0038394713774323463, 0.007043336518108845, -0.01905258372426033, -0.0036688048858195543, -0.019273605197668076, 0.0226573683321476, -0.045401591807603836, 0.036781929433345795, 0.06120860204100609, 0.06052664667367935, -0.11616679280996323, -0.07275678962469101, 0.036738764494657516, 0.02521001733839512, -0.03400536999106407, -0.014531359076499939, 0.040041111409664154, 0.030136646702885628, 0.03380711376667023, -0.015840595588088036, -0.005864948034286499, -0.018770376220345497, -0.026892727240920067, -0.08262220025062561, -0.026768485084176064, -0.023937026038765907, 0.05338273569941521, -0.01863309182226658, -0.011956769973039627, 0.07658375054597855, 0.029290327802300453, -0.03358820825815201, -0.02195160649716854, 0.08654363453388214, -0.06721803545951843, -0.006436671130359173, -0.014643020927906036, -0.06817985326051712, 0.015313245356082916, -0.0018420808482915163, -0.016194414347410202, 0.0198967382311821, 0.045905936509370804, 0.007335127796977758, 0.007207346148788929, -0.06264225393533707, 0.03936147689819336, -0.025246497243642807, 0.055941808968782425, 0.03665611892938614, 0.08754720538854599, -0.008935718797147274, 0.05281035229563713, 0.059888679534196854, -0.031066294759511948, 0.027840837836265564, 0.004225724842399359, -0.008942628279328346, 0.03507264330983162, 0.057245057076215744, 0.0677008330821991, 0.05932852253317833, -0.042903125286102295, -0.07156428694725037, 0.039431050419807434, -5.472756311064586e-05, -0.07206074893474579, -0.037414729595184326, 0.019366540014743805, -0.030156314373016357, 0.029127174988389015, 0.021497685462236404, 0.06542680412530899, -0.04297267273068428, -0.021796179935336113, 0.023356515914201736, -0.011721267364919186, -0.010080356150865555, 0.045089349150657654, -0.0005623706383630633, -0.03601072356104851, 0.015796151012182236, 0.027861110866069794, -0.0015174623113125563, 0.030148539692163467, 0.020550640299916267, -0.01516775507479906, 0.0003221266670152545, -0.05400577932596207, -0.0005777603364549577, 0.04106144607067108, 0.04962814599275589, 0.00924425944685936, 0.06444267183542252, 0.006587071809917688, -0.028617123141884804, -0.029719440266489983, 0.013624315150082111, -0.0603080689907074, -0.00435339380055666, 0.019582083448767662, 0.010580028407275677, -0.027548659592866898, 0.010787698440253735, 0.08221195638179779, 0.034745242446660995, -0.06375015527009964, -0.03795444592833519, -0.009100737050175667, 0.00030466943280771375, 0.016020536422729492, -0.055109478533267975, -0.011390749365091324, -0.016775719821453094, 0.0013125777477398515, -0.04782969132065773, -0.0893782377243042, -0.02671055495738983, 0.012867210432887077, 2.886749257413612e-07, 0.00568943889811635, 0.0002738184994086623, 0.06367884576320648, -0.05971889942884445, 0.0030029118061065674, -0.0032234136015176773, -0.005719973240047693, 0.018910184502601624, 0.01585058681666851, -0.0407133586704731, 0.04813810810446739, -0.015257464721798897, -0.037774067372083664, -0.024443872272968292, -0.050803642719984055, 0.01019361987709999, 0.01309350598603487, 0.02504194714128971, -0.02983774244785309, 0.011880739592015743, 0.026888558641076088, 0.07550333440303802, 0.017297813668847084, -0.027008850127458572, 0.05045970156788826, 0.024094579741358757, 0.008918911218643188, 0.009630272164940834, 0.05386294052004814, -0.01588538847863674, -0.03158772364258766, -0.01851605996489525, -0.0561942495405674, 0.03691413253545761, 0.009221362881362438, 0.057084523141384125, 0.024227267131209373, -0.020138539373874664, -0.03783946484327316, 0.0177577193826437, 0.026135442778468132, 0.03412124887108803, 0.02812150865793228, -0.01711580902338028, 0.019047042354941368, -0.04876682162284851, -0.015749217942357063, -0.045212987810373306, -0.03607441484928131, 0.019778335466980934, 0.04016727954149246, 0.025570819154381752, -0.009783703833818436, -0.004166694357991219, 0.009146247059106827, -0.023198658600449562, -0.026165373623371124, -0.04373973608016968, 0.015036970376968384, 0.009387800469994545, -0.03874412178993225, 0.02478780969977379, -0.026145337149500847, -0.012910651974380016, 0.10183320939540863, -0.018638279289007187, 0.010547003708779812, 2.2990263412084604e-34, -0.06587532162666321, 0.005935986526310444, 0.039025578647851944, 0.015178372152149677, -0.0365557037293911, -0.015109333209693432, -0.021609565243124962, 0.02557922899723053, 0.002738606883212924, 0.012127707712352276, -0.026447247713804245]

['Jun Liu', 'Amir Shahroudy', 'Dong Xu', 'Gang Wang']

1607.07043v1

3D action recognition - analysis of human actions based on 3D skeleton data - becomes popular recently due to its succinctness, robustness, and view-invariant representation. Recent attempts on this problem suggested to develop RNN-based learning methods to model the contextual dependency in the temporal domain. In this paper, we extend this idea to spatio-temporal domains to analyze the hidden sources of action-related information within the input data over both domains concurrently. Inspired by the graphical structure of the human skeleton, we further propose a more powerful tree-structure based traversal method. To handle the noise and occlusion in 3D skeleton data, we introduce new gating mechanism within LSTM to learn the reliability of the sequential input data and accordingly adjust its effect on updating the long-term context information stored in the memory cell. Our method achieves state-of-the-art performance on 4 challenging benchmark datasets for 3D human action analysis.

Spatio-Temporal LSTM with Trust Gates for 3D Human Action Recognition

http://arxiv.org/pdf/1607.07043v1

Title SpatioTemporal LSTM Trust Gates 3D Human Action Recognition Summary 3D action recognition analysis human action based 3D skeleton data becomes popular recently due succinctness robustness viewinvariant representation Recent attempt problem suggested develop RNNbased learning method model contextual dependency temporal domain paper extend idea spatiotemporal domain analyze hidden source actionrelated information within input data domain concurrently Inspired graphical structure human skeleton propose powerful treestructure based traversal method handle noise occlusion 3D skeleton data introduce new gating mechanism within LSTM learn reliability sequential input data accordingly adjust effect updating longterm context information stored memory cell method achieves stateoftheart performance 4 challenging benchmark datasets 3D human action analysis Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.012921557761728764, 0.017357636243104935, 0.0009066946222446859, 0.07766448706388474, -0.0021652295254170895, 0.03554300218820572, -0.007129453122615814, -0.007529738824814558, 0.0005641651805490255, -0.051401954144239426, -0.04626976698637009, -0.05487972870469093, 0.04389138147234917, 0.0846305638551712, 0.04092299938201904, -0.07391296327114105, -0.0005052305059507489, 0.015357717871665955, -0.02311418578028679, 0.000669534842018038, 0.0026901420205831528, -0.003991262521594763, -0.02879268489778042, 0.025049231946468353, -0.04481956735253334, 0.05904668569564819, -0.04424135014414787, -0.01346957590430975, 0.044178687036037445, -0.052340224385261536, -0.017111970111727715, -0.011035764589905739, 0.08071408420801163, 0.019020117819309235, 2.350810063944664e-06, 0.000711630389560014, 0.023277172818779945, -0.04552064090967178, 0.016977638006210327, -0.04019758477807045, -0.031675323843955994, 0.011861947365105152, -0.024320414289832115, 0.00530070997774601, -0.053650397807359695, 0.009868077002465725, 0.023340633139014244, 0.04650350660085678, 0.046435825526714325, 0.01829339750111103, -0.031049933284521103, -0.009924812242388725, 0.04369865357875824, -0.01985655352473259, 0.061419107019901276, 0.030808554962277412, 0.019709967076778412, 0.006841064430773258, 0.04559490457177162, -0.0068321023136377335, -0.06292743980884552, -0.0038496400229632854, 0.01247976440936327, 0.03021882474422455, 0.062401507049798965, 0.053148332983255386, 0.05569330230355263, 0.02003748156130314, -0.004623088054358959, 0.06572995334863663, -0.009815949946641922, 0.04654820263385773, 0.04542367160320282, -0.0012340762186795473, 0.0003340532712172717, 0.007097297348082066, 0.006150030996650457, 0.011169036850333214, -0.001019142335280776, -0.015701955184340477, -0.06805538386106491, 0.03236517682671547, 0.013203754089772701, 0.016841435804963112, 0.022070087492465973, -0.020755482837557793, 0.0020446674898266792, 0.04775606468319893, -0.030407723039388657, -0.014086086302995682, 0.04519526660442352, -0.016412563621997833, 0.012979695573449135, 0.007037346716970205, 0.006202871445566416, -0.02599162794649601, -0.023323554545640945, 0.02811896614730358, -0.0060728141106665134, -0.03148651495575905, -0.008339686319231987, 0.009035168215632439, -0.019970210269093513, 0.03762628138065338, 0.0008165771141648293, 0.055262502282857895, -0.08102676272392273, 0.032785721123218536, 0.009235939010977745, 0.0637119933962822, -0.009435830637812614, -0.02274983562529087, -0.00708718691021204, 0.02424490638077259, -0.010976271703839302, -0.01803870126605034, -0.05958789959549904, 0.031186316162347794, -0.02074423059821129, -0.059072401374578476, 0.020068710669875145, 0.08386670053005219, 0.04970153421163559, 0.005594228394329548, -0.024897795170545578, -0.02481129765510559, 0.0258238036185503, 0.03160775452852249, -0.08499941974878311, -0.011895345523953438, -0.01928994245827198, 0.04501117765903473, 0.008118776604533195, 0.029858026653528214, -0.003070872975513339, 0.030425522476434708, -0.008197278715670109, -0.01940234750509262, 0.0003950093232560903, 0.02432376891374588, 0.005031299311667681, 0.02041563391685486, 0.039802782237529755, -0.056505974382162094, -0.025617802515625954, -0.0561554841697216, -0.0268963985145092, -0.015093719586730003, -0.012249692343175411, -0.0009732994949445128, 0.0005196125712245703, 0.044408928602933884, 0.006601929198950529, -0.028763992711901665, 0.05186666548252106, -0.012029406614601612, 0.04187379404902458, -0.035867299884557724, 0.06534763425588608, 0.02425127662718296, -0.050472576171159744, 0.02069692686200142, 0.04652128741145134, 0.006237672176212072, -0.037038255482912064, -0.003946730401366949, -0.025295838713645935, -0.04014384001493454, 0.030341478064656258, 0.07356803864240646, 0.031094197183847427, -0.012223692610859871, -0.042453523725271225, -0.05354892089962959, 0.01586475409567356, 0.0651455819606781, -0.04262650012969971, -0.035050198435783386, 0.04014778137207031, -0.020401520654559135, 0.020283378660678864, -0.0306337121874094, -0.010670973919332027, 0.08204018324613571, 0.015481757000088692, -0.04653288424015045, -0.10742593556642532, -0.016151154413819313, -0.03975797817111015, -0.02108939178287983, 0.014321817085146904, -0.05507093295454979, 0.04718250781297684, -0.01556377299129963, 0.049601953476667404, -0.033208850771188736, -0.0099555728957057, 0.04160476475954056, -0.028240717947483063, 0.0008512998465448618, -0.024657152593135834, -0.022913934662938118, -0.0139882517978549, 0.005805458873510361, -0.02318408153951168, 0.004466148559004068, -0.03344511613249779, -0.0412222295999527, 0.021583182737231255, -0.02520143799483776, -0.020893918350338936, 0.0082406522706151, 0.04412579536437988, -0.03886845335364342, -0.0982576310634613, -0.021493664011359215, 0.029958458617329597, 0.04509904980659485, -0.005132734309881926, -0.004489685874432325, 0.0019746634643524885, 0.04911762475967407, 0.04421265795826912, 0.005729327909648418, -0.05321022495627403, 0.009495037607848644, -0.009026247076690197, 0.02402799017727375, 0.0458439439535141, 0.01554979756474495, 0.01344815269112587, -0.03737904503941536, 0.029509149491786957, -0.009738321416079998, 0.0046377358958125114, 0.032868076115846634, -0.07616186887025833, -0.010491915047168732, -0.005760459695011377, 0.036309123039245605, -0.019654368981719017, 0.01017068512737751, -0.00396233843639493, -0.07780922949314117, 0.06220394745469093, -0.010874278843402863, -0.021105565130710602, -0.030155707150697708, -0.0026551869232207537, 0.05930245295166969, 0.001053753076121211, -0.04774700477719307, 0.032670602202415466, -0.03823165223002434, -0.014876228757202625, 0.00042167454375885427, 0.04045047238469124, 0.040629416704177856, -0.04004787281155586, -0.02743520401418209, 0.004720060620456934, -0.03108023665845394, -0.011368170380592346, -0.0016743609448894858, 0.03677738085389137, 0.006914937403053045, 0.07067744433879852, -0.005638815462589264, -0.032016247510910034, 0.017710497602820396, 0.003097373293712735, -0.03116290643811226, 0.027500316500663757, -0.014352505095303059, -0.040099963545799255, -0.038354407995939255, 0.03053734451532364, 0.022449441254138947, -0.06824174523353577, 0.027838200330734253, 0.023305129259824753, -0.02924586832523346, 0.005753036122769117, 0.061262063682079315, 0.024639682844281197, 0.01757017895579338, 0.04153314605355263, -0.11474597454071045, 0.021633008494973183, -0.019741496071219444, 0.012098819017410278, 0.04546183720231056, -0.03117595799267292, -0.033489521592855453, 0.005864941049367189, -0.038139376789331436, -0.011984037235379219, 0.01324781496077776, -0.013251394964754581, 0.02055296301841736, -0.011797059327363968, 0.06223857402801514, -0.001985335722565651, 0.026644470170140266, 0.006453314330428839, 0.05471721664071083, -0.019143644720315933, -0.0062598842196166515, 0.009821546263992786, 0.036198679357767105, 0.02522476390004158, 0.06743081659078598, -0.005972157698124647, -0.06887684017419815, 0.014135397039353848, -0.0046170903369784355, -0.025039466097950935, -0.04161515086889267, -0.06472256034612656, -0.04282207414507866, -0.013846882618963718, -0.01465492695569992, -0.04635291546583176, 0.042322609573602676, -0.028827667236328125, 0.05193290114402771, 0.017019685357809067, -0.03015252761542797, 0.08042266964912415, 0.041530076414346695, 0.015578432008624077, -0.016264230012893677, -0.02822413668036461, 0.004357560537755489, -0.032901935279369354, 0.034913454204797745, 0.010783732868731022, -0.08375034481287003, -0.06341490894556046, 0.03681884706020355, -0.03849630057811737, -0.02845078520476818, 0.014048390090465546, -0.013559105806052685, -0.06336722522974014, -0.048750828951597214, -0.0586397610604763, -0.029643099755048752, 0.04781227186322212, 0.002549589378759265, -0.003427717601880431, 0.013164146803319454, -0.021544091403484344, 0.02019200101494789, 0.03214026242494583, 0.0639130249619484, 0.014153722673654556, 0.029895085841417313, -0.06979452818632126, 0.011700814589858055, -0.022834062576293945, 0.06246433034539223, -0.02753954753279686, -0.007311870809644461, -0.11002916842699051, 0.05000763386487961, 0.018538927659392357, 0.07499940693378448, -0.03923637419939041, 0.01616739109158516, 0.007999105378985405, -0.01734224334359169, 0.04201364889740944, 0.004290201235562563, -0.006725167389959097, -0.04199118912220001, -0.005877451039850712, 0.03972752392292023, -0.03238914534449577, -0.02683514729142189, -0.0382104218006134, -0.02329472079873085, -0.032342579215765, -0.06117821857333183, -0.040409576147794724, 0.03384163975715637, -0.04839438572525978, 0.031491175293922424, -0.01999412290751934, 0.06914498656988144, 0.007488514296710491, -0.06145060434937477, -0.040633153170347214, 0.013355055823922157, 0.04550968483090401, -0.008764386177062988, -0.040449969470500946, 0.02073407545685768, 0.004091329872608185, -0.010333570651710033, 0.02775631844997406, -0.0506649985909462, -0.03555300086736679, 0.0663314014673233, 0.010636016726493835, -0.011268144473433495, -0.012075042352080345, 0.026083940640091896, -0.02455747127532959, -0.06016834080219269, 0.007285560015588999, 0.023146910592913628, 0.05039079859852791, -0.015735777094960213, 0.0014032777398824692, 0.031957123428583145, -0.007264286745339632, -0.002714809263125062, 0.0421842560172081, -0.013316657394170761, 0.0006749429740011692, -0.06481310725212097, 0.053019747138023376, -0.09567269682884216, 0.04964033514261246, -0.05361746996641159, -0.034175291657447815, 0.018952323123812675, -0.00101690914016217, -0.02433575503528118, 0.009312628768384457, -0.05338316410779953, 0.01039915718138218, -0.015435499139130116, -0.016513394191861153, -0.04086468368768692, -0.028541503474116325, 0.006722963415086269, -0.008869536221027374, -0.04871933162212372, 0.007052435074001551, 0.011874332092702389, 0.04733782261610031, -0.04919422045350075, 0.02212061919271946, -0.028173668310046196, 0.03201952576637268, -0.05658331140875816, 0.004192661959677935, -0.018293388187885284, 0.037670571357011795, 0.013250725343823433, 0.038674186915159225, 0.021285589784383774, -0.035392243415117264, 0.024873243644833565, -0.049009960144758224, -0.04273015633225441, 0.022655129432678223, -0.002587013179436326, 0.022433973848819733, 0.0016525601968169212, 0.03948225453495979, -0.0014168175403028727, 0.024174317717552185, 0.02395276352763176, -0.038630738854408264, 0.0071378061547875404, -0.001100086490623653, 0.057715389877557755, 0.015125375241041183, -0.07273931056261063, -0.007849883288145065, -0.021261796355247498, 0.02324025146663189, -0.006034854333847761, -0.0632043108344078, -0.06267350912094116, -0.05496058985590935, -0.06922496855258942, -0.03974343091249466, 0.08044657111167908, -0.0038642273284494877, 0.046029672026634216, -0.025119701400399208, 0.026059884577989578, 0.017837975174188614, 0.05793376639485359, -0.08531452715396881, 0.007172772195190191, 0.05079125985503197, -0.016302021220326424, -0.03308730572462082, -0.023787427693605423, 0.01400432363152504, -0.02811462990939617, -0.04645213112235069, 0.0239200871437788, 0.031182654201984406, -0.0015284140827134252, -0.05955477058887482, 0.013679422438144684, -0.010700172744691372, 0.04775463417172432, 0.013646591454744339, -0.03439462557435036, 0.03435681387782097, -0.015952613204717636, -0.007754938211292028, 0.0019279926782473922, 0.00861442368477583, 0.031177248805761337, -0.019290674477815628, 0.024815475568175316, -0.030706709250807762, -0.02675708942115307, 0.0714271068572998, 0.001389730954542756, -0.008559872396290302, -0.0032546159345656633, 0.013976474292576313, 0.01905164308845997, 0.06136453151702881, -0.010831923224031925, -0.03746054321527481, 0.09063981473445892, -0.0023833471350371838, -0.023749863728880882, 0.035641659051179886, 0.02239229343831539, 0.07261752337217331, -0.018877895548939705, 0.03745221719145775, -0.034439899027347565, -0.0057695284485816956, 0.002685708459466696, 0.0033133169636130333, -0.01313064806163311, -0.02545277401804924, 0.015337628312408924, 0.009690873324871063, -0.03768739476799965, 0.01670481078326702, -0.044748466461896896, 0.03491618111729622, -0.01713539846241474, 0.08616368472576141, 0.0014388751005753875, 0.015573002398014069, 0.03032945655286312, -0.013531416654586792, -0.04350229352712631, 0.01910240389406681, -0.024035094305872917, -0.05597837641835213, -5.736990260954589e-33, 0.040028758347034454, -0.04442915692925453, 0.022513948380947113, -0.027585741132497787, -0.006159610580652952, 0.005269365385174751, -0.05075995996594429, -0.022184737026691437, 0.0008099772385321558, 0.011402816511690617, 0.020568573847413063, 0.019403059035539627, 0.012953574769198895, -0.0008733367430977523, 0.0399981327354908, 0.011435153894126415, -0.025373298674821854, -0.05301773175597191, 0.02401883341372013, 0.04559147730469704, 0.02179890125989914, -0.010247788392007351, 0.09318143129348755, -0.058056626468896866, -0.03126901388168335, 0.0026129046455025673, -0.04765790328383446, -0.003869240637868643, -0.025001592934131622, -0.006514814216643572, -0.03552870824933052, -0.05463181063532829, 0.012410791590809822, -0.034702323377132416, 0.02960253320634365, -0.023258594796061516, -0.03411122038960457, -0.045323099941015244, -0.050531331449747086, 0.016263894736766815, -0.05594303831458092, 0.03517783433198929, -0.028582416474819183, 0.0038790563121438026, -0.040649235248565674, 0.01134399976581335, 0.008221123367547989, -0.023219026625156403, -0.018235284835100174, -0.088651642203331, 0.00865257903933525, 0.061059046536684036, -0.022121170535683632, -0.03647695854306221, 0.01535925641655922, -0.007915202528238297, -0.029198823496699333, -0.03510187566280365, 0.01238106470555067, 0.01662357710301876, -0.04780304804444313, -0.011919817887246609, 0.014277310110628605, 0.034094858914613724, 0.024532170966267586, 0.030776647850871086, -0.03941744565963745, -0.020713580772280693, -0.007082246709614992, 0.0199179258197546, -0.003426402574405074, 0.10296162217855453, 0.05309144780039787, 0.06082458794116974, 0.017695242539048195, 0.005446011666208506, -0.0541289858520031, 0.05441228672862053, -0.0036906173918396235, 0.08319881558418274, -0.02862209640443325, 0.023651592433452606, 0.004217291250824928, 0.0006877024425193667, 0.0852653831243515, 0.02195640094578266, 0.02442905679345131, 0.005523887928575277, -0.020860854536294937, 0.008086930960416794, 0.03456481546163559, -0.010032310150563717, 0.03885345160961151, 0.021126776933670044, 0.043800950050354004, 0.03536033630371094, 0.007234241347759962, 0.01373548898845911, 0.04242117330431938, -0.037990860641002655, 0.020914655178785324, -0.029594261199235916, 0.006730147171765566, 0.008329478092491627, -0.018990017473697662, 0.011690257117152214, -0.009772342629730701, 0.048649467527866364, 0.07065786421298981, -0.041639186441898346, 0.01925179921090603, -0.005721613764762878, -0.006925198249518871, 0.045815467834472656, 0.04935796558856964, -0.043460145592689514, -0.015786629170179367, 0.08155758678913116, -0.059262823313474655, -0.015672054141759872, -0.05148443952202797, 0.029868658632040024, -0.05457040295004845, 0.03503718972206116, -0.041437484323978424, -0.0195156279951334, -0.021597491577267647, 0.003998650703579187, 0.0171952024102211, -0.07835110276937485, 0.004934647586196661, 0.00411766953766346, 3.026286776730558e-07, -0.0519036240875721, -0.008568428456783295, 0.012021570466458797, -0.05107317119836807, 0.01641257293522358, 0.01308719627559185, -0.006811289116740227, 0.06766192615032196, -0.001479148748330772, -0.016253847628831863, 0.08693457394838333, 0.01467581931501627, -0.004952470771968365, -0.014289053156971931, -0.08126772195100784, 0.036461472511291504, -0.037167686969041824, 0.015037688426673412, -0.017385877668857574, 0.030902620404958725, 0.03279751539230347, 0.030258219689130783, 0.030448224395513535, -0.01906372793018818, 0.019298722967505455, 0.0004778728471137583, 0.03311967849731445, -0.015864834189414978, 0.02715720608830452, -0.07425955682992935, 0.0481196828186512, 0.0029751963447779417, -0.00888263713568449, -0.006570239085704088, -0.06168439984321594, 0.015968356281518936, -0.01147857028990984, 0.02541493996977806, -0.05364212021231651, 0.0074097695760428905, 0.0025789865758270025, -0.0015110232634469867, 0.031416088342666626, -0.014037600718438625, 0.02340330369770527, 0.006140463519841433, -0.0019699030090123415, 0.01671467535197735, -0.0014481524704024196, -0.01290394738316536, 0.024935375899076462, 0.03214642405509949, -0.013546577654778957, -0.0333489328622818, 0.005089521408081055, -0.07696272432804108, -0.0013311691582202911, -0.09280615299940109, 0.0226021446287632, -0.026107193902134895, -0.04258503392338753, 0.030326178297400475, 0.028726711869239807, 0.0034632431343197823, 0.03888343274593353, 0.039840877056121826, -0.058117203414440155, 2.4231112493747726e-34, -0.006051819771528244, 0.020602412521839142, -0.0020154635421931744, -0.01189012173563242, -0.008748377673327923, 0.0416538268327713, 0.059235114604234695, 0.044728729873895645, 0.026058979332447052, -0.027102520689368248, -0.010077281855046749]

['Suraj Srinivas', 'R. Venkatesh Babu']

1611.06791v1

Deep Neural Networks often require good regularizers to generalize well. Dropout is one such regularizer that is widely used among Deep Learning practitioners. Recent work has shown that Dropout can also be viewed as performing Approximate Bayesian Inference over the network parameters. In this work, we generalize this notion and introduce a rich family of regularizers which we call Generalized Dropout. One set of methods in this family, called Dropout++, is a version of Dropout with trainable parameters. Classical Dropout emerges as a special case of this method. Another member of this family selects the width of neural network layers. Experiments show that these methods help in improving generalization performance over Dropout.

Generalized Dropout

http://arxiv.org/pdf/1611.06791v1

Title Generalized Dropout Summary Deep Neural Networks often require good regularizers generalize well Dropout one regularizer widely used among Deep Learning practitioner Recent work shown Dropout also viewed performing Approximate Bayesian Inference network parameter work generalize notion introduce rich family regularizers call Generalized Dropout One set method family called Dropout version Dropout trainable parameter Classical Dropout emerges special case method Another member family selects width neural network layer Experiments show method help improving generalization performance Dropout Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.016172297298908234, 0.060791682451963425, -0.006108471658080816, 0.029795153066515923, 0.00688586849719286, -0.0159979946911335, 0.0460902638733387, 0.006665560882538557, -0.02113274671137333, 0.038688767701387405, 0.014540540054440498, 0.020467763766646385, 0.005920268129557371, 0.06350425630807877, 0.017433755099773407, -0.06322598457336426, -0.005202899221330881, 0.01698034442961216, 0.0016415109857916832, -0.03169082850217819, 0.03466794267296791, -0.013393147848546505, 0.015212454833090305, 0.05418750271201134, -0.030120354145765305, 0.03275325149297714, 0.0073225838132202625, 0.04466365650296211, 0.023508375510573387, -0.016781717538833618, 0.031192602589726448, -0.022719543427228928, -0.018521443009376526, 0.020133601501584053, 2.1759160517831333e-06, -0.05653827264904976, -0.009334679692983627, -0.010792020708322525, -0.012009350582957268, 0.022480422630906105, -0.015163052827119827, -0.025922393426299095, 0.026681922376155853, -0.009283828549087048, 0.00584840914234519, -0.03752388432621956, 0.06485485285520554, 0.07167162746191025, -0.01000205148011446, 0.05937592312693596, -0.002673353534191847, 0.004584833048284054, 0.034401096403598785, -0.033075910061597824, 0.03890610486268997, -0.06943890452384949, 0.012654418125748634, 0.010429001413285732, -0.048719391226768494, -0.08651629835367203, -0.003335375338792801, -0.00048383590183220804, 0.07389023154973984, -0.0055379122495651245, 0.04741158336400986, 0.048990555107593536, -0.029613999649882317, -0.017649656161665916, -0.015745198354125023, 0.05852876976132393, -0.04269271343946457, 0.0210886113345623, -0.008428358472883701, -0.05584084615111351, -0.0069217137061059475, 0.01889895275235176, -0.06643083691596985, -0.014513736590743065, 0.0029704428743571043, 0.014077279716730118, -0.024504266679286957, 0.0465368926525116, 0.05101785063743591, 0.039234407246112823, -0.03551413118839264, 0.04699619114398956, 0.00482857134193182, 0.011310725472867489, -0.005152456928044558, 0.0021037363912910223, -0.05305314064025879, -0.03721071407198906, 0.05796860158443451, 0.013803303241729736, 0.008034110069274902, -0.029182905331254005, -0.026967350393533707, -0.046736206859350204, -0.006949234288185835, -0.014186213724315166, 0.029029086232185364, 0.0016053059371188283, -0.023807857185602188, 0.004636038094758987, -0.005293183960020542, 0.025546591728925705, -0.05107457563281059, 0.042696159332990646, -0.00023394470917992294, 0.01740085519850254, -0.0173678919672966, 0.00798739492893219, -0.025421572849154472, 0.061966218054294586, 0.03474707156419754, -0.04517154023051262, -0.051455672830343246, -0.009428076446056366, -0.032497718930244446, -0.034081924706697464, 0.03175286576151848, 0.09237317740917206, -0.035117313265800476, -0.052298590540885925, 0.0014360889326781034, 0.04345158860087395, -0.04650244116783142, 0.034138813614845276, 0.014520862139761448, -0.027101268991827965, 0.020384037867188454, 0.012833228334784508, 0.038048963993787766, 0.007304886821657419, 0.0075357225723564625, 0.05064092576503754, 0.02495451457798481, -0.01494150422513485, -0.06060443073511124, 0.009654488414525986, -0.01722518913447857, -0.05802580714225769, -0.02369670569896698, -0.05617145076394081, -0.000539174594450742, -0.030224647372961044, 0.013598834164440632, -0.08549580723047256, -0.013336420990526676, -0.032634638249874115, -0.006400960497558117, 0.007372015621513128, -0.04264477640390396, -0.06487308442592621, 0.11709272861480713, -0.000658384757116437, -0.017370881512761116, 0.0669284462928772, 0.020639050751924515, 0.02593902312219143, 0.003165737958624959, -0.02274297922849655, -0.014782650396227837, 0.025112200528383255, -0.017316017299890518, -0.01768799126148224, -0.051057327538728714, -0.06773729622364044, -0.02573597989976406, 0.05446122586727142, 0.04942137375473976, 0.03402107581496239, -0.033519197255373, -0.0443044975399971, 0.029840689152479172, 0.035943496972322464, 0.05334550887346268, 0.004048408009111881, 0.03989466279745102, -0.015187734737992287, -0.029858341440558434, 0.010377353988587856, -0.0011039447272196412, 0.013226713985204697, 0.024152137339115143, -0.05228044465184212, -0.01849157176911831, 0.01804231107234955, -0.0677705705165863, -0.06389226764440536, 0.0415615439414978, -0.04197557270526886, 0.010037291795015335, 0.021976245567202568, 0.08748608827590942, -0.017304224893450737, 0.016019124537706375, 0.018463635817170143, 0.020477961748838425, -0.020069142803549767, 0.027870455756783485, -0.019874833524227142, 0.04911281168460846, -0.015682972967624664, -0.032013166695833206, -0.03775417432188988, -0.03128001093864441, -3.8610789488302544e-05, -0.025288820266723633, -0.010501104407012463, 0.03400811925530434, -1.701227665762417e-05, 0.0673423632979393, -0.05168336629867554, -0.013686370104551315, 0.030151888728141785, 0.024787498638033867, 0.014012554660439491, -0.05556980520486832, 0.006785082630813122, 0.09206480532884598, -0.03281616047024727, -0.025133972987532616, 0.031549207866191864, -0.04471082612872124, -0.01860150508582592, 0.0348784439265728, 0.0304423701018095, -0.014153916388750076, 0.0157861839979887, 0.026577835902571678, -0.006999759469181299, 0.03702874854207039, -0.044269904494285583, -0.040617987513542175, -0.06340650469064713, -0.02963836118578911, -0.007802634034305811, 0.019070228561758995, -0.045291878283023834, 0.08190714567899704, 0.0590532124042511, -0.03009612485766411, -0.05779304355382919, 0.02727905474603176, 0.013473044149577618, 0.021698201075196266, 0.003643450792878866, -0.01933686062693596, 0.005373943131417036, 0.03423868864774704, -0.0043605612590909, -0.006234960164874792, -0.00984782725572586, -0.0088856415823102, -0.0271866824477911, -0.012245794758200645, 0.007605656050145626, -0.0553603321313858, -0.04201047122478485, 0.02241884171962738, -0.059533052146434784, -0.012074995785951614, 0.028550995513796806, 0.022410156205296516, 0.003426585579290986, 0.07037702947854996, -0.01792493835091591, 0.008056742139160633, -0.022851252928376198, -0.025930574163794518, -0.006768223829567432, 0.04519699141383171, 0.008762715384364128, -0.019363315775990486, -0.015000035986304283, 0.045162852853536606, -0.022045478224754333, -0.04361407086253166, -0.025499721989035606, 0.028695743530988693, 0.003353986656293273, -0.03082244284451008, -0.07040004432201385, 0.044842012226581573, 0.05211460590362549, -0.012878739275038242, -0.02095913328230381, -0.026439674198627472, 0.026800917461514473, -0.04961629584431648, 0.002750757383182645, -0.014452709816396236, -0.024624109268188477, -0.03882209584116936, -0.044940244406461716, -0.04466532915830612, 0.06797288358211517, -0.01985400915145874, -0.019896306097507477, -0.011096857488155365, 0.11458324640989304, -0.03482818976044655, 0.003141599241644144, -0.03230646625161171, 0.00757948262616992, 0.0014412269229069352, 0.006683374289423227, -0.044183507561683655, 0.03319622576236725, 0.008010782301425934, 0.022149495780467987, -0.011422847397625446, 0.004482703749090433, -0.015586880967020988, -0.027849605306982994, 0.0017676486168056726, 0.026035873219370842, -0.0006197645561769605, 0.02224484086036682, 0.00021576073777396232, -0.057769134640693665, 0.007506292778998613, 0.03213239833712578, 0.03288719058036804, 0.0336129255592823, -0.05420767143368721, -0.012883911840617657, -0.008106900379061699, 0.008391601964831352, -0.012535003013908863, 0.015906866639852524, -0.05076776444911957, -0.02759665995836258, 0.023270420730113983, -0.0326196663081646, 0.0010979307116940618, 0.03659386560320854, 0.02252144366502762, 0.006200497969985008, 0.008901325985789299, -0.011764917522668839, -0.024034960195422173, 0.010610886849462986, -0.05014018714427948, -0.004366141278296709, 0.007471032906323671, -0.009257491677999496, 0.013774839229881763, -0.004052211996167898, -0.05120087042450905, 0.08281814306974411, -0.05860477313399315, 0.023411642760038376, -0.01135314628481865, 0.07605641335248947, 0.03606569021940231, 0.0023219543509185314, -0.030583949759602547, 0.014191526919603348, 0.031445033848285675, 0.02550165168941021, -0.020442210137844086, 0.03491723909974098, -0.11511842161417007, -0.023595932871103287, 0.016722893342375755, 0.01795012690126896, -0.03519349917769432, 0.03510931134223938, 0.03650553151965141, -0.07697237282991409, 0.025393463671207428, 0.023829054087400436, -0.036828815937042236, -0.10828261822462082, -0.01744120940566063, -0.03499651700258255, 0.04130236431956291, 0.01096319779753685, -0.01755089871585369, -0.01885317452251911, -0.02427911013364792, 0.003579744603484869, -0.020863622426986694, 0.0040505677461624146, -0.04493670538067818, 0.0337388813495636, -0.03711475804448128, 0.0015497264685109258, 0.025691885501146317, -0.0168699212372303, -0.011175530031323433, -0.02588205225765705, 0.03555307909846306, -0.0680888444185257, 0.03572511300444603, 0.010797617956995964, 0.014918923377990723, -0.037201907485723495, 0.07658469676971436, -0.015949999913573265, -0.012163596227765083, 0.004595874343067408, -0.07026245445013046, -0.025617193430662155, 0.027163224294781685, -0.008225400932133198, -0.04406950622797012, -0.03073100931942463, 0.018288861960172653, -0.018370194360613823, -0.018439749255776405, -0.02582654543220997, 0.07589742541313171, 0.03096102550625801, 0.010723267681896687, 0.042014334350824356, 0.06517858058214188, -0.011713286861777306, 0.033404748886823654, 0.001394347520545125, 0.07114730030298233, -0.016630787402391434, -0.03864266350865364, -0.023591404780745506, 0.01648727059364319, -0.007819784805178642, 0.0011527207680046558, 0.014353965409100056, -0.03982224687933922, 0.009870965965092182, -0.0164259634912014, 0.018017210066318512, -0.05080247297883034, 0.03801870718598366, 0.016151342540979385, 0.03638574853539467, -0.09123482555150986, -0.01990910805761814, 0.009645416401326656, -0.020191438496112823, 0.0484035350382328, 0.0035427219700068235, -0.00402126694098115, 0.0245219673961401, 0.012414218857884407, -0.015532990917563438, 0.007582669146358967, 0.03459795564413071, -0.0034849978983402252, 0.015373625792562962, 0.027361001819372177, -0.01377019751816988, -0.028673281893134117, -0.013524521142244339, 0.010735761374235153, -0.09426221996545792, -0.025604380294680595, -0.02214866131544113, 0.05664714425802231, 0.01698531210422516, -0.02109367959201336, -0.007603885140269995, -0.08817999809980392, 0.006243197247385979, 0.0015187588287517428, 0.03170439600944519, -0.01372432429343462, 0.04810553416609764, -0.031626928597688675, -0.016909752041101456, 0.022251827642321587, -0.01700221188366413, 0.07889445871114731, 0.019281528890132904, -0.01244459766894579, -0.04638929292559624, -0.008269771002233028, 0.021693171933293343, -0.025076378136873245, 0.06039828434586525, -0.011995463632047176, -0.03728826716542244, -0.04337623715400696, 0.009668373502790928, 0.022376032546162605, 0.02552179992198944, -0.030902350321412086, 0.027698449790477753, 0.06418002396821976, 0.035568006336688995, 0.018112100660800934, -0.07988190650939941, 0.03208867460489273, 0.00782166700810194, -0.07280435413122177, 0.00327924988232553, 0.053086623549461365, 0.0361679308116436, 0.0008816063636913896, 0.01385190337896347, -0.00919349119067192, 0.0018363365670666099, 0.0398532971739769, -0.0277955811470747, -0.01935035176575184, 0.015106947161257267, 0.01731221005320549, 0.028095703572034836, -0.055325448513031006, -0.0499432273209095, -0.00904088094830513, -0.05859068036079407, -0.05008341372013092, 0.023845776915550232, 0.031812287867069244, -0.007262161932885647, -0.012722630985081196, 0.04045578092336655, -0.015218827873468399, -0.05654902756214142, 0.05847272276878357, 0.004512268118560314, -0.006917805410921574, 0.023764580488204956, -0.012168098241090775, -0.00977974385023117, 0.02988739125430584, 0.036006275564432144, 0.054982684552669525, 0.0012074662372469902, -0.02260960265994072, 0.012312483973801136, -0.031122982501983643, 0.03606942296028137, 0.022755548357963562, 0.08859261870384216, -0.024690279737114906, -0.007001421879976988, 0.003583813551813364, -0.04098548740148544, 0.021309874951839447, -0.031179046258330345, 0.09300877153873444, 0.019291281700134277, 0.026063578203320503, 0.01979457028210163, -0.06142111495137215, -0.0013066952815279365, -0.016002019867300987, -0.0174071304500103, 0.002336262259632349, 0.013089731335639954, -0.024855978786945343, -6.396390796546059e-33, 0.027369391173124313, 0.0025860953610390425, -0.0210610032081604, 0.01332645770162344, -0.02160436473786831, 0.04817723482847214, -0.01571974717080593, -0.013051317073404789, -0.003026719903573394, -0.0024770251475274563, -0.00126655213534832, 0.007726071868091822, 0.015126756392419338, 0.029830047860741615, 0.0199569221585989, -0.034284405410289764, 0.017230618745088577, -0.027290375903248787, 0.04364728927612305, 0.008750131353735924, -0.0032462161034345627, 0.05152500048279762, 0.06702406704425812, -0.0488373264670372, -0.014076649211347103, -0.0011441668029874563, -0.050053671002388, -0.03302199766039848, 0.017414860427379608, -0.0054570939391851425, -0.014637913554906845, 0.07540807127952576, 0.03511814773082733, -0.0022739002015441656, -0.014186962507665157, -0.012231201864778996, -0.029011240229010582, -0.015253335237503052, -0.05948760360479355, -0.021059511229395866, -0.0324724018573761, -0.018510576337575912, 0.0891481339931488, 0.02671990543603897, -0.03342420607805252, -0.038511984050273895, 0.05896087363362312, 0.02151394449174404, -0.07822516560554504, 0.007660663686692715, -0.045083317905664444, 0.033138033002614975, -0.015494294464588165, -0.005405489820986986, -0.0386410728096962, 0.041396211832761765, -0.03931711986660957, 0.0333060696721077, -0.01996321603655815, -0.022994669154286385, 0.03694045543670654, 0.03457068279385567, 0.019697468727827072, 0.013113990426063538, -0.015178438276052475, 0.05014171078801155, 0.049852509051561356, 0.0184843298047781, -0.01852680929005146, -0.0308168213814497, 0.024478085339069366, 0.04518745094537735, 0.008547798730432987, 0.005889235995709896, 0.1137877106666565, -0.06999010592699051, -0.07425051927566528, -0.008304327726364136, -0.02110454998910427, 0.03775828331708908, -0.0013365489430725574, 0.05639965087175369, -0.017266109585762024, -0.002631407929584384, 0.023654663935303688, -0.11327338963747025, 0.00791600439697504, -0.04402356594800949, -0.018581753596663475, 0.030255358666181564, 0.009103729389607906, 0.045516423881053925, -0.0054032448679208755, -0.01284659095108509, 0.06792648136615753, 0.008781791664659977, -0.007046947255730629, 0.04144909605383873, 0.011512287892401218, -0.04027288779616356, -0.013501054607331753, -0.06868845969438553, -0.05064407363533974, -0.03228399530053139, 0.044041991233825684, -0.007839898578822613, 0.04870980232954025, 0.001969661796465516, 0.030973266810178757, -0.05773063004016876, -0.048971813172101974, -0.02827553078532219, 0.037125490605831146, 0.11006085574626923, 0.03872225061058998, -0.01337792631238699, -0.007687216158956289, 0.0726722851395607, -0.010249068960547447, -0.004241536371409893, -0.03778166323900223, -0.035762060433626175, 0.058070577681064606, 0.00723104877397418, -0.04465476796030998, -0.017860539257526398, 0.008071690797805786, -0.04057137295603752, 0.019759010523557663, -0.07813460379838943, -0.025337297469377518, -0.015119603835046291, 2.7507948630045576e-07, -0.011915604583919048, -0.028578614816069603, -0.03762334585189819, -0.045636050403118134, -0.00910047348588705, -0.012333964928984642, 0.010958013124763966, 0.022641681134700775, -0.029128126800060272, 0.0030471165664494038, 0.060194049030542374, -0.014025569893419743, 0.024016274139285088, -0.015118048526346684, -0.06874021142721176, -0.028602086007595062, 0.004340263083577156, 0.05274844542145729, -0.009935523383319378, -0.01087652426213026, 0.0056627606973052025, 0.08975695073604584, 0.03990417346358299, -0.05284785479307175, 0.06481248140335083, -0.009690266102552414, 0.01611516624689102, -0.008927999064326286, 0.03656682372093201, 0.007662140764296055, 0.05825461819767952, 0.005572506692260504, 0.014469326473772526, 0.04599284008145332, 0.003752904012799263, 0.03771539777517319, 0.07727446407079697, 0.06256186962127686, -0.010884334333240986, -0.0025648484006524086, -0.011228584684431553, 0.03752557188272476, 0.03357766941189766, -0.0439964234828949, 0.031007353216409683, 0.0030610053800046444, 0.011279392056167126, -0.018684890121221542, -0.05601447448134422, 0.010698690079152584, 0.040294546633958817, -0.015183513052761555, 0.045248840004205704, -8.627973147667944e-05, -0.006696849595755339, -0.06388038396835327, -0.041095297783613205, -0.024830883368849754, 0.003645635209977627, 0.04567866027355194, -0.08866466581821442, -0.008445813320577145, -0.006054397206753492, -0.07020553946495056, 0.036986809223890305, 0.030243849381804466, -0.011868860572576523, 2.293942787318635e-34, 0.008520388975739479, -0.011005229316651821, -0.017533818259835243, 0.03930157795548439, -0.0013685175217688084, -0.03605100139975548, -0.005020203534513712, 0.007482131943106651, -0.0020118814427405596, 0.0026824255473911762, -0.006823609583079815]

['I. Theodorakopoulos', 'V. Pothos', 'D. Kastaniotis', 'N. Fragoulis']

1701.05221v5

A new, radical CNN design approach is presented in this paper, considering the reduction of the total computational load during inference. This is achieved by a new holistic intervention on both the CNN architecture and the training procedure, which targets to the parsimonious inference by learning to exploit or remove the redundant capacity of a CNN architecture. This is accomplished, by the introduction of a new structural element that can be inserted as an add-on to any contemporary CNN architecture, whilst preserving or even improving its recognition accuracy. Our approach formulates a systematic and data-driven method for developing CNNs that are trained to eventually change size and form in real-time during inference, targeting to the smaller possible computational footprint. Results are provided for the optimal implementation on a few modern, high-end mobile computing platforms indicating a significant speed-up of up to x3 times.

Parsimonious Inference on Convolutional Neural Networks: Learning and applying on-line kernel activation rules

http://arxiv.org/pdf/1701.05221v5

Title Parsimonious Inference Convolutional Neural Networks Learning applying online kernel activation rule Summary new radical CNN design approach presented paper considering reduction total computational load inference achieved new holistic intervention CNN architecture training procedure target parsimonious inference learning exploit remove redundant capacity CNN architecture accomplished introduction new structural element inserted addon contemporary CNN architecture whilst preserving even improving recognition accuracy approach formulates systematic datadriven method developing CNNs trained eventually change size form realtime inference targeting smaller possible computational footprint Results provided optimal implementation modern highend mobile computing platform indicating significant speedup x3 time Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.01892285794019699, 0.03176836296916008, -0.02030724287033081, 0.06722205877304077, -0.006590038072317839, -0.007452232763171196, 0.0459536537528038, 0.019313611090183258, -0.02842235006392002, -0.026905441656708717, 0.021887587383389473, 0.051471006125211716, -0.00291715981438756, 0.038893792778253555, 0.010177318006753922, -0.011305693536996841, 0.013187614269554615, 0.04068724438548088, 0.0044576083309948444, -0.019751643761992455, 0.0031505103688687086, -0.002275544684380293, 0.007109115831553936, 0.032819461077451706, -0.08610014617443085, -0.003673272905871272, 0.012708106078207493, 0.03438509628176689, 0.003601432079449296, -0.044350940734148026, 0.042713697999715805, 0.009756907820701599, -0.008484913036227226, 0.024489834904670715, 2.6530112791078864e-06, -0.023848051205277443, -0.02463095635175705, -0.029296861961483955, 0.019668474793434143, 0.022498920559883118, 0.05163023993372917, 0.003633362939581275, 0.0010402088519185781, -0.03462682291865349, -0.04226979985833168, -0.004718015901744366, 0.05301482975482941, 0.08928278833627701, -0.030180027708411217, 0.045819491147994995, -0.01427889708429575, -0.049271661788225174, -0.024933140724897385, 0.014990360476076603, -0.03614724427461624, -0.040299296379089355, 0.011518538929522038, 0.00528286537155509, -0.05447855591773987, -0.04855039343237877, -0.016306491568684578, 0.04618225246667862, 0.053557705134153366, 0.005309166852384806, 0.04655637964606285, 0.03272324055433273, -0.030028000473976135, -0.031963665038347244, 0.0036462245043367147, 0.05088864639401436, -0.09900209307670593, 0.00599256157875061, 0.014477486722171307, -0.012587410397827625, -0.040593624114990234, -0.029860518872737885, -0.010559549555182457, 0.003749361727386713, -0.039423808455467224, 0.03245554491877556, -0.03182637318968773, 0.025843311101198196, 0.013885337859392166, 0.0605941116809845, -0.044459015130996704, 0.03594081103801727, -0.01811031997203827, 0.03367317095398903, -0.010221327655017376, -0.024371758103370667, -0.08139427751302719, -0.02859445847570896, 0.028715426102280617, 7.379048474831507e-05, -0.0037643341347575188, -0.021837033331394196, -0.004381410777568817, -0.05063192918896675, 0.006626483052968979, -0.09372217208147049, 0.017982251942157745, 0.01441666204482317, -0.04003354534506798, -0.0027641449123620987, -0.046730779111385345, -0.004033264238387346, -0.05075041577219963, 0.03588872030377388, -0.03832441568374634, 0.02045927383005619, -0.029605772346258163, 0.02776838093996048, 0.01714988425374031, 0.03447830304503441, -0.001852493267506361, -0.014770815148949623, -0.06398732215166092, 0.007125969510525465, -0.023182859644293785, -0.03869393467903137, -0.040841568261384964, 0.06919598579406738, -0.00794993806630373, -0.025752384215593338, 0.01993744820356369, 0.012705637142062187, -0.028888918459415436, 0.04637983813881874, -0.03828985616564751, -0.08329743891954422, 0.030288714915513992, 0.023242579773068428, 0.040759507566690445, 0.009225989691913128, 0.017661817371845245, 0.019635677337646484, -0.007178022991865873, -0.02352353185415268, -0.05170484632253647, 0.0012437975965440273, -0.010613841935992241, -0.011032070964574814, 0.012230497784912586, -0.06437323987483978, -0.023265982046723366, -0.05064716190099716, -0.005952237173914909, 0.0032539116218686104, 0.006897227838635445, -0.02684010937809944, -0.022602388635277748, 0.040470801293849945, 0.0028391636442393064, -0.005532662384212017, 0.09842075407505035, 0.00045811725431121886, -0.03807607293128967, 0.054824382066726685, 0.03214069455862045, 0.016845455393195152, -0.014465497806668282, -0.02860359475016594, -0.0359334759414196, -0.007990259677171707, 0.004049715586006641, -0.020654914900660515, -0.04288080707192421, -0.031278759241104126, -0.04276002570986748, 0.01640383154153824, 0.00046014756662771106, 0.03202441334724426, -0.0017270727548748255, 0.019694795832037926, 0.015976861119270325, 0.03161470592021942, 0.006358967162668705, 0.032039862126111984, -0.04832068830728531, 0.021417103707790375, -0.012417896650731564, -0.053805191069841385, -0.010226314887404442, 0.04773661494255066, -0.006122744642198086, -0.06162543594837189, -0.05829877778887749, 0.010619675740599632, -0.026710424572229385, -0.04397518187761307, -0.014796865172684193, -0.040227390825748444, -0.0392332449555397, 0.00099588290322572, 0.06753729283809662, -0.013021890074014664, 0.01641540601849556, 0.007245691958814859, 0.024766704067587852, 0.01068668533116579, -0.02484159916639328, -0.07167909294366837, 0.03870977461338043, -0.04729985073208809, 0.007348621729761362, -0.014718432910740376, -0.019104784354567528, 0.01844913698732853, 0.04240959510207176, -0.05049087479710579, 0.005643106997013092, 0.010995691642165184, 0.04342734441161156, -0.06830770522356033, -0.006814161781221628, 0.03213229775428772, -0.010791262611746788, 0.00041421406785957515, 0.017191782593727112, 0.03455961123108864, 0.03637469559907913, 0.02952670492231846, -0.008838406763970852, 0.02370275929570198, 0.06909694522619247, 0.010354534722864628, 0.08128023147583008, 0.07511404901742935, 0.01587483286857605, -0.011789497919380665, 0.012919534929096699, -0.06462910771369934, 0.03824910521507263, -0.048435475677251816, -0.01866821013391018, 0.025806119665503502, -0.05314641818404198, -0.004924597218632698, 0.01132437027990818, -0.04920310154557228, 0.03898752108216286, 0.028851788491010666, -0.04902125895023346, -0.0343765951693058, 0.03263624384999275, -0.005343883763998747, 0.03989727795124054, -0.011986739933490753, -0.018589138984680176, 0.016846712678670883, 0.035338714718818665, -0.01178301777690649, 0.03187773749232292, 0.02053261362016201, 0.006945923436433077, -0.008195891045033932, 0.02624444290995598, 0.04012947902083397, -0.013608022592961788, 0.010355028323829174, -0.032733675092458725, -0.08798640966415405, -0.03596393018960953, -0.030771544203162193, 0.01338043063879013, 0.0030603790655732155, -0.004135011229664087, -0.019853392615914345, -0.0014368696138262749, -0.002879612846300006, -0.02379550039768219, -0.0028173227328807116, -0.002545683877542615, 0.0224112868309021, -0.0687810555100441, 0.007691703271120787, 0.08364108949899673, -0.03304004296660423, -0.006227388512343168, 0.016823967918753624, -0.03161273151636124, 0.0030411090701818466, 0.023500818759202957, -0.030510297045111656, -0.005907027050852776, 0.031270116567611694, 0.05421686917543411, -0.05422372743487358, 0.001939894282259047, -0.018430091440677643, -0.005314475391060114, 0.030622834339737892, 0.012502207420766354, -0.0452963151037693, -0.017932450398802757, -0.016047948971390724, -0.01696580834686756, 0.09362804144620895, 0.028526445850729942, -0.02078653872013092, -0.004752479027956724, 0.030156778171658516, -0.010014024563133717, 0.02752530202269554, -0.006331045646220446, -0.017843740060925484, 0.021496815606951714, -0.008461181074380875, -0.07053888589143753, -0.01961934193968773, 0.0018285397673025727, 0.05225769057869911, -0.00799594447016716, -0.03871095925569534, -0.026878055185079575, -0.016333183273673058, -0.06823544204235077, 0.021907441318035126, 0.005141009576618671, -0.024250207468867302, -0.0010871796403080225, -0.03218115493655205, 0.03227207064628601, 0.04862666502594948, -0.035194482654333115, -0.012618587352335453, -0.03771360218524933, 0.025483829900622368, 0.03776514530181885, 0.03819414973258972, 0.030740266665816307, 0.020733898505568504, -0.015030087903141975, -0.024934491142630577, -0.004343527834862471, 0.011602869257330894, -0.044767268002033234, 0.028752805665135384, -0.003953081555664539, -0.0032595894299447536, -0.034131716936826706, -0.03003471903502941, -0.0714607983827591, -0.0021279873326420784, 0.00021760548406746238, -0.04398807883262634, -0.07569463551044464, -0.03097294643521309, 0.01953982375562191, 0.0036483558360487223, -0.037875644862651825, 0.04550085961818695, 0.0058548650704324245, -0.004658891353756189, -0.002778325229883194, 0.023284558206796646, 0.041566457599401474, 0.03054657205939293, -0.014448728412389755, 0.0647500529885292, 0.043096356093883514, 0.06220213323831558, -0.03537486493587494, 0.010925986804068089, -0.08975730091333389, 0.022911053150892258, -0.009124797768890858, 0.018964700400829315, 0.007184329442679882, 0.034995462745428085, 0.018236838281154633, -0.05504115670919418, 0.018124576658010483, 0.03242552652955055, -0.022977448999881744, -0.06970218569040298, 0.021208349615335464, 0.03642033040523529, -0.06932131946086884, -0.011350621469318867, 0.004134243819862604, -0.05002429336309433, -0.03532610461115837, 0.0075851380825042725, 0.008937245234847069, -0.027581071481108665, -0.012966240756213665, 0.011609308421611786, -0.016255345195531845, 0.05503573641180992, -0.012237472459673882, -0.028498977422714233, -0.006856908556073904, -0.022440120577812195, -0.011257420293986797, -0.02584640122950077, -0.011847386136651039, -0.010693651624023914, 0.018922830000519753, -0.007298442535102367, 0.028033075854182243, -0.03416427597403526, 0.037662405520677567, 0.030277429148554802, -0.06437365710735321, -0.05276152119040489, 0.025379717350006104, 0.008974945172667503, -0.021135499700903893, -0.10246561467647552, 0.03762946277856827, -0.021821103990077972, 0.00515360850840807, -0.038480304181575775, 0.04890751838684082, 0.03317708522081375, -0.03109164722263813, 0.005274592433124781, 0.07040751725435257, -0.039866991341114044, -0.008971820585429668, 0.017109517008066177, 0.05462600663304329, 0.00021635921439155936, 0.022810522466897964, -0.031058799475431442, -0.006358699407428503, 0.024675417691469193, -0.01289441529661417, 0.004718045238405466, 0.0036678507458418608, -0.059329964220523834, 0.010855337604880333, 0.011237051337957382, -0.028861837461590767, 0.05509335920214653, 0.04480794817209244, 0.016617415472865105, -0.0902044028043747, -0.03225225582718849, 0.02246478758752346, -0.05738193914294243, 0.052569907158613205, 0.004953431431204081, -0.0039811646565794945, 0.05333881080150604, 0.02650788426399231, -0.07097122818231583, 0.005428746808320284, 0.027582500129938126, 0.022652581334114075, 0.0039493246003985405, 0.054872144013643265, 0.04947853088378906, -0.006498988717794418, -0.021817199885845184, -0.05685438960790634, -0.0789487212896347, -0.017945189028978348, 0.007385723292827606, 0.011665917001664639, 0.005062214098870754, -0.0014732255367562175, -0.05866525322198868, -0.02321743778884411, 0.036595847457647324, 0.03928773105144501, -0.008397875353693962, -0.00567116541787982, 0.04198942705988884, -0.02585054188966751, 0.0006279355147853494, 0.03252202272415161, -0.006977495271712542, 0.09089992940425873, 0.029838884249329567, -0.047542132437229156, -0.017943179234862328, -0.0061690229922533035, -0.00904788076877594, 0.007022429723292589, 0.09884175658226013, 0.03763015568256378, -0.021793264895677567, -0.02149575762450695, 0.05815936625003815, 0.06248458847403526, 0.00921420007944107, -0.018367676064372063, 0.0017932414775714278, -0.00834613386541605, 0.06224554404616356, 0.008948571048676968, 0.0013254673685878515, 0.0781940147280693, -0.039017923176288605, -0.008939442224800587, 0.008679188787937164, -0.010542139410972595, 0.026170672848820686, -0.03593123331665993, 0.008106047287583351, -0.032344263046979904, 0.028660612180829048, 0.04174281656742096, 0.038687773048877716, -0.012335703708231449, 0.026860035955905914, 0.01486961543560028, 0.0023359230253845453, -0.050365906208753586, 0.004702524747699499, -2.300954110978637e-05, -0.003393719205632806, -0.03138342499732971, 0.02202751860022545, 0.06996065378189087, -0.04415601119399071, -0.007222754415124655, -0.02843761071562767, 0.04237162321805954, -0.03345806896686554, 0.059846505522727966, -0.04737139493227005, -0.008753548376262188, 0.05394291132688522, -0.021277597174048424, -0.015566516667604446, -0.009368896484375, -0.026289915665984154, 4.485552562982775e-05, 0.007894039154052734, -0.04302133619785309, 0.01149829477071762, -0.01627536304295063, 0.006043965928256512, -0.014608502388000488, 0.015611640177667141, -0.008574794977903366, 0.04427452012896538, 0.03007851168513298, -0.03395133465528488, 0.03368888795375824, -0.023831456899642944, 0.04819082096219063, -0.03906584158539772, 0.013466190546751022, 0.013514701277017593, 0.019417759031057358, -0.07585207372903824, -0.025304226204752922, -0.0045480080880224705, 0.0148951830342412, 0.017877191305160522, -0.055139899253845215, -7.403618273835921e-33, 0.0720222219824791, -0.02190297283232212, -0.04094410315155983, 0.023783082142472267, -0.030893700197339058, 0.02856449969112873, -0.017870163545012474, -0.026693902909755707, -0.03616957366466522, -0.01418774202466011, -0.02679581195116043, 0.03111719712615013, 0.02728392742574215, 0.04426106438040733, -0.0031207348220050335, -0.01118340715765953, 0.01344625186175108, 0.0008357773185707629, 0.058175913989543915, -0.0018363817362114787, 0.058276932686567307, 0.040175870060920715, 0.056555937975645065, -0.03991851583123207, -0.08396536856889725, 0.016390997916460037, -0.016808997839689255, -0.014288517646491528, -0.016566675156354904, 0.006898495368659496, -0.0011433662148192525, 0.008326933719217777, 0.03463847190141678, 0.029817434027791023, 0.015619775280356407, -0.022807125002145767, -0.06299814581871033, -0.02535177394747734, -0.07405577600002289, 0.09195162355899811, -0.031101664528250694, 0.012873108498752117, 0.12605847418308258, 0.005104918498545885, -0.0637565329670906, 0.0042310371063649654, 0.019509777426719666, -0.02139352448284626, -0.0419967956840992, 0.008963881060481071, -0.05144837126135826, 0.048460885882377625, 0.017426950857043266, 0.024144086986780167, 0.02551043964922428, -0.01664150506258011, -0.01389341615140438, -0.012676016427576542, -0.07232744991779327, -0.022699762135744095, -0.04170124605298042, 0.01738525554537773, 0.038356564939022064, 0.06239503249526024, 0.0027498872950673103, 0.018572263419628143, 0.020887425169348717, -0.03147241100668907, -0.05014878511428833, -0.021025152876973152, 0.040062155574560165, 0.04810318723320961, 0.041194524616003036, 0.030894743278622627, 0.1249891072511673, -0.09799764305353165, -0.08385732769966125, 0.01235595066100359, 0.033144183456897736, 0.0432116836309433, 0.0032531172037124634, 0.009645272046327591, -0.04373122751712799, 0.023999791592359543, 0.022218871861696243, -0.02683665044605732, -0.02162983827292919, -0.028667060658335686, 0.0008251420222222805, -0.006395410280674696, -0.0190807543694973, 0.05790485814213753, -0.009131111204624176, -0.024880118668079376, 0.08651356399059296, -0.06660033017396927, 0.04659773036837578, 0.03101050667464733, 0.02420942485332489, -0.015446732752025127, -0.06394974142313004, -0.05346236377954483, -0.01168131735175848, 0.030199488624930382, 0.026073502376675606, 0.01898912340402603, 0.03781881555914879, 0.02489675208926201, -0.004685187712311745, 0.0009451330988667905, -0.017215069383382797, -0.040302082896232605, 0.03721733018755913, 0.044743139296770096, 0.04538188502192497, -0.002575840801000595, 0.021888261660933495, 0.018218841403722763, 0.007566235028207302, -0.008666163310408592, -0.035346318036317825, -0.03963621333241463, 0.04570116475224495, 0.022102179005742073, -0.04725028574466705, -0.021621016785502434, -0.04924768581986427, -0.03258650004863739, -0.03320636972784996, -0.09562601894140244, -0.014756180346012115, 0.023509489372372627, 3.36813798185176e-07, -0.02065293863415718, -0.027048731222748756, -0.016826845705509186, -0.04315084591507912, -0.01006222702562809, -0.0019181364914402366, 0.02342301234602928, 0.011514849029481411, -0.03325225040316582, -0.015519256703555584, 0.029729370027780533, -0.016202609986066818, 0.0568247064948082, 0.0410911962389946, -0.010307534597814083, -0.015211598947644234, -0.051188863813877106, 0.06704738736152649, -0.0008101576240733266, 0.04416864365339279, 0.07450473308563232, 0.10163799673318863, 0.03641394525766373, -0.05876610800623894, 0.07190025597810745, -0.016384238377213478, -0.005377265624701977, 0.04643288627266884, 0.0700400173664093, -0.02000334858894348, -0.02388148382306099, 0.008010434918105602, -0.007509692572057247, 0.029196249321103096, -0.015787847340106964, -0.0025256623048335314, -0.010356161743402481, 0.039294108748435974, -0.039607007056474686, 0.01590627059340477, -0.025113310664892197, -0.0046155634336173534, 0.044654976576566696, -0.05687385052442551, 0.08076898753643036, 0.006147479172796011, 0.005015202332288027, -0.04825091361999512, 0.014853964559733868, 0.026458436623215675, 0.03749684989452362, -0.0013333489187061787, -0.0006706085405312479, 0.003281660843640566, 0.025475529953837395, -0.04526827484369278, -0.03636470437049866, -0.08291473239660263, 0.03224888816475868, 0.008328232914209366, -0.005758232902735472, -0.014894617721438408, -0.03250725939869881, 0.020753083750605583, 0.09511447697877884, 0.04158065468072891, -0.026652948930859566, 3.228810459873975e-34, -0.03376709297299385, -0.020072439685463905, 0.004088861867785454, 0.013172254897654057, -0.03748800978064537, 0.028870942071080208, 0.0002667269145604223, -0.00663868198171258, -0.003336617024615407, -0.025883395224809647, -0.03745675086975098]

['Chelsea Finn', 'Pieter Abbeel', 'Sergey Levine']

1703.03400v3

We propose an algorithm for meta-learning that is model-agnostic, in the sense that it is compatible with any model trained with gradient descent and applicable to a variety of different learning problems, including classification, regression, and reinforcement learning. The goal of meta-learning is to train a model on a variety of learning tasks, such that it can solve new learning tasks using only a small number of training samples. In our approach, the parameters of the model are explicitly trained such that a small number of gradient steps with a small amount of training data from a new task will produce good generalization performance on that task. In effect, our method trains the model to be easy to fine-tune. We demonstrate that this approach leads to state-of-the-art performance on two few-shot image classification benchmarks, produces good results on few-shot regression, and accelerates fine-tuning for policy gradient reinforcement learning with neural network policies.

Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks

http://arxiv.org/pdf/1703.03400v3

Title ModelAgnostic MetaLearning Fast Adaptation Deep Networks Summary propose algorithm metalearning modelagnostic sense compatible model trained gradient descent applicable variety different learning problem including classification regression reinforcement learning goal metalearning train model variety learning task solve new learning task using small number training sample approach parameter model explicitly trained small number gradient step small amount training data new task produce good generalization performance task effect method train model easy finetune demonstrate approach lead stateoftheart performance two fewshot image classification benchmark produce good result fewshot regression accelerates finetuning policy gradient reinforcement learning neural network policy Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.008136829361319542, 0.023955857381224632, -0.03234463930130005, 0.029733700677752495, 0.04428404942154884, 0.005840153433382511, 0.04772241786122322, 0.0074520595371723175, -0.05295838415622711, 0.00922408513724804, -0.034250665456056595, 0.10482901334762573, -0.027029139921069145, 0.01720396988093853, 0.02204885147511959, -0.0599769651889801, 0.011933642439544201, 0.002274740021675825, 0.03656858950853348, -0.023462513461709023, 0.028223197907209396, -0.020719371736049652, -0.015981854870915413, 0.006787454709410667, -0.017822692170739174, 0.039239849895238876, -0.009096287190914154, 0.012896459549665451, 0.03585009276866913, -0.008393523283302784, 0.05074869841337204, 0.015852227807044983, 0.010127880610525608, 0.07624157518148422, 2.39265523305221e-06, -0.04248795285820961, 0.0011917041847482324, -0.01733899489045143, 0.02884146012365818, -0.0520956926047802, 0.01873980462551117, -0.05491196736693382, -0.04240284115076065, 0.011820078827440739, -0.027846943587064743, -0.05672862008213997, 0.058546166867017746, 0.08671050518751144, -0.00010644264693837613, 0.05178020894527435, -0.006534363608807325, -0.024884864687919617, 0.015456988476216793, -0.028228867799043655, -0.0151781365275383, 0.00048029402387328446, 0.015141780488193035, 0.009379246272146702, -0.05078580230474472, -0.03337733820080757, -0.037294235080480576, 0.029273992404341698, 0.005592936184257269, 0.022090258076786995, 0.009879063814878464, 0.0065459441393613815, -0.05401603877544403, -0.006195032503455877, -0.03875007480382919, 0.04332992807030678, -0.07554525136947632, 0.007157744374126196, -0.01609663851559162, -0.01881532557308674, -0.016418974846601486, -0.019207561388611794, -0.016798561438918114, -0.0003888600040227175, -0.007990873418748379, -0.010436550714075565, -0.05870627611875534, 0.03537476062774658, 0.015974363312125206, 0.04668382182717323, -0.049089718610048294, -0.02037317119538784, -0.02959604747593403, 0.017924996092915535, 0.01910547912120819, -0.00862643588334322, -0.01815401017665863, -0.0016177346697077155, 0.009083114564418793, 0.0224140677601099, -0.036136988550424576, -0.04472533240914345, -0.03930011764168739, -0.045091304928064346, 0.013515476137399673, 0.0010504423407837749, 0.09918685257434845, 0.01163607370108366, -0.05636915564537048, 0.045875027775764465, -0.08857239782810211, 0.009818228892982006, -0.03539908677339554, 0.045254822820425034, -0.0060522123239934444, 0.016675356775522232, -0.025385990738868713, 0.03778247907757759, -0.056191351264715195, 0.014452171511948109, 0.030880901962518692, -0.04052765294909477, -0.03582708165049553, -0.020550508052110672, -0.01237800158560276, -0.034805793315172195, 0.01954454742372036, 0.04560679942369461, -0.04881695285439491, 0.0004059269849676639, -0.011891127564013004, 0.036907393485307693, -0.01834338717162609, 0.07151419669389725, 0.015174170024693012, -0.0012547409860417247, 0.022445207461714745, -0.0007934595341794193, 0.04315636307001114, 0.023707494139671326, 0.05197201669216156, 0.11258050799369812, -0.01676270179450512, 0.021714797243475914, -0.04837946966290474, 0.023934969678521156, 0.010243016295135021, 0.0060438611544668674, 0.011023428291082382, -0.04004267230629921, 0.01534336432814598, -0.03408055007457733, -0.002279906766489148, -0.012706318870186806, -0.009908156469464302, -0.03885543346405029, -0.03288412094116211, 0.053214941173791885, -0.03182332217693329, -0.04630453884601593, 0.07816816866397858, -0.017392972484230995, -0.035648126155138016, 0.04071524366736412, 0.05468640848994255, 0.03401998057961464, -0.0036772231105715036, -0.00286875176243484, -0.028624704107642174, 0.004434723407030106, -0.008102583698928356, -0.008713580667972565, 0.008674442768096924, -0.06370613723993301, -0.037186361849308014, 0.0346432663500309, 0.02239105850458145, -0.043959684669971466, 0.04389997571706772, -0.023302579298615456, 0.02701195701956749, 0.014110625721514225, 0.0635065883398056, 0.05940350145101547, 8.811639418127015e-06, -0.0037849885411560535, -0.03365849703550339, -0.05415792390704155, -0.00253768521361053, 0.0668056309223175, -0.07876339554786682, -0.042280931025743484, -0.035024289041757584, -0.009768967516720295, -0.06406277418136597, -0.058758050203323364, 0.04729301854968071, -0.011855472810566425, 0.009187550283968449, -0.004158199764788151, 0.04257361218333244, 0.009389089420437813, -0.00699976459145546, -0.04211099073290825, 0.028696071356534958, 0.04465265944600105, -0.056337010115385056, -0.05246507376432419, 0.04284406080842018, -0.032710280269384384, -0.033784639090299606, -0.04568101465702057, -0.06798456609249115, -0.04695315286517143, 0.040279943495988846, 0.007282820530235767, 0.020910140126943588, 0.012735073454678059, 0.05270892009139061, -0.04330088570713997, -0.004308733623474836, 0.04979734867811203, -0.0016609488520771265, 0.027562348172068596, -0.013071974739432335, -0.01851392723619938, 0.033701393753290176, 0.0407167412340641, 0.01511214580386877, 0.04159029945731163, 0.01634533330798149, -0.0033852250780910254, 0.06147106736898422, 0.0522184781730175, -0.0007519653881900012, -0.0323621965944767, 0.012095428071916103, -0.06181804835796356, 0.008522594347596169, -0.032481469213962555, 0.0010451405541971326, -0.023433391004800797, -0.006360842380672693, 0.029455509036779404, 0.042188625782728195, -0.014071227982640266, 0.0419020801782608, 0.022895747795701027, -0.02208993025124073, -0.04797310009598732, 0.02048691175878048, 0.012693649157881737, 0.010218425653874874, 0.0054121557623147964, -0.012254409492015839, 0.002029749331995845, 0.06589540094137192, -0.02288048155605793, 0.011062569916248322, 0.015074982307851315, -0.031753648072481155, -0.05258217453956604, -0.011170538142323494, 0.011340896598994732, -0.04522041603922844, -0.002260480308905244, -0.012585964053869247, -0.026063011959195137, 0.026210004463791847, 0.009004678577184677, 0.05331152677536011, 0.011367937549948692, 0.01710452139377594, -0.016981935128569603, -0.005438016261905432, -0.025638842955231667, -0.04047536477446556, 0.009759278036653996, 0.007735180668532848, -0.0014309415128082037, -0.032537803053855896, -0.006670795381069183, 0.07897800952196121, -0.01588253490626812, -0.05715547502040863, 0.045669663697481155, 0.030878372490406036, 0.06238773837685585, -0.030773619189858437, -0.011901915073394775, 0.009332248009741306, -0.007962143048644066, -0.004900171887129545, -0.022099649533629417, -0.03080647997558117, -0.029480407014489174, -0.04746546968817711, 0.03485250845551491, -0.0026817484758794308, -0.055295754224061966, -0.03715522959828377, -0.02413741499185562, -0.014463567174971104, 0.03663171827793121, 0.0356207899749279, 0.00841253250837326, -0.003197017591446638, 0.1131281852722168, -0.0352589413523674, 0.005777812097221613, -0.006428158842027187, -0.03162848949432373, 0.013240555301308632, 0.025814563035964966, -0.030726421624422073, -0.018006296828389168, -0.004922743421047926, 0.02185378596186638, -0.048131026327610016, 0.03547908738255501, 0.03745751455426216, -0.01627207174897194, -0.052591416984796524, 0.05112865939736366, 0.0333736278116703, -0.01090185809880495, -0.03052990697324276, -0.012020470574498177, 0.01155161950737238, 0.06330589205026627, 0.00935904961079359, 0.004735911265015602, -0.07944677770137787, 0.00407054927200079, -0.043842751532793045, -0.001375813502818346, 0.0520196408033371, 0.000764301628805697, -0.001459194696508348, -0.03606071323156357, -0.04487151280045509, 0.04059907793998718, -0.022277534008026123, 0.050644442439079285, 0.010279892943799496, -0.01356332004070282, -0.025525430217385292, -0.010194612666964531, -0.03245024383068085, 0.0030974249821156263, -0.016709234565496445, 0.026076624169945717, -0.09692426025867462, -0.03834758326411247, -0.035436179488897324, 0.0001848627143772319, 0.02105696313083172, 0.054245565086603165, -0.029117265716195107, -0.008609849028289318, -0.027878068387508392, 0.03189954161643982, 0.02411680296063423, 0.022389402613043785, -0.030806606635451317, 0.013602286577224731, 0.06705503910779953, 0.013361150398850441, -0.027194472029805183, 0.009064245037734509, -0.15812648832798004, 0.011771767400205135, -0.018669642508029938, -0.00030521745793521404, -0.003018065821379423, -0.012536732479929924, -0.027171161025762558, -0.05652293562889099, 0.052569303661584854, -0.003449580166488886, -0.01848333142697811, -0.08926384150981903, -0.026639871299266815, -0.008509409613907337, 0.030711619183421135, 0.01355271227657795, 0.019478846341371536, 0.02138393186032772, -0.02426421269774437, -0.004104308318346739, 0.010875498875975609, 0.0009444519528187811, -0.013094766065478325, 0.009360991418361664, -0.01123736146837473, 0.020701304078102112, -0.0008266383083537221, -0.11013437062501907, -0.06235949322581291, 0.012310930527746677, 0.04339991882443428, -0.013733981177210808, -0.008401349186897278, 0.0422092080116272, 0.0017020193627104163, -0.060997143387794495, 0.07152116298675537, -0.026141606271266937, -0.045876212418079376, -0.020686477422714233, -0.026637693867087364, -0.021586446091532707, 0.05854324251413345, 0.005604499019682407, -0.04731407389044762, -0.0017347662942484021, 0.03330235928297043, 0.0016849326202645898, 0.030622825026512146, -0.06448447704315186, 0.06922004371881485, 0.025540636852383614, -0.007197334431111813, 0.06491269916296005, 0.07631679624319077, 0.007831867784261703, 0.04846063628792763, 0.03471285477280617, 0.02438638173043728, 0.018925867974758148, 0.015249771066009998, -0.04305625334382057, -0.02950231172144413, 0.023107357323169708, -0.05367110297083855, -0.024130793288350105, -0.029104016721248627, -0.03181883692741394, -0.013680470176041126, -0.016811301931738853, -0.027008941397070885, -0.0069562639109790325, -0.022427018731832504, -0.013086341321468353, -0.030006680637598038, -0.022647907957434654, 0.01734405942261219, -0.019269702956080437, 0.063546322286129, 0.017838528379797935, -0.017552895471453667, 0.008578448556363583, 0.029820559546351433, -0.0660247951745987, 0.022310255095362663, 0.0038556866347789764, 0.02003468945622444, -0.03288224712014198, 0.015085417777299881, 0.0445575937628746, -0.04828663170337677, -0.0023494248744100332, -0.06176441162824631, -0.05172105133533478, -0.013359378091990948, -0.04723493382334709, 0.06470344960689545, 0.0001336036075372249, 0.0033002228010445833, -0.04505651071667671, -0.06598342210054398, 0.062319185584783554, -0.033364471048116684, 0.008387277834117413, -0.0006636044709011912, 0.06558122485876083, -0.02548573911190033, -0.04382980242371559, -0.004342691972851753, -0.014789902605116367, 0.08901994675397873, 0.032736025750637054, -0.059787195175886154, -0.018289880827069283, 0.03539327532052994, -0.006316120736300945, -0.03764821216464043, 0.0651279166340828, 0.01536149438470602, -0.015604776330292225, -0.03289274498820305, 0.0530875027179718, 0.07178807258605957, -0.004026697017252445, -0.011541099287569523, 0.005055551882833242, 0.01747279241681099, -0.010194867849349976, -0.004977087955921888, -0.08944159746170044, 0.08748187124729156, -0.031864434480667114, -0.04776992276310921, 0.06919016689062119, -0.003282021265476942, 0.06753398478031158, -0.01820104941725731, 0.05211063474416733, 0.006386961322277784, 0.034974437206983566, 0.03631842881441116, 0.024153687059879303, -0.03151093050837517, 0.008191590197384357, 0.041986919939517975, 0.024420132860541344, -0.0598125159740448, 0.03433544188737869, 0.022410714998841286, -0.028771916404366493, -0.07172965258359909, 0.04561682045459747, 0.04723990336060524, -0.0569043830037117, -0.027601314708590508, 0.028837213292717934, -0.003786528715863824, -0.03727381303906441, 0.03785933926701546, -0.026515470817685127, 0.014838735572993755, 0.03962298110127449, -0.001113237114623189, 0.034989580512046814, 0.044950831681489944, 0.015284165740013123, -0.014792392961680889, -0.027793332934379578, -0.007394988555461168, 0.020747080445289612, -0.05167892202734947, 0.03197624534368515, 0.013140200637280941, 0.011711494997143745, 0.003967524040490389, 0.019286558032035828, 0.049260880798101425, -0.022025534883141518, -0.04135740548372269, -0.009868673980236053, 0.0673193708062172, -0.000579986022785306, 0.021559352055191994, 0.0007183466223068535, 0.008790036663413048, 0.0063094585202634335, -0.00733183603733778, -0.029397418722510338, -0.004092920105904341, 0.02060859277844429, -0.04228297621011734, -6.346949504150474e-33, 0.00011888329754583538, 0.018898826092481613, 0.0002709237451199442, -0.026770342141389847, -0.02855631709098816, -0.007356626447290182, -0.00929765123873949, -0.006190279498696327, -0.026769328862428665, -0.003789718961343169, -0.0289920624345541, 0.010835055261850357, 0.008254995569586754, 0.009171471931040287, 0.0007550053996965289, 0.005398081615567207, 0.03212159872055054, -0.008026900701224804, 0.032193008810281754, 0.009593062102794647, -0.004930675029754639, 0.033568933606147766, 0.010796249844133854, -0.08096123486757278, -0.08885440230369568, 0.045182004570961, -0.026073668152093887, -0.06097986176609993, -0.007476273458451033, 0.03641517460346222, 0.02864830754697323, 0.030050689354538918, 0.0008759204647503793, 0.0031361342407763004, -0.009454731829464436, -0.008144471794366837, -0.07275484502315521, -0.008629370480775833, -0.08280856162309647, 0.038462527096271515, 0.003414345905184746, 0.011370329186320305, 0.043181467801332474, -0.0005579441785812378, -0.016739431768655777, -0.004908126313239336, 0.06393066793680191, -0.05034180358052254, -0.023346971720457077, -0.019249506294727325, -0.04686886444687843, 0.03146574646234512, -0.014187699183821678, -0.011192764155566692, 0.043529536575078964, 0.05060949921607971, -0.01464657112956047, 0.02834087796509266, -0.028959060087800026, 0.017864152789115906, 0.031095195561647415, 0.05004259571433067, 1.0281829418090638e-05, 0.05846307799220085, -0.012274389155209064, -0.00601391214877367, -0.029219483956694603, -0.02840343862771988, 0.04240414872765541, -0.014147844165563583, 0.035186052322387695, 0.04535680264234543, 0.04776780679821968, -0.007428921293467283, 0.07547135651111603, -0.0820830836892128, -0.03829994797706604, 0.01872195303440094, 0.0001854402362369001, 0.0590064600110054, -0.01565374806523323, 0.009631241671741009, -0.023644305765628815, 0.03853815048933029, -0.0035509502049535513, -0.01878303848206997, -0.01850084960460663, -0.03929148614406586, -0.0009045024635270238, 0.02082342654466629, -0.021441563963890076, -0.012156317010521889, 0.00816267915070057, -0.07475008815526962, 0.05462658405303955, 0.03176627680659294, -0.00699278898537159, 0.038510892540216446, 0.036287643015384674, -0.029681622982025146, -0.023182470351457596, -0.048439789563417435, 0.002518481109291315, 0.023806333541870117, 0.02289719507098198, 0.0038989076856523752, 0.04035644233226776, 0.020821815356612206, -0.03159886971116066, -0.013572863303124905, 0.020886749029159546, 0.0011189163196831942, 0.016299309208989143, 0.041899118572473526, -0.024029884487390518, -0.016531527042388916, 0.005221976432949305, 0.007625283673405647, -0.018701663240790367, -0.050468798726797104, -0.014216558076441288, 0.014930397272109985, -0.01143641583621502, 0.024379383772611618, -0.06096302717924118, -0.0032065955456346273, -0.013997976668179035, 0.015905939042568207, 0.006167943589389324, -0.060961224138736725, 0.015486091375350952, 0.008855263702571392, 3.0323991495606606e-07, -0.04098302498459816, 0.03914462774991989, -0.02764730155467987, -0.0663732960820198, -0.012829851359128952, 0.005992966238409281, -0.026648100465536118, 0.03201065585017204, 0.007798020262271166, 0.03313607722520828, 0.05270732566714287, -0.0006959979073144495, 0.007471124175935984, 0.0033139584120362997, -0.007459305226802826, 0.0018223238876089454, 0.008817982859909534, 0.08408460766077042, -0.0334264300763607, 0.02769114449620247, -0.0048806993290781975, 0.10465896129608154, -0.0026426920667290688, -0.04164998605847359, 0.05594544857740402, 0.02962476760149002, -0.008657475933432579, -0.02381008118391037, 0.05406783148646355, -0.03313334286212921, 0.04519585892558098, 0.06442292034626007, -0.05799706280231476, 0.022574616596102715, 0.006320582702755928, 0.07189356535673141, -0.021737752482295036, -0.01226606871932745, -0.034846074879169464, 0.010339309461414814, 0.02869456447660923, 0.0725635439157486, 0.053435470908880234, -0.014703962951898575, 0.02270733006298542, -0.02475588209927082, 0.01160535216331482, -0.07398098707199097, -0.005556503310799599, 0.022287990897893906, 0.01885075680911541, -0.017919626086950302, -0.012717019766569138, -0.026865864172577858, 0.04595310613512993, -0.03744504973292351, -0.04552070051431656, -0.0927567258477211, 0.02762286178767681, 0.048370618373155594, -0.010167982429265976, 0.0055984631180763245, -0.024267839267849922, -0.014863874763250351, 0.06604623049497604, 0.006028397008776665, -0.03772159665822983, 2.3852070666905233e-34, -0.019364096224308014, -0.012815945781767368, 0.011731509119272232, -0.015756260603666306, -0.045251667499542236, 0.008665231987833977, 0.04545595496892929, 0.01547084841877222, 0.03900876268744469, -0.02806573174893856, -0.04108525812625885]

['Asit Mishra', 'Jeffrey J Cook', 'Eriko Nurvitadhi', 'Debbie Marr']

1704.03079v1

For computer vision applications, prior works have shown the efficacy of reducing the numeric precision of model parameters (network weights) in deep neural networks but also that reducing the precision of activations hurts model accuracy much more than reducing the precision of model parameters. We study schemes to train networks from scratch using reduced-precision activations without hurting the model accuracy. We reduce the precision of activation maps (along with model parameters) using a novel quantization scheme and increase the number of filter maps in a layer, and find that this scheme compensates or surpasses the accuracy of the baseline full-precision network. As a result, one can significantly reduce the dynamic memory footprint, memory bandwidth, computational energy and speed up the training and inference process with appropriate hardware support. We call our scheme WRPN - wide reduced-precision networks. We report results using our proposed schemes and show that our results are better than previously reported accuracies on ILSVRC-12 dataset while being computationally less expensive compared to previously reported reduced-precision networks.

WRPN: Training and Inference using Wide Reduced-Precision Networks

http://arxiv.org/pdf/1704.03079v1

Title WRPN Training Inference using Wide ReducedPrecision Networks Summary computer vision application prior work shown efficacy reducing numeric precision model parameter network weight deep neural network also reducing precision activation hurt model accuracy much reducing precision model parameter study scheme train network scratch using reducedprecision activation without hurting model accuracy reduce precision activation map along model parameter using novel quantization scheme increase number filter map layer find scheme compensates surpasses accuracy baseline fullprecision network result one significantly reduce dynamic memory footprint memory bandwidth computational energy speed training inference process appropriate hardware support call scheme WRPN wide reducedprecision network report result using proposed scheme show result better previously reported accuracy ILSVRC12 dataset computationally le expensive compared previously reported reducedprecision network Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.0358797088265419, 0.044300444424152374, -0.024891357868909836, 0.0524381622672081, 0.0145856449380517, -0.03891358897089958, 0.03083834797143936, 0.008303012698888779, -0.06069585680961609, 0.050226014107465744, -0.016413861885666847, 0.0038845674134790897, 0.03238734230399132, -0.008598925545811653, 0.020039036870002747, -0.035102035850286484, 0.005615250673145056, 0.022067422047257423, -0.021319415420293808, -0.01944834366440773, 0.022436805069446564, -0.0033824313431978226, -0.01905621774494648, 0.03956994041800499, -0.07212864607572556, 0.0022655793000012636, 0.01619885116815567, 0.015026761218905449, 0.007121869828552008, -0.027822114527225494, 0.04150518402457237, -0.01448836363852024, 0.04374203085899353, 0.03838639706373215, 2.4196608592319535e-06, -0.02630985714495182, 0.029595954343676567, 0.010876479558646679, -0.017463641241192818, 0.02473011426627636, 0.014996463432908058, 0.021885596215724945, -0.012004632502794266, 0.005589801352471113, 0.014760859310626984, -0.031143682077527046, 0.0639650747179985, 0.06578341126441956, -0.01767357997596264, 0.015342987142503262, 0.011821341700851917, -0.021365389227867126, -0.007919086143374443, -0.0034436448477208614, 0.0018861402058973908, -0.0008492755005136132, 0.011532343924045563, 0.031949713826179504, -0.05574249476194382, -0.0415797121822834, -0.005894468631595373, 0.03189544007182121, 0.057454630732536316, 0.052046336233615875, -0.035309404134750366, 0.04631491005420685, -0.029599672183394432, -0.03514770418405533, 0.021849388256669044, 0.033460915088653564, -0.06908074021339417, -0.012016105465590954, -0.01255551353096962, -0.006135361734777689, -0.032341454178094864, -0.03146065026521683, -0.04469980299472809, -0.0035811143461614847, 0.014314945787191391, 0.037736617028713226, -0.1258491724729538, 0.04416925087571144, 0.02122487872838974, 0.031537994742393494, -0.0011366086546331644, 0.008547840639948845, -0.01593092828989029, 0.07572150230407715, -0.018383968621492386, -0.0012167872628197074, -0.028407301753759384, -0.021649520844221115, 0.019341716542840004, -0.021752813830971718, 0.0044790394604206085, -0.024882743135094643, -0.04916887357831001, -0.004621301777660847, 0.034199684858322144, -0.06191190704703331, 0.046479735523462296, 0.03090360388159752, -0.022641316056251526, 0.009837666526436806, -0.07177174091339111, -0.005830863490700722, -0.059062711894512177, 0.017367657274007797, -0.020262323319911957, -0.013061211444437504, 0.007534419186413288, -0.005808723624795675, -0.012840691022574902, 0.02692188136279583, -0.03188128024339676, -0.032058458775281906, -0.07293863594532013, -0.06525412201881409, -0.0031330371275544167, -0.06460575759410858, 0.036315713077783585, 0.08237133175134659, -0.0388825424015522, -0.0330783948302269, -0.006197972223162651, 0.03849765658378601, -0.010999997146427631, 0.04587412625551224, -0.0020086225122213364, -0.014292359352111816, -0.049623630940914154, 0.009583305567502975, 0.030007254332304, 0.00789404846727848, 0.052772026509046555, 0.07203729450702667, -0.004995572846382856, 0.021236542612314224, -0.08457286655902863, -0.0165850892663002, -0.002662050072103739, 0.0056783780455589294, -0.003998201340436935, -0.08805625140666962, 0.001419857726432383, -0.02945202961564064, -0.03639092668890953, -0.010839476250112057, 0.026080459356307983, 0.016422318294644356, -0.02100731059908867, 0.04454563558101654, -0.07387801259756088, -0.028172049671411514, 0.040098123252391815, -0.02786983549594879, -0.00027990128728561103, 0.027807554230093956, 0.08015943318605423, 0.06378795206546783, -0.01218668557703495, -0.0020608194172382355, -0.06816812604665756, 0.037552833557128906, 0.0005398446810431778, -0.06427001953125, -0.05933171138167381, -0.08071205019950867, 0.010459073819220066, 0.032865460962057114, 0.04514988884329796, -0.0015848694602027535, -0.01873253658413887, -0.06433708220720291, 0.04991849511861801, 0.010783323086798191, 0.059591252356767654, 0.05241141468286514, -0.009952148422598839, -0.0046978723257780075, 0.005367069970816374, -0.04842475429177284, -0.00438603525981307, 0.041895609349012375, -0.050177086144685745, -0.03917146846652031, -0.039768368005752563, -0.015543169341981411, -0.050101686269044876, -0.04580776393413544, -0.014843299984931946, -0.021615782752633095, -0.0069589014165103436, -0.014962493441998959, 0.053293630480766296, 0.009150616824626923, -0.003670308506116271, 0.06149793043732643, 0.05983121693134308, 0.03670954331755638, -0.04700593277812004, -0.04297400638461113, -0.0069273305125534534, -0.09209813922643661, -0.03790785372257233, -0.06025588512420654, -0.018930263817310333, 0.026003753766417503, -0.0077363187447190285, -0.05303828790783882, 0.027326175943017006, 0.011633520014584064, 0.049776941537857056, -0.041661687195301056, 0.03114536963403225, 0.01139606349170208, -0.006194058805704117, 0.009096408262848854, 0.04169036075472832, -0.01028241217136383, 0.028996028006076813, -0.04796100780367851, -0.02574574016034603, 0.0235032569617033, 0.014099284075200558, 0.021143492311239243, 0.01743628829717636, 0.03346889466047287, -0.02437838539481163, 0.027974411845207214, 0.04406442120671272, -0.04261056333780289, 0.0405009463429451, -0.041224781423807144, 0.02075486071407795, -0.0894545242190361, -0.03258540853857994, -0.013330057263374329, 0.03604462742805481, -0.04483894631266594, 0.06995221227407455, 0.06544691324234009, 0.005688429344445467, -0.031207967549562454, -0.020476406440138817, -0.017227523028850555, 0.005434342660009861, -0.038871683180332184, -0.02420685440301895, 0.011103236116468906, 0.0573699027299881, 0.0057659572921693325, -0.010801275260746479, 0.01355675421655178, 0.016598813235759735, 0.01929970271885395, -0.017739620059728622, 0.019792158156633377, 0.0063957637175917625, -0.0071495347656309605, -0.03848760575056076, -0.040866054594516754, -0.011319327168166637, 0.027133380994200706, 0.04541691020131111, 0.00939151830971241, 0.0032667014747858047, -0.02379465661942959, 0.03037448786199093, -0.0039979806169867516, 0.012266029603779316, 0.023758070543408394, 0.00653606653213501, 0.03253849223256111, -0.013591730035841465, 0.009123421274125576, 0.05584053322672844, -0.012439466081559658, -0.03485845774412155, 0.027270860970020294, 0.03703553229570389, 0.0059448410756886005, -0.009218660183250904, -0.05852596461772919, 0.031120317056775093, 0.05046243593096733, 0.02942086197435856, -0.051904093474149704, -0.00022467387316282839, 0.03737514466047287, -0.013249746523797512, 0.03289896994829178, -0.009103632532060146, -0.0834437906742096, -0.009664718061685562, -0.01761935092508793, -0.05511203780770302, 0.06097675859928131, -0.023705502972006798, -0.0018373088678345084, 0.0024486365728080273, 0.06959199905395508, -0.08122575283050537, -0.016669657081365585, -0.02018975280225277, 0.008695350028574467, 0.04390869289636612, 0.006823324598371983, -0.06213788315653801, 0.00473323930054903, -0.03219478949904442, -0.002829230623319745, 0.006518390495330095, 0.03739778324961662, 0.03557572141289711, -0.009008553810417652, -0.026433786377310753, 0.02414248138666153, 0.00311843678355217, -0.018469037488102913, 0.021487107500433922, 0.002186230383813381, -0.02595842443406582, -0.02134806662797928, -0.022140853106975555, 0.036845266819000244, -0.043309640139341354, 0.04357001185417175, 0.01769300550222397, 0.06706493347883224, 0.018984153866767883, -0.053382162004709244, -0.015297165140509605, -0.07088177651166916, 0.028397660702466965, -0.009776342660188675, 0.007672212552279234, 0.016440995037555695, 0.016547296196222305, 0.009210996329784393, -0.05953411012887955, -0.025732196867465973, -0.060441985726356506, 0.019677991047501564, 0.0278920941054821, 0.027485016733407974, -0.046809058636426926, -0.002868986688554287, 0.006037748418748379, 0.030459081754088402, 0.01784171536564827, 0.0735672116279602, -0.022395886480808258, 0.002683509374037385, -0.027261817827820778, 0.002203285461291671, 0.003772979136556387, -0.020831359550356865, 0.0628814548254013, 0.024494558572769165, 0.0294786486774683, 0.05913693457841873, -0.002762350020930171, 0.04602513462305069, -0.12179668992757797, -0.03021097742021084, 0.012937769293785095, 0.04320015758275986, 0.0027634918224066496, 0.026108842343091965, 0.06757533550262451, -0.07326067984104156, 0.04934892803430557, 0.004705958999693394, -0.015182707458734512, -0.07755222916603088, -0.00477562565356493, 0.01787584275007248, -0.02544000931084156, -0.006630054209381342, -0.011791075579822063, 0.008298857137560844, -0.00964397843927145, 0.03050358034670353, -0.034152206033468246, -0.014856605790555477, -0.02701054885983467, -0.0030596095602959394, -0.04810222610831261, 0.03854002803564072, 0.005443539936095476, -0.02405841462314129, -0.024266159161925316, 0.02521834895014763, 0.008395525626838207, -0.0010887812823057175, -0.0037282726261764765, 0.00652995053678751, -0.00819083210080862, -0.024293791502714157, 0.05810065567493439, -0.03609650954604149, -0.00440813135355711, 0.023303605616092682, -0.07275372743606567, -0.04960748925805092, 0.017830079421401024, 0.014707417227327824, -0.04197349399328232, -0.038629449903964996, 0.048264529556035995, -0.005266769323498011, 0.022312939167022705, -0.010182597674429417, 0.0753074362874031, 0.041862692683935165, -0.009093002416193485, 0.020593564957380295, 0.07704877108335495, -0.024301107972860336, 0.010810493491590023, -0.03585653007030487, 0.0037644957192242146, -0.004516859073191881, 0.042799632996320724, -0.02361067198216915, 0.008572117425501347, -0.01369832456111908, -0.009595541283488274, 0.019110027700662613, -0.012300078757107258, 0.004113855306059122, -0.010333062149584293, 0.01483951322734356, -0.034847669303417206, -0.05278957635164261, 0.00023590603086631745, 0.023807639256119728, -0.07510823011398315, -0.033443331718444824, 0.03082270920276642, 0.017090102657675743, 0.05233492702245712, -0.004545482341200113, -0.04966218024492264, 0.03461221978068352, 0.03115515597164631, -0.040911756455898285, 0.061651140451431274, -0.008600114844739437, 0.030247798189520836, -0.015894846990704536, 0.037798456847667694, 0.06075374037027359, -0.05614061281085014, -0.005151231773197651, -0.019769279286265373, -0.08376637101173401, 0.02511979639530182, -0.012461090460419655, 0.08051969110965729, 0.010508758947253227, 0.004744320642203093, 0.002254094462841749, -0.04202891141176224, -0.00029791329870931804, 0.016546117141842842, 0.0056962561793625355, -0.002373467432335019, 0.021056784316897392, -0.03855776786804199, -0.000772628525737673, -0.00778633588925004, -0.03473719581961632, 0.0852249413728714, 0.036606281995773315, -0.01925211027264595, -0.02060641348361969, -0.010140055790543556, 0.01900581829249859, 0.0038616794627159834, 0.09745929390192032, 0.048440854996442795, 0.014437125064432621, -0.05854419246315956, 0.05497286096215248, 0.02970881573855877, 0.0403192974627018, -0.05091151222586632, 0.031441472470760345, -0.00341280410066247, 0.034956738352775574, -0.034516267478466034, -0.04071121662855148, 0.11367431282997131, -0.06811608374118805, 0.002782056573778391, 0.01898234523832798, 0.02385994791984558, 0.043637629598379135, -0.0285190436989069, 0.000449236948043108, -0.05859610438346863, -0.05548597127199173, -0.00949519407004118, 0.034003179520368576, -0.013394908048212528, -0.02222905121743679, 0.026810402050614357, 0.018692513927817345, -0.09279591590166092, 0.018847215920686722, 0.030155902728438377, -0.0558258481323719, -0.051049403846263885, 0.05389576405286789, 0.053265564143657684, -0.020882098004221916, -0.07447829097509384, -0.003249567234888673, 0.011565277352929115, -0.03405687212944031, 0.03056528978049755, 0.0074881576001644135, 0.04897375404834747, 0.026923874393105507, -0.009724855422973633, -0.008410333655774593, -0.009425737895071507, 0.0119236521422863, -0.018674995750188828, 0.025308776646852493, -0.008477853611111641, 0.0009601510828360915, 0.014646373689174652, -0.014663069508969784, -0.009548071771860123, 0.010942946188151836, -0.013996249996125698, 0.012583182193338871, 0.018747812137007713, -0.03152167797088623, 0.008577658794820309, 0.010655807331204414, 0.006293248850852251, -0.00973479263484478, 0.00859864242374897, -0.0032550396863371134, 0.01207658275961876, -0.061123453080654144, 0.062228620052337646, -0.03718312084674835, 0.027463587000966072, 0.0243255402892828, -0.03629477322101593, -5.938841742773977e-33, 0.024324387311935425, 0.01568213850259781, -0.007201214320957661, -0.04704597219824791, -0.05136437341570854, 0.007614209782332182, 0.01768411137163639, -0.03352097049355507, -0.02002262882888317, -0.007838222198188305, -0.03263784945011139, 0.007870996370911598, 0.01982623152434826, 0.025938190519809723, -0.011266139335930347, 0.02382439374923706, 0.056857336312532425, -0.011224143207073212, 0.05565711110830307, -0.05039869248867035, -0.005616497714072466, 0.03252904489636421, 0.0645512193441391, -0.005994707811623812, -0.09184638410806656, 0.03197745606303215, 0.0020554810762405396, -0.01948043331503868, -0.0007192896446213126, -0.011946486309170723, -0.00539392651990056, 0.012592523358762264, -0.0009659099159762263, -0.0021853770595043898, -0.03149744123220444, -0.03933769837021828, -0.04239170625805855, -0.03918197751045227, -0.025308944284915924, 0.07426311820745468, 0.018597980961203575, -0.0008622736786492169, 0.09621893614530563, -0.001082106726244092, -0.006409940775483847, -0.011509072035551071, 0.0340597964823246, -0.04675988852977753, -0.01911715231835842, 0.0015228681731969118, -0.02003132551908493, 0.010692532174289227, 0.0065823690965771675, -0.012037169188261032, 0.02007233165204525, 0.032462961971759796, -0.041828546673059464, -0.019275374710559845, -0.11988400667905807, -0.01969347707927227, 0.03562173992395401, 0.06591564416885376, -0.034617144614458084, 0.030617715790867805, 0.03705909103155136, 0.022440792992711067, 0.03433585166931152, -0.04705365002155304, -0.003802485065534711, -0.0389210470020771, 0.025681214407086372, 0.04641832783818245, 0.06360825896263123, 0.014199535362422466, 0.1153138130903244, -0.07421525567770004, -0.0888187512755394, 0.023702166974544525, -0.07760448753833771, 0.03553543612360954, 0.00687387166544795, -0.008088435046374798, 0.007853730581700802, 0.0048951623030006886, 0.04152274504303932, 0.009358343668282032, -0.010774994269013405, -0.018313851207494736, -0.0024181657936424017, -0.012423845008015633, -0.007278557866811752, 0.04459836333990097, -0.004307415336370468, -0.06620198488235474, 0.08204196393489838, -0.04649493843317032, 0.0248451866209507, 0.024563323706388474, 0.022258473560214043, -0.00886294711381197, -0.025250835344195366, -0.012042448855936527, -0.027888154610991478, -0.016501961275935173, 0.025611739605665207, 0.044589392840862274, 0.01098280493170023, 0.026302242651581764, 0.028619926422834396, -0.0253616850823164, -0.033242397010326385, -0.01779949851334095, 0.03845501318573952, 0.047634705901145935, 0.033927638083696365, -0.0024692537263035774, 0.01322512049227953, 0.010249354876577854, -0.022929292172193527, -0.013188752345740795, 0.013643177226185799, -0.0073276907205581665, 0.04342256858944893, 0.07080734521150589, -0.06378574669361115, -0.027261855080723763, -0.038866106420755386, 0.023153863847255707, -0.019055642187595367, -0.04787147417664528, -0.03433001786470413, 0.03997517004609108, 3.0759431979276997e-07, -0.012759031727910042, -0.011452960781753063, -0.019402001053094864, 0.0006703176186420023, -0.017440011724829674, -0.03405679762363434, 0.02370358444750309, -0.0033863375429064035, -0.01312362402677536, -0.04730028659105301, 0.05596184358000755, -0.0063678910955786705, 0.00495219137519598, -0.0001474072487326339, -0.042939234524965286, 0.005363532807677984, 0.026137663051486015, 0.01298639364540577, 0.019305020570755005, 0.0008852917235344648, 0.02198290266096592, 0.07350394129753113, 0.026729067787528038, -0.014796407893300056, 0.04141818359494209, 0.06111280620098114, 0.009873511269688606, -0.011740635149180889, 0.03558909147977829, -0.02142014168202877, 0.03559640049934387, -0.015544457361102104, -0.00886835902929306, -0.005264027044177055, 0.024676842615008354, 0.044667452573776245, 0.018518101423978806, 0.0007302250596694648, -0.052618321031332016, 0.030161013826727867, -0.008751749992370605, 0.04393065348267555, -0.0022336761467158794, -0.019288158044219017, 0.03232733532786369, -0.032174333930015564, -0.008322746492922306, -0.01732868142426014, 0.04758960008621216, 0.01532028242945671, 0.0017934392672032118, -0.018899139016866684, 0.050347574055194855, -0.0022500152699649334, -0.006346742156893015, -0.08019235730171204, -0.012565487995743752, -0.03547193109989166, 0.03319638594985008, -0.011513771489262581, -0.04771874472498894, -0.00901110377162695, 0.004959973506629467, -0.04607052728533745, 0.03870777040719986, 0.009643216617405415, -0.053872011601924896, 2.8678469096276634e-34, -0.05053010210394859, 0.010504048317670822, 0.00155848718713969, -0.00988498143851757, -0.04105359688401222, 0.003202956635504961, 0.03928137570619583, 0.030188104137778282, -0.044251177459955215, 0.01810634508728981, -0.06932497024536133]

['David Rolnick', 'Andreas Veit', 'Serge Belongie', 'Nir Shavit']

1705.10694v3

Deep neural networks trained on large supervised datasets have led to impressive results in image classification and other tasks. However, well-annotated datasets can be time-consuming and expensive to collect, lending increased interest to larger but noisy datasets that are more easily obtained. In this paper, we show that deep neural networks are capable of generalizing from training data for which true labels are massively outnumbered by incorrect labels. We demonstrate remarkably high test performance after training on corrupted data from MNIST, CIFAR, and ImageNet. For example, on MNIST we obtain test accuracy above 90 percent even after each clean training example has been diluted with 100 randomly-labeled examples. Such behavior holds across multiple patterns of label noise, even when erroneous labels are biased towards confusing classes. We show that training in this regime requires a significant but manageable increase in dataset size that is related to the factor by which correct labels have been diluted. Finally, we provide an analysis of our results that shows how increasing noise decreases the effective batch size.

Deep Learning is Robust to Massive Label Noise

http://arxiv.org/pdf/1705.10694v3

Title Deep Learning Robust Massive Label Noise Summary Deep neural network trained large supervised datasets led impressive result image classification task However wellannotated datasets timeconsuming expensive collect lending increased interest larger noisy datasets easily obtained paper show deep neural network capable generalizing training data true label massively outnumbered incorrect label demonstrate remarkably high test performance training corrupted data MNIST CIFAR ImageNet example MNIST obtain test accuracy 90 percent even clean training example diluted 100 randomlylabeled example behavior hold across multiple pattern label noise even erroneous label biased towards confusing class show training regime requires significant manageable increase dataset size related factor correct label diluted Finally provide analysis result show increasing noise decrease effective batch size Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.030910776928067207, 0.05125641077756882, -0.01859557442367077, 0.03943230211734772, 0.03508317098021507, 0.0039650918915867805, 0.05846835672855377, -0.0035400555934756994, -0.01660863310098648, 0.018252722918987274, -0.02822532132267952, 0.0233351718634367, -0.023831773549318314, 0.04866470396518707, 0.029610130935907364, -0.04638080298900604, 0.010066423565149307, 0.005119325127452612, 0.033816803246736526, -0.01933894492685795, 0.0010020958725363016, -0.045480258762836456, -0.014880402944982052, 0.023353641852736473, -0.0732446163892746, -0.0015472091035917401, 0.0062727793119847775, 0.020881040021777153, 0.0017021207604557276, -0.036769088357686996, 0.05195608362555504, -0.007252570241689682, 0.006188829895108938, 0.06683047115802765, 2.19511548493756e-06, -0.02869071252644062, 0.01138429343700409, -0.0006677519413642585, -0.009645571000874043, 0.011133227497339249, 0.018397828564047813, 0.022730840370059013, -0.02995488978922367, -0.02191626839339733, 0.0433342270553112, -0.04216012358665466, 0.06400903314352036, 0.09816158562898636, 0.01611746847629547, 0.009765769354999065, -0.006151789799332619, -0.03936755284667015, 0.01146000251173973, -0.021723128855228424, 0.04095907509326935, -0.06810138374567032, 0.03409162908792496, -0.007423209026455879, -0.026876728981733322, 0.0035354439169168472, -0.010301243513822556, 0.047997597604990005, 0.04071461036801338, -0.025020038709044456, 0.013974916189908981, 0.05223064497113228, -0.023799074813723564, -0.04825371876358986, 0.0050471266731619835, 0.06106571480631828, -0.028556179255247116, 0.02518301270902157, -0.03468724712729454, -0.016663093119859695, 0.01550806500017643, -0.04302116483449936, -0.00263384310528636, 0.015053772367537022, 0.007862044498324394, 0.014006532728672028, -0.0599820613861084, 0.049620505422353745, 0.03530193492770195, 0.008147993125021458, -0.010572201572358608, 0.023195995017886162, -0.006386426743119955, -0.020312393084168434, 0.03512059524655342, -0.015526904724538326, -0.031050780788064003, -0.02640250138938427, 0.028257275000214577, 0.0018238779157400131, -0.01865389756858349, -0.018221814185380936, -0.05346757546067238, -0.08319766074419022, 0.02344052493572235, -0.051396746188402176, -0.029011916369199753, -0.052375536412000656, -0.08658333122730255, 0.023074982687830925, -0.01622350700199604, 0.025416051968932152, -0.011798168532550335, 0.0633212998509407, 0.014983110129833221, -0.02669977769255638, -0.01000742893666029, 0.03278893604874611, -0.0381171889603138, 0.06619090586900711, 0.038614798337221146, 0.014671441167593002, -0.08077260106801987, -0.011734186671674252, -0.04383322224020958, 0.015128713101148605, -0.006785258185118437, 0.06951414048671722, -0.03743603453040123, 0.006704497616738081, -0.004383545834571123, -0.0019937732722610235, 0.001768898218870163, 0.04009176790714264, 0.018837595358490944, -0.01133089791983366, 0.027668939903378487, 0.03428763151168823, -0.0004325589688960463, -0.011985245160758495, 0.048707809299230576, 0.08922194689512253, -0.0014541897689923644, -0.011891951784491539, -0.08569570630788803, 0.014777163043618202, -0.03727865591645241, 0.0081492830067873, -0.019637083634734154, -0.04622844234108925, -0.03510734438896179, -0.04868806526064873, 0.01247356180101633, -0.03890323266386986, -0.005694455932825804, -0.023944323882460594, -0.05306873098015785, 0.045275431126356125, -0.04941662400960922, -0.022458162158727646, 0.10938786715269089, 0.012165965512394905, 0.014287637546658516, -0.017399532720446587, 0.03279700502753258, 0.021778957918286324, 0.050718486309051514, -0.010546374134719372, 0.03799264878034592, 0.005823406856507063, 0.0037215230986475945, -0.015592407435178757, -0.02285088412463665, -0.032744165509939194, 0.004185345023870468, 0.019968416541814804, 0.0034998313058167696, 0.04588887467980385, 0.007098508067429066, -0.04134262725710869, 0.07031062245368958, -0.010574893094599247, 0.0050744651816785336, 0.004776259418576956, -0.02162558026611805, -0.012977557256817818, -0.02176128514111042, -0.02593246102333069, -0.015537962317466736, 0.01114470511674881, -0.04584906995296478, -0.0303107351064682, 0.030254224315285683, -0.03692205250263214, -0.061892662197351456, -0.08243736624717712, 0.005723048001527786, -0.019565647467970848, -0.07258038967847824, 0.008942793123424053, 0.06220528110861778, 0.015792066231369972, -0.00015516579151153564, 0.004070321563631296, 0.027766361832618713, 0.03000129759311676, -0.028232339769601822, -0.06820256263017654, 0.05297290161252022, -0.027486911043524742, -0.051534660160541534, -0.05094161629676819, -0.025153670459985733, -0.01960877515375614, 0.02092168480157852, 0.006675608456134796, -0.00039200327591970563, 0.009768785908818245, 0.0614129900932312, -0.033091407269239426, -0.014580112881958485, 0.02021024189889431, 0.010997277684509754, 0.017934024333953857, -0.0021235523745417595, 0.004016631282866001, 0.022025713697075844, -0.03719909489154816, -0.07453035563230515, 0.023379771038889885, 0.0501442588865757, -0.048938751220703125, 0.055964965373277664, 0.04533149674534798, 0.025096340104937553, 0.003208024427294731, -0.030926836654543877, -0.03350449725985527, 0.02744077332317829, -0.008172585628926754, -0.0053713638335466385, -0.03950415924191475, -0.01989147625863552, 0.03211238980293274, 0.03022822178900242, -0.03363006189465523, -0.03878425806760788, -0.003641113406047225, -0.05109945684671402, -0.015671582892537117, 0.0036926651373505592, 0.00937864650040865, -0.06642718613147736, -0.004152752924710512, -0.00437585823237896, 0.006324147805571556, 0.04260652884840965, -0.010904298163950443, 0.04158739745616913, 0.027675630524754524, -0.001165080931968987, -0.03207927942276001, 0.03597432002425194, 0.04134766012430191, -0.018599513918161392, -0.04491966590285301, -0.021521972492337227, -0.05091552808880806, 0.00918966718018055, -0.011778026819229126, 0.0281845536082983, 0.0023287651129066944, 0.006949611008167267, 0.04011184722185135, -0.010254929773509502, -0.024599900469183922, -0.055104345083236694, -0.009185184724628925, -0.019207609817385674, 0.01469197403639555, -0.032527513802051544, -0.026146629825234413, 0.06179336458444595, 0.021945543587207794, -0.018847787752747536, 0.043493520468473434, 0.02173381671309471, -0.01806671917438507, -0.016710961237549782, -0.02103167586028576, 0.021375419571995735, 0.004556857980787754, 0.04862344264984131, -0.06943532824516296, -0.04691147431731224, 0.03545183315873146, -0.011241803877055645, 0.0442887507379055, 0.022923780605196953, -0.051524218171834946, -0.014347904361784458, -0.017314018681645393, -0.022866293787956238, 0.028304878622293472, -0.019841622561216354, -0.008608078584074974, 0.019413020461797714, 0.09391248971223831, 0.016620200127363205, 0.002447976265102625, -0.0019483003998175263, -0.04718375951051712, 0.009167318232357502, -0.028081461787223816, -0.01670253276824951, 0.016945647075772285, -0.007465248927474022, 0.0020668820943683386, 0.014529612846672535, -0.020304961130023003, -0.005039888899773359, -0.019574159756302834, -0.07054784893989563, 0.010935477912425995, 0.015213852748274803, 0.03468713164329529, 0.0021179241593927145, -0.02740454487502575, 0.05752959102392197, 0.021034561097621918, -0.014686914160847664, 0.005344799719750881, -0.08103600889444351, 0.05079038068652153, -0.006030116230249405, 0.009942173026502132, 0.01998043805360794, 0.06524241715669632, -0.044176630675792694, -0.021959388628602028, -0.03599259629845619, 0.003921923227608204, -0.015194750390946865, -0.008273569867014885, -0.0315328985452652, 0.004807477816939354, -0.01903506927192211, -0.021306872367858887, -0.0655234232544899, 0.014558900147676468, 0.0020342443604022264, -0.0036549605429172516, -0.00798484031111002, 0.0005631845560856164, -0.0262409970164299, -0.007058434188365936, 0.019133327528834343, 0.02858949452638626, 0.0007267278269864619, -0.016543306410312653, 0.004087175242602825, 0.06589401513338089, 0.03691286966204643, -0.009227876551449299, 0.03723101317882538, -0.0004900178173556924, -0.017069999128580093, 0.016979409381747246, -0.015460346825420856, 0.005414332263171673, -0.09001107513904572, 0.008661956526339054, -0.009991190396249294, 0.04708656296133995, 0.0006904900656081736, 0.023261578753590584, 0.02618514373898506, -0.03334750980138779, -0.012447911314666271, 0.05620270222425461, -0.008418826386332512, -0.04546922445297241, -0.0048693022690713406, 0.025640999898314476, 0.038515616208314896, 0.02059137262403965, -0.002100285841152072, -0.012070824392139912, -0.015945475548505783, -0.01029615756124258, 0.004092772491276264, -0.003547950414940715, -0.027197765186429024, 0.012492874637246132, -0.052322641015052795, 0.040034644305706024, 0.005268440581858158, -0.048988860100507736, -0.07285215705633163, -0.008907865732908249, -0.005356133449822664, -0.03012685477733612, 0.0681069865822792, -0.02671569213271141, 0.07067044079303741, -0.021334964781999588, 0.05863075703382492, -0.012519938871264458, -0.04847358167171478, 0.009524143300950527, -0.07049398124217987, 0.059827469289302826, 0.020386429503560066, -0.012432115152478218, -0.06374283879995346, -0.0383230485022068, 0.06915256381034851, 0.02782014198601246, -0.012098518200218678, 0.01218167133629322, 0.10352417081594467, 0.017517853528261185, -0.03704769164323807, -0.001382400980219245, 0.023460082709789276, -0.030471717938780785, 0.03311317041516304, 0.019642774015665054, 0.0343654565513134, 0.007470033131539822, 0.02073596604168415, -0.04479256272315979, -0.0015729264123365283, 0.03249073773622513, 0.0004339459992479533, 0.01286955364048481, -0.04092062637209892, -0.024791397154331207, -0.0277392715215683, 0.03603854775428772, -0.029376298189163208, 0.011470889672636986, 0.0839703232049942, -0.039316628128290176, -0.10540333390235901, -0.040595825761556625, -0.034435175359249115, 0.0007652136264368892, 0.028036219999194145, 0.025781435891985893, -0.03952964395284653, -0.008275037631392479, 0.03514297306537628, -0.026269124820828438, -0.0024200663901865482, 0.021678274497389793, 0.004810880403965712, -0.08049646019935608, 0.026159947738051414, 0.0358918234705925, -0.00785104837268591, -0.015727227553725243, 0.018848933279514313, -0.05599498748779297, -0.04099707677960396, 0.011134368367493153, 0.03827838599681854, 0.005887812934815884, 0.006467709317803383, -0.03183765709400177, -0.10759662091732025, 0.02738337777554989, 0.06315527111291885, 0.029821103438735008, -0.026094170287251472, 0.07565435767173767, -0.054774943739175797, -0.013586647808551788, 0.016644952818751335, -0.03332296758890152, 0.08895062655210495, 0.03713425248861313, -0.05544440448284149, -0.03292715549468994, -0.013304589316248894, 0.013312709517776966, 0.006485707126557827, 0.08137600123882294, -0.014440540224313736, -0.0194257665425539, -0.026293190196156502, 0.04299800097942352, 0.0587146058678627, -0.022696811705827713, -0.002664172789081931, 0.018383599817752838, 0.04522965848445892, 0.001536207040771842, -0.020631687715649605, 0.0226826723664999, 0.06382973492145538, 0.04120323061943054, 0.015654010698199272, 0.0011215341510251164, -0.027314621955156326, 0.048735182732343674, -0.005406567361205816, 0.026404643431305885, -0.012128820642828941, 0.01618218794465065, 0.07813534885644913, 0.040823858231306076, 0.02313392609357834, -0.020693976432085037, 0.026602964848279953, 0.025714881718158722, -0.01714450865983963, -0.03004266507923603, -0.02812374196946621, -0.027101464569568634, -0.04367194324731827, 0.025273552164435387, 0.07137450575828552, -0.022605765610933304, -0.052986081689596176, -0.01868879236280918, -0.022464530542492867, -0.043931327760219574, 0.015691319480538368, 0.007467175833880901, 0.02703624591231346, 0.031206319108605385, -0.013668050989508629, 0.02020004205405712, 0.009166904725134373, 0.03806207701563835, 0.06416967511177063, 0.0030557510908693075, -0.018801918253302574, -0.0024618590250611305, -0.042535923421382904, 0.043279413133859634, 0.00033029846963472664, 0.0069581433199346066, -0.008707691915333271, 0.008192642591893673, 0.05276711285114288, -0.0653548464179039, 0.00741093885153532, 0.0003987794043496251, 0.05886681750416756, 0.0066072107292711735, -0.0026423116214573383, 0.010394567623734474, 0.026282763108611107, -0.021123068407177925, 0.0046230279840528965, -0.0035613058134913445, 0.07650386542081833, -0.014759580604732037, -0.014799198135733604, -6.078943036976731e-33, 0.012655841186642647, -0.024657852947711945, -0.019223131239414215, -0.04165797308087349, 0.010185114108026028, 0.012674805708229542, -0.0024031861685216427, -0.01977246254682541, -0.027157315984368324, 0.057697102427482605, -0.021449051797389984, 0.017115766182541847, 0.016704954206943512, 0.03831817954778671, 0.021476291120052338, -0.03299026936292648, 0.04920721426606178, -0.04055076837539673, 0.05154557526111603, 0.032944731414318085, -0.01142534427344799, 0.027449831366539, 0.04097016155719757, -0.16109004616737366, -0.027387553825974464, 0.03062601014971733, -0.0008287213859148324, -0.0330086424946785, -0.015369698405265808, 0.018780693411827087, 0.0013313887175172567, 0.07328666001558304, -0.010182645171880722, 0.004054682329297066, -0.01783546432852745, -0.03490881621837616, -0.07254157215356827, 0.0004799838934559375, -0.08867296576499939, 0.05141299217939377, -0.020515626296401024, -0.011227786540985107, 0.10068533569574356, -0.004415661562234163, -0.03706589713692665, 0.003033199580386281, 0.06640511006116867, -0.05138138681650162, -0.03041008487343788, -0.05486961454153061, 0.003305409336462617, 0.016127310693264008, -0.0011804793030023575, 0.016214987263083458, 0.005725409369915724, -0.01688966527581215, -0.013899918645620346, 0.06182850897312164, -0.10057040303945541, 0.01203323807567358, 0.026011068373918533, 0.03665315359830856, -0.0023240307345986366, 0.05738463252782822, -0.0033894244115799665, 0.020263221114873886, 0.08445438742637634, 0.03519628196954727, 0.03156271204352379, -0.050927698612213135, -0.010029318742454052, 0.05299028009176254, 0.08602336794137955, 0.04039345681667328, 0.07832338660955429, -0.06455297023057938, -0.07442860305309296, 0.01550365798175335, -0.03414057195186615, -0.049433961510658264, -0.023256342858076096, 0.01100945845246315, -0.02314118482172489, 0.005052017979323864, 0.031839899718761444, -0.02329045906662941, -0.02213091030716896, 0.03700662776827812, 0.0021902071312069893, -0.011078610084950924, 0.011639541946351528, 0.013245729729533195, -0.013132081367075443, -0.03719116002321243, -0.017095714807510376, -0.05280233174562454, 0.045895013958215714, 0.02599344588816166, 0.009432613849639893, -0.020265547558665276, -0.01097608171403408, -0.03991641104221344, -0.00597847905009985, 0.049081962555646896, 0.017097117379307747, 0.0026627557817846537, 0.06855324655771255, 0.0020368522964417934, -0.035436391830444336, 0.00119766965508461, 0.004353606607764959, -0.01104220375418663, 0.06306245177984238, -0.003068087389692664, -0.0014551816275343299, -0.03486989438533783, 0.021307390183210373, 0.05992067977786064, 0.03769175708293915, 0.0017369510605931282, 0.008958274498581886, -0.010868189856410027, -0.0241291094571352, 0.01158088631927967, -0.05578288063406944, -0.02641933597624302, -0.035665180534124374, -0.008099166676402092, 0.0567755401134491, -0.08416642248630524, 0.0030031066853553057, -0.03574618324637413, 2.809526051805733e-07, -0.037033721804618835, 0.0104212062433362, -0.0009665892575867474, -0.049748461693525314, 0.028859980404376984, 0.0551428385078907, -0.03291879966855049, -0.01630028709769249, -0.01917904056608677, -0.05233556777238846, 0.026691660284996033, -0.04495757445693016, 0.0032899980433285236, 0.010539541952311993, -0.013104693032801151, -0.029056446626782417, -0.02489038184285164, 0.03895345702767372, -0.025154544040560722, 0.05949058756232262, 0.057365093380212784, 0.12738260626792908, 0.03500721976161003, -0.06715427339076996, 0.06141820549964905, -0.03783060237765312, -0.014448055066168308, -0.0018009616760537028, 0.07718312740325928, -0.002279982203617692, 0.00654265470802784, 0.02789725922048092, 0.0019539925269782543, 0.023990681394934654, -0.030306395143270493, -0.032564155757427216, 0.025065196678042412, 0.008549644611775875, -0.036303721368312836, -0.013073231093585491, -0.020115021616220474, 0.034325290471315384, 0.023799408227205276, -0.0140191949903965, 0.03577675670385361, -0.023814862594008446, -0.0177351962774992, -0.017294932156801224, -0.02156997099518776, -0.01937374658882618, 0.04108221083879471, -0.016511287540197372, 0.007517281919717789, -0.03168360888957977, -0.007381483446806669, -0.029808420687913895, -0.03857387229800224, -0.05216256156563759, 0.0427158959209919, -0.000850212702061981, -0.04524204134941101, -0.00851086899638176, 0.007886435836553574, -0.016832420602440834, 0.05057964101433754, 0.010644118301570415, -0.013937599025666714, 2.149057828038759e-34, 0.019079918041825294, -0.0116083063185215, 0.02999812364578247, -0.014830537140369415, -0.03779127076268196, -0.003614681074395776, -0.04070468246936798, -0.04020865261554718, -0.021202480420470238, 0.01889013685286045, -0.043841805309057236]

['Stefan Lattner', 'Maarten Grachten']

1707.01357v1

Content-invariance in mapping codes learned by GAEs is a useful feature for various relation learning tasks. In this paper we show that the content-invariance of mapping codes for images of 2D and 3D rotated objects can be substantially improved by extending the standard GAE loss (symmetric reconstruction error) with a regularization term that penalizes the symmetric cross-reconstruction error. This error term involves reconstruction of pairs with mapping codes obtained from other pairs exhibiting similar transformations. Although this would principally require knowledge of the transformations exhibited by training pairs, our experiments show that a bootstrapping approach can sidestep this issue, and that the regularization term can effectively be used in an unsupervised setting.

Improving Content-Invariance in Gated Autoencoders for 2D and 3D Object Rotation

http://arxiv.org/pdf/1707.01357v1

Title Improving ContentInvariance Gated Autoencoders 2D 3D Object Rotation Summary Contentinvariance mapping code learned GAEs useful feature various relation learning task paper show contentinvariance mapping code image 2D 3D rotated object substantially improved extending standard GAE loss symmetric reconstruction error regularization term penalizes symmetric crossreconstruction error error term involves reconstruction pair mapping code obtained pair exhibiting similar transformation Although would principally require knowledge transformation exhibited training pair experiment show bootstrapping approach sidestep issue regularization term effectively used unsupervised setting Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[0.008513077162206173, 0.07667741179466248, 0.014725294895470142, 0.057814229279756546, -0.0029120943509042263, 0.034956950694322586, 0.01792016439139843, 0.006903417408466339, -0.054473649710416794, -0.026799369603395462, -0.033115796744823456, 0.0428788922727108, 0.03869888186454773, 0.10498959571123123, 0.05432824417948723, -0.06904219090938568, -0.015455926768481731, -0.00778018357232213, -0.08035693317651749, -0.043097060173749924, -0.020765671506524086, 0.0025782263837754726, -0.010845004580914974, -0.003284524194896221, -0.10050191730260849, 0.02893024869263172, -0.01494328211992979, 0.028747783973813057, 0.03157167509198189, -0.02928146906197071, 0.013582964427769184, 0.029747726395726204, 0.049460381269454956, -0.03565765544772148, 2.6883326427196153e-06, 0.004898866638541222, -0.00026785468799062073, -0.025747377425432205, 0.030971691012382507, 0.01495089940726757, 0.01739521510899067, -0.04716663807630539, -0.0233666580170393, -0.015399882569909096, -0.018905917182564735, -0.05835801362991333, 0.05658801645040512, 0.013403298333287239, 0.02701147273182869, 0.022956112399697304, -0.03421339392662048, -0.023189786821603775, 0.036085549741983414, -0.03671855852007866, 0.03459317609667778, -0.036193978041410446, 0.01861678436398506, 0.047396667301654816, -0.05256137251853943, 0.01578797772526741, -0.06455422192811966, 0.03335609659552574, 0.026082342490553856, -0.0015143852215260267, 0.04013273864984512, 0.0306160356849432, 0.012767135165631771, -0.011809487827122211, -0.06532935798168182, 0.04572785645723343, -0.018791554495692253, 0.03196833282709122, -0.025765258818864822, 0.005930307786911726, -0.03805667534470558, 0.05135272070765495, 0.005300473887473345, 0.018803352490067482, 0.009591089561581612, -0.02940613403916359, -0.10371086001396179, 0.024580825120210648, -0.02702881395816803, -0.05060752108693123, -0.058941278606653214, 0.006755643989890814, 0.05045570433139801, 0.044891607016325, -0.02098979242146015, -0.011482369154691696, 0.018943097442388535, 0.014925995841622353, 0.0006288688164204359, -0.014711566269397736, 0.024283140897750854, -0.015300356782972813, -0.025733837857842445, 0.03930302709341049, -0.028828253969550133, -0.012963269837200642, 0.019930286332964897, 0.015111309476196766, 0.001816073781810701, 0.042489707469940186, -0.0579805001616478, 0.06462476402521133, -0.05655190348625183, 0.052068695425987244, -0.04847598075866699, -0.033263836055994034, 0.0014053643681108952, -0.009418911300599575, -0.0025314062368124723, -0.010767988860607147, 0.038137149065732956, -0.06154442951083183, -0.03200198709964752, 0.01715259812772274, 0.006103785242885351, 0.002125325845554471, -0.004937252961099148, 0.09943060576915741, -0.039480749517679214, -0.036610446870326996, -0.008727901615202427, 0.03599950298666954, 0.002549996366724372, 0.039371177554130554, -0.002598835388198495, -0.007306055631488562, 0.025680754333734512, 0.05113422870635986, 0.04207092151045799, 0.004568780772387981, 0.015356829389929771, 0.05872013792395592, 0.01240616850554943, 0.01650887355208397, -0.02179989218711853, 0.04144107177853584, -0.023704690858721733, 0.009337250143289566, 0.0428742840886116, -0.03899702429771423, 0.014972750097513199, -0.016747144982218742, 0.0048337760381400585, -0.055097997188568115, 0.016087166965007782, -0.05507313832640648, -0.006124397274106741, 0.06901291012763977, -0.023405658081173897, -0.040868256241083145, 0.08670861274003983, -0.012528066523373127, 0.02499166503548622, 0.02819027565419674, -0.010080622509121895, 0.0019538032356649637, -0.02601659670472145, -0.03578920289874077, -0.006799645256251097, 0.04797115549445152, -0.00741448812186718, 0.016457777470350266, -0.0663972720503807, -0.033896394073963165, 0.05033218115568161, 0.03601781651377678, 0.020860403776168823, 0.03212035819888115, 0.006673010997474194, -0.03291863948106766, 0.02384120598435402, 0.01608240231871605, -0.06963298469781876, 0.022974887862801552, 0.02757003903388977, -0.01376410387456417, -0.01251501776278019, -0.00800910871475935, 0.025630289688706398, 0.0858074426651001, 0.014006426557898521, -0.005070108454674482, -0.028043121099472046, 0.00427065696567297, -0.04476962611079216, -0.05413326993584633, 0.02686258964240551, -0.038882870227098465, 0.025148680433630943, -0.019365504384040833, 0.05367539823055267, 0.05154828727245331, -0.03633222356438637, -0.03348711133003235, -0.001406479743309319, -0.04108468443155289, 0.010347802191972733, 0.029060576111078262, 0.032947152853012085, -0.051066555082798004, 0.00951455533504486, 0.042424172163009644, -0.06073019653558731, -0.022111980244517326, -0.01855468936264515, 0.02287576161324978, -0.020079603418707848, -0.012055709958076477, 0.023465195670723915, -0.015120185911655426, -0.07874830067157745, 0.023706801235675812, 0.027644949033856392, 0.019681302830576897, -0.007380537688732147, 0.001152328448370099, 0.026782222092151642, 0.015388485044240952, 0.06269325315952301, 0.002603990025818348, -0.016144149005413055, -0.0008192378445528448, 0.027817241847515106, 0.048837121576070786, 0.025018593296408653, 0.015675516799092293, 0.06114813685417175, -0.03580721467733383, 0.035222943872213364, -0.03708752617239952, -0.0077166445553302765, -0.010517938993871212, -0.05609855800867081, -0.04504450038075447, -0.0021579302847385406, -0.06294146180152893, -0.002979820128530264, 0.01842464506626129, 0.0016841123579069972, -0.06196381896734238, 0.019167134538292885, -0.006451694294810295, -0.007355043198913336, 0.045421238988637924, 0.0009180221240967512, 0.006976005155593157, -0.017571646720170975, -0.020528724417090416, 0.001413307269103825, -0.04264305159449577, -0.0007793311378918588, -0.016718072816729546, -0.06622876971960068, 0.07316887378692627, 0.039553605020046234, 0.0003326595469843596, 0.008787903003394604, 0.006712517701089382, -0.02011685073375702, 0.06499268859624863, 0.010988459922373295, 0.00024076153931673616, 0.005434778518974781, 0.07127886265516281, -0.027358926832675934, -0.005021878983825445, 0.009880788624286652, 0.05167265608906746, 0.06325598061084747, 0.0011613662354648113, -0.0020874461624771357, -0.023946627974510193, 0.046578530222177505, -0.029295053333044052, -0.024776170030236244, 0.03896447271108627, 0.019691959023475647, 0.014707994647324085, 0.006024188362061977, -0.016545478254556656, -0.029741384088993073, 0.07189899682998657, 0.04604140296578407, -0.0009199845371767879, -0.016292249783873558, -0.0020932238548994064, -0.018462829291820526, -0.022849438712000847, 0.004478550516068935, -0.05015542358160019, 0.017725946381688118, -0.031981270760297775, 0.026393398642539978, 0.060631051659584045, 0.010138377547264099, -0.015390468761324883, -0.047122906893491745, 0.031184710562229156, -0.04669628292322159, -0.0034855357371270657, -0.06600718945264816, -0.02886267378926277, -0.015372620895504951, -0.03221466392278671, 0.028357116505503654, -0.007747878320515156, 0.032922904938459396, 0.031751345843076706, -0.013085580430924892, 0.03568776324391365, 0.018229980021715164, -0.02503814920783043, -0.00411292165517807, -0.050345201045274734, 0.04357141628861427, -0.013032723218202591, -0.029545845463871956, 0.03523667901754379, 0.0007098612259142101, -0.009032483212649822, 0.0071518439799547195, 0.005942970514297485, 0.061800241470336914, -0.004223136231303215, -0.0058197821490466595, 0.014354342594742775, 0.03141189366579056, -0.004927340429276228, -0.015135388821363449, -0.0008698973688296974, 0.015430462546646595, 0.05041876062750816, 0.049336522817611694, -0.06473319977521896, -0.001669348101131618, -0.010178168304264545, 0.017823781818151474, -0.008240360766649246, -0.028814159333705902, 0.058377865701913834, 0.04016677290201187, -0.0220294538885355, 0.014011300168931484, -0.03833962604403496, -0.0067123365588486195, -0.026414260268211365, -0.011034957133233547, 0.030722517520189285, -0.025988757610321045, -0.025149736553430557, 0.005942301359027624, 0.011159294284880161, 0.028960000723600388, -0.013091649860143661, -0.043720994144678116, -0.015164832584559917, -0.03394049033522606, 0.03451308235526085, -0.06913499534130096, 0.0037796401884406805, -0.08467017859220505, 0.05122463405132294, 0.03220077231526375, 0.055083710700273514, 0.009763669222593307, -0.019764307886362076, 0.01366538554430008, -0.03248121589422226, 0.000943142338655889, 0.01586250029504299, -0.009227970615029335, -0.09201540052890778, -0.01417663972824812, -0.005797370802611113, -0.017300719395279884, 0.026967104524374008, -0.0014767431421205401, 0.016453368589282036, -0.016288017854094505, -0.033775657415390015, -0.02589203603565693, 0.04623500630259514, -0.010702461004257202, 0.03966064751148224, -0.03651672229170799, 0.03177450969815254, 0.017049824818968773, -0.05188274756073952, -0.13100972771644592, -0.02714131772518158, 0.03121253475546837, -0.05824549123644829, -0.030653059482574463, -0.050002314150333405, 0.003099797060713172, -0.00712387403473258, 0.024072077125310898, 0.01701480522751808, -0.03611615672707558, -0.059101544320583344, -0.03705186769366264, -0.007502391934394836, 0.057447731494903564, 0.030132604762911797, -0.019292736425995827, -0.09231031686067581, 0.020071957260370255, 0.051214564591646194, 0.005471901036798954, -0.04473781958222389, 0.022293590009212494, -0.0020167361944913864, 0.007049388252198696, 0.039182525128126144, 0.07284002751111984, -0.030891750007867813, 0.06480567902326584, -0.02509472519159317, 0.02534075267612934, -0.006530590821057558, 0.03833487629890442, -0.05705467239022255, -0.05527257174253464, 0.05011595040559769, -0.02978159859776497, 0.008330980315804482, -0.00439502252265811, 0.03751259669661522, -0.036488357931375504, 0.04149661585688591, 0.012617424130439758, -0.01616622693836689, -0.050542090088129044, 0.038909003138542175, 0.00920395739376545, -0.07254193723201752, 0.048391472548246384, -0.005330985877662897, 0.05160258710384369, -0.008200976997613907, -0.09237994998693466, 0.048645488917827606, -0.01480092853307724, -0.056081824004650116, -0.026775186881422997, 0.041908226907253265, -0.025593861937522888, -0.003962158691138029, 0.01650175452232361, 0.023313915356993675, -0.035920415073633194, -0.01011632289737463, -0.07319438457489014, -0.023990368470549583, 0.01917152665555477, -0.009164384566247463, 0.05872999504208565, -0.005507981404662132, 0.07150726020336151, 0.0038067835848778486, 0.06468793749809265, 0.04089696332812309, 0.007214602082967758, -0.023120244964957237, -0.006851698271930218, 0.03267981484532356, 0.023007497191429138, -0.02888772264122963, -0.027913741767406464, -0.018391858786344528, 0.0403304286301136, -0.030283495783805847, -0.04403318092226982, 0.036457259207963943, -0.06400639563798904, -0.01457188930362463, -0.05161702632904053, 0.03800445795059204, 0.0011347179533913732, 0.042122725397348404, -0.03995766490697861, 0.042292315512895584, 0.001338744768872857, 0.001660337089560926, -0.02779380790889263, -0.005105616990476847, 0.05841180682182312, -0.004489915445446968, -0.020774774253368378, 0.022026268765330315, 0.04638902470469475, 0.000651411188300699, -0.04280424118041992, 0.012135268189013004, -0.0009608964319340885, -0.004694418516010046, -0.0856928601861, 0.014600636437535286, 0.010944697074592113, 0.032343026250600815, 0.02472924254834652, 0.0256144180893898, -0.05398857966065407, 0.018433187156915665, 0.006158646661788225, 0.013248257339000702, -0.0002553090744186193, 0.020733248442411423, 0.016178980469703674, -0.002905322704464197, -0.08771948516368866, 0.008387310430407524, -0.01867404393851757, -0.022792352363467216, 0.03860468789935112, -0.012505641207098961, 0.009769757278263569, -0.019084593281149864, 0.04480047523975372, -0.017282553017139435, -0.02871064469218254, 0.055654123425483704, -0.04502213001251221, 0.040032945573329926, -0.006378419231623411, 0.042708124965429306, 0.015042398124933243, 0.02178076095879078, -0.04133804887533188, -0.014193128794431686, -0.03509160876274109, 0.05514834448695183, 0.05320953205227852, -0.043247923254966736, -0.010396395809948444, 0.042516954243183136, 0.05358057841658592, -0.029267609119415283, -0.049932945519685745, -0.0029104978311806917, 0.0023689591325819492, 0.029558194801211357, 0.057073138654232025, 0.02418271265923977, -0.021664826199412346, 0.010797715745866299, -0.006023719906806946, -0.015664799138903618, 0.005349727347493172, -0.005343063268810511, -0.005959466099739075, -7.128866305798382e-33, -0.002944496227428317, -0.031724609434604645, -0.04331110417842865, -0.015687914565205574, -0.003355592954903841, -0.021177878603339195, -0.03730929270386696, -0.022002000361680984, -0.01457095704972744, -0.0008943313150666654, 0.03749090060591698, -0.0018444955348968506, -0.008992426097393036, 0.040923941880464554, 0.05494691804051399, 0.02442481555044651, 0.015373176895081997, 0.003209065878763795, -0.011273125186562538, 0.018488585948944092, -0.01126132346689701, 0.048032667487859726, 0.07154522836208344, -0.11276403814554214, -0.040133945643901825, 0.04642285779118538, -0.016058042645454407, -0.03387957066297531, -0.0002816400956362486, -0.0002737660543061793, -0.027503496035933495, -0.04556901007890701, -0.017937328666448593, -0.033536963164806366, -0.003867475548759103, -0.0682762861251831, -0.07692453265190125, -0.05281928554177284, -0.09139764308929443, 0.04920879751443863, -0.049470823258161545, 0.019680220633745193, 0.0330171138048172, -0.025708438828587532, -0.0027528589125722647, -0.045866698026657104, 0.02512008138000965, 0.016362177208065987, 0.004897930193692446, -0.0672038346529007, -0.0637085884809494, 0.010555604472756386, -0.04844517633318901, -0.07167860120534897, 0.0022768049966543913, -0.010121703147888184, 0.005239569116383791, 0.02078527770936489, 0.033831968903541565, 0.03059397079050541, -0.06587929278612137, 0.04763946682214737, 0.04624687507748604, -0.006749577820301056, 0.020234670490026474, 0.0333697572350502, -0.00403778487816453, -0.027674568817019463, -0.04478205367922783, -0.04062199592590332, 0.04965537041425705, 0.030209794640541077, 0.016238922253251076, 0.03581184148788452, 0.06491188704967499, -0.04681108146905899, -0.02232319861650467, 0.07569527626037598, -0.11579912900924683, 0.08230043947696686, -0.05197780206799507, -0.0001650484773563221, -0.028963277116417885, -0.029722299426794052, -0.019466349855065346, -0.029321061447262764, -0.0048987711779773235, -0.007186511531472206, 0.009561648592352867, 0.006010956130921841, -0.05235749110579491, 0.0005484717548824847, 0.031520288437604904, -0.02534405142068863, 0.02136220410466194, 0.004336187615990639, -0.009052824229001999, 0.06575097143650055, 0.015976522117853165, -0.02942725084722042, -0.013959922827780247, 0.004361082799732685, 0.013099255971610546, -0.013894702307879925, 0.016000967472791672, -0.01013960875570774, 0.03909607604146004, 0.09220666438341141, 0.02351335808634758, -0.04426820948719978, -0.030358830466866493, -0.03376369550824165, 0.050762973725795746, 0.026195425540208817, 0.015352264046669006, 0.009334918111562729, -0.004623533692210913, 0.0554293617606163, -0.006866281386464834, 0.012233925051987171, -0.04970456287264824, -0.0639689713716507, 0.0054999664425849915, 0.04811602458357811, -0.062048714607954025, -0.037386659532785416, -0.031133947893977165, -0.023891253396868706, 0.002372417598962784, -0.062290847301483154, -0.0320122167468071, 0.004850888159126043, 3.2564747698415886e-07, 0.03399351239204407, 0.041459668427705765, 0.047401104122400284, -0.025317596271634102, -0.03149491548538208, -0.001798243261873722, 0.009340662509202957, 0.07049579918384552, -0.04382074996829033, 0.005765833891928196, 0.030271310359239578, 0.015410860069096088, 0.008530004881322384, -0.0030656042508780956, -0.0031144602689892054, 0.06499330699443817, 0.0009086091886274517, 0.030539214611053467, -0.011286063119769096, 0.03207641839981079, 0.04201506823301315, 0.04780275374650955, -0.01281615998595953, -0.015073467046022415, 0.040159597992897034, 0.07163380831480026, 0.02500220201909542, -0.0036329180002212524, 0.04425584152340889, -0.003790175775066018, -0.008359101600944996, 0.05692445859313011, 0.0028502685017883778, 0.019780553877353668, -0.011604782193899155, 0.018520405516028404, 0.04056686535477638, -0.05654611811041832, -0.025048187002539635, -0.020378094166517258, 0.02011800929903984, 0.045819420367479324, 0.01917552761733532, -0.01728249341249466, 0.02996506169438362, -0.03231391683220863, 0.004330054856836796, -0.04281450808048248, -0.044585805386304855, 0.07407522946596146, 0.047525420784950256, -0.035182543098926544, 0.002450294094160199, -0.01903681457042694, 0.02740520052611828, -0.014224975369870663, -0.017198897898197174, -0.008205873891711235, 0.047573890537023544, -0.019661853089928627, -0.04139936715364456, 0.029012858867645264, -0.018517745658755302, -0.03053710237145424, 0.030788684263825417, 0.04958880692720413, -0.030658461153507233, 2.7132735350918597e-34, -0.04052417725324631, 0.011963430792093277, -0.003927818965166807, -0.008431161753833294, -0.0007200553664006293, -0.017992408946156502, 0.018444105982780457, -0.002522969152778387, -0.03191612660884857, -0.003361126407980919, -0.05115591362118721]

['Jindong Wang', 'Yiqiang Chen', 'Shuji Hao', 'Xiaohui Peng', 'Lisha Hu']

1707.03502v2

Sensor-based activity recognition seeks the profound high-level knowledge about human activities from multitudes of low-level sensor readings. Conventional pattern recognition approaches have made tremendous progress in the past years. However, those methods often heavily rely on heuristic hand-crafted feature extraction, which could hinder their generalization performance. Additionally, existing methods are undermined for unsupervised and incremental learning tasks. Recently, the recent advancement of deep learning makes it possible to perform automatic high-level feature extraction thus achieves promising performance in many areas. Since then, deep learning based methods have been widely adopted for the sensor-based activity recognition tasks. This paper surveys the recent advance of deep learning based sensor-based activity recognition. We summarize existing literature from three aspects: sensor modality, deep model, and application. We also present detailed insights on existing work and propose grand challenges for future research.

Deep Learning for Sensor-based Activity Recognition: A Survey

http://arxiv.org/pdf/1707.03502v2

Title Deep Learning Sensorbased Activity Recognition Survey Summary Sensorbased activity recognition seek profound highlevel knowledge human activity multitude lowlevel sensor reading Conventional pattern recognition approach made tremendous progress past year However method often heavily rely heuristic handcrafted feature extraction could hinder generalization performance Additionally existing method undermined unsupervised incremental learning task Recently recent advancement deep learning make possible perform automatic highlevel feature extraction thus achieves promising performance many area Since deep learning based method widely adopted sensorbased activity recognition task paper survey recent advance deep learning based sensorbased activity recognition summarize existing literature three aspect sensor modality deep model application also present detailed insight existing work propose grand challenge future research Authors 0 Ahmed Osman Wojciech Samek 1 Ji Young Lee Franck Dernoncourt 2 Iulian Vlad Serban Tim Klinger Gerald Tesau 3 Sebastian Ruder Joachim Bingel Isabelle Aug 4 Iulian V Serban Chinnadhurai Sankar Mathie 40995 Vitaly Feldman Pravesh Kothari Jan Vondrák 40996 Orly Avner Shie Mannor 40997 Ran Zhao Deanna Needell Christopher Johanse 40998 Zongyan Huang Matthew England David Wilson 40999 Imen Trabelsi Dorra Ben Ayed Name author Length 41000 dtype object

[-0.04772906005382538, 0.004994967021048069, -0.011839666403830051, 0.05454079434275627, 0.0062690130434930325, 0.02029799297451973, 0.038358382880687714, -0.0038154057692736387, 0.004776395857334137, -0.018325598910450935, -0.011894668452441692, 0.03594629466533661, 0.018405994400382042, 0.027837131172418594, 0.0009971256367862225, 0.01503636036068201, 0.031968262046575546, 0.04599876329302788, 0.015994420275092125, 0.046615783125162125, 0.005080902483314276, -0.015071000903844833, -0.02318033017218113, 0.04385916143655777, -0.049463722854852676, 0.017851796001195908, -0.0025740659330040216, -0.04454095661640167, 0.049206431955099106, -0.04138495400547981, 0.010030506178736687, -0.039074961096048355, 0.03658824786543846, 0.05413654074072838, 1.8628736597747775e-06, 0.004486489575356245, 0.01368116494268179, -0.014570090919733047, -0.05458350479602814, -0.10267270356416702, 0.017874592915177345, 0.043080199509859085, 0.046484820544719696, 0.013788455165922642, -0.014283019118010998, -0.008654465898871422, -0.014220129698514938, 0.0025927016977220774, -0.02098987251520157, 0.023769933730363846, 0.005348954815417528, 0.015846000984311104, 0.03260894864797592, 0.008682120591402054, 0.033941224217414856, -2.53058551606955e-05, -4.481767973629758e-05, 0.00668133981525898, 0.001704042311757803, -0.009354502893984318, -0.013705102726817131, -0.039284028112888336, 0.014609596692025661, 0.06475251913070679, 0.03255908563733101, 0.02052605338394642, 0.011241520754992962, 0.031111635267734528, 0.0029018546920269728, 0.05013754591345787, -0.03035138174891472, 0.01955120824277401, 0.028227919712662697, -0.0010154021438211203, -0.0321761853992939, -0.055197685956954956, -0.024891436100006104, -0.014374157413840294, 0.00371476705186069, 0.01658666506409645, 0.00904165767133236, 0.07311180979013443, 0.03993407264351845, 0.013243315741419792, 0.0006663169478997588, -0.005648257676512003, -0.027652347460389137, 0.05080108717083931, -0.02323334477841854, -0.010840017348527908, 0.07389089465141296, -0.010044991038739681, 0.01088725309818983, -0.004226847551763058, -0.03276194632053375, -0.045283813029527664, -0.0541672445833683, -0.03694866970181465, -0.02510106936097145, 0.009809779934585094, -0.017168672755360603, 0.02883877418935299, 0.020399346947669983, 0.055645789951086044, 0.06176195666193962, 0.02750236541032791, -0.035662904381752014, 0.0009138904279097915, -0.029430337250232697, -0.006643534637987614, -0.014372158795595169, 0.038185250014066696, -0.001478484831750393, 0.040730059146881104, -0.03353921324014664, -0.05460198223590851, -0.05571698769927025, -0.012002605013549328, -0.002596315462142229, -0.05899124965071678, -0.0034748490434139967, 0.05775298550724983, -0.01122447568923235, -0.011648005805909634, 0.024606505408883095, -0.00634309696033597, 0.019131071865558624, 0.085115447640419, -0.01069704256951809, -0.037828732281923294, 0.02886030450463295, 0.028495127335190773, 0.020878227427601814, -0.015108722262084484, -0.007834534160792828, -0.007160313427448273, 0.03302161023020744, -0.025547103956341743, 0.004216018132865429, 0.034310225397348404, 0.05640353262424469, -0.009231396950781345, 0.016614126041531563, -0.07554253935813904, 0.01496994961053133, -0.060282427817583084, -0.02706564962863922, -0.03045332431793213, -0.009188385680317879, -0.046417560428380966, -0.013571863062679768, 0.0821487158536911, -0.016035258769989014, 0.0034227122087031603, 0.05572054535150528, -0.020574180409312248, 0.013995197601616383, -0.023101812228560448, 0.07599987089633942, 0.01891312189400196, -0.039913784712553024, 0.010663819499313831, -0.015404373407363892, 0.02354288659989834, -0.037464674562215805, -0.09719442576169968, 0.029747217893600464, -0.030855026096105576, -0.011792121455073357, 0.03063133917748928, 0.00033388371230103076, -0.004611284472048283, -0.0024468693882226944, 0.015380054712295532, 0.02469542808830738, 0.042020224034786224, 0.004858882166445255, -0.015705090016126633, 0.012964040040969849, -0.013848945498466492, -0.03265633061528206, -0.047160740941762924, -0.006758036091923714, -0.0017943865386769176, 0.026214085519313812, -0.07654067873954773, -0.02248166687786579, -0.017681121826171875, -0.05203663557767868, -0.05785224586725235, 0.01050021406263113, -0.04725765436887741, 0.04216165468096733, 0.04703325778245926, 0.0633229911327362, -0.055883169174194336, 0.04853573814034462, 0.03317281976342201, -0.009974867105484009, 0.04519829899072647, 0.04288074001669884, -0.04319554939866066, 0.010678764432668686, 0.013758352026343346, 0.0004154127964284271, -0.0403788760304451, 0.0220411978662014, -0.020858922973275185, 0.02763999067246914, -0.08710882067680359, -0.01826651208102703, 0.02228829264640808, 0.07562130689620972, -0.0612676665186882, -0.08379539102315903, -0.016249466687440872, 0.018641553819179535, 0.005943268537521362, -0.0840066447854042, 0.0026756972074508667, 0.0269167497754097, 0.007237659767270088, -0.013606240041553974, 0.04852239415049553, -0.017118971794843674, -0.031382083892822266, 0.0380808524787426, 0.06495250016450882, 0.04455382004380226, 0.04362095519900322, 0.009180697612464428, -0.01793583296239376, 0.06061570718884468, -0.06929604709148407, 0.007154447492212057, 0.021224431693553925, -0.011776980012655258, -0.0004225987649988383, 0.020571591332554817, 0.015141098760068417, 0.015135791152715683, 0.009535690769553185, -0.02819281443953514, -0.05946021527051926, 0.02892395108938217, -0.01920311152935028, -0.01236526109278202, -0.018205799162387848, -0.023512760177254677, 0.05469163507223129, 0.006165717728435993, -0.01716051809489727, 0.02068539708852768, 0.004072471056133509, -0.009624666534364223, 0.014628566801548004, 0.008016502484679222, 0.038638681173324585, -0.049500636756420135, -0.005309729371219873, -0.018128085881471634, -0.07340530306100845, -0.014664237387478352, 0.016794821247458458, 0.06650107353925705, 0.005183219909667969, 0.060023996978998184, -0.044564876705408096, 0.01707891933619976, -0.03952888771891594, -0.038789838552474976, -0.0455031655728817, 0.05921241268515587, 0.024758242070674896, -0.042807742953300476, -0.021950040012598038, 0.023472759872674942, -0.02646106295287609, -0.014986233785748482, 0.015860846266150475, 0.03368435055017471, 0.004595024976879358, 0.020200539380311966, 0.020347818732261658, 0.0006162686622701585, 0.01278508547693491, 0.014521392993628979, 0.007424565032124519, 0.012800371274352074, -0.047937653958797455, 0.009228984825313091, 0.03598145395517349, -0.001377926324494183, -0.011104545556008816, 0.020996706560254097, -0.008295475505292416, 0.021090300753712654, 0.03646942973136902, 0.031960830092430115, -0.014070572331547737, 0.005312626250088215, 0.0010295065585523844, 0.0021293528843671083, 0.04330311715602875, -0.02862093783915043, 0.02503652684390545, -0.04848053678870201, 0.009107759222388268, -0.031092047691345215, 0.013513768091797829, 0.011748800054192543, 0.03690532594919205, 0.037957239896059036, -0.009814592078328133, -0.021863745525479317, -0.02995123527944088, -0.05879826471209526, 0.03681560605764389, -0.05411211773753166, 0.020937714725732803, 0.007799582555890083, -0.007242870982736349, -0.0414411760866642, 0.03533995896577835, -0.013885408639907837, -0.01989382691681385, -0.028667189180850983, -0.007173996418714523, 0.055512621998786926, 0.022395430132746696, 0.0329432338476181, -0.035580042749643326, -0.053915105760097504, 0.002954003866761923, -0.04539055749773979, -0.03942784667015076, -0.03541366755962372, -0.015383484773337841, -0.021233191713690758, 0.018740909174084663, -0.037615835666656494, -0.04447872191667557, -0.04116510599851608, -0.014371651224792004, -0.031999293714761734, -0.01564863696694374, -0.044651180505752563, 0.02290758118033409, 0.02425646036863327, -0.04469558969140053, -0.022694654762744904, 0.03709730878472328, 0.029897641390562057, 0.034081608057022095, -0.0015611002454534173, 0.04920950531959534, 0.06882163137197495, 0.031239451840519905, -0.05221850052475929, 0.04062911495566368, -0.037758421152830124, 0.025284316390752792, -0.033681903034448624, 0.006783456541597843, -0.10973244905471802, 0.0019570267759263515, 0.002146693877875805, 0.0347832590341568, -0.026824578642845154, 0.04851739481091499, 0.04634065553545952, -0.039064884185791016, 0.03203948959708214, 0.046973276883363724, -0.0034336906392127275, -0.032067131251096725, 0.0369541235268116, 0.048826225101947784, -0.047138556838035583, -0.004902308341115713, -0.04012387990951538, -0.026929741725325584, -0.04457377642393112, -0.008010288700461388, -0.002204437041655183, 0.0002535843523219228, -0.012671809643507004, 0.021228816360235214, -0.03699495270848274, 0.0332869328558445, 0.005033435299992561, -0.034532517194747925, -0.06443389505147934, -0.017929434776306152, 0.015092124231159687, -0.048013437539339066, -0.007181677967309952, -0.04613782837986946, 0.026138566434383392, -0.02733040787279606, 0.023191964253783226, -0.09886977076530457, -0.019117292016744614, 0.04575434327125549, -0.05224599689245224, 0.035891707986593246, -0.010474102571606636, 0.03601323068141937, -0.01834099553525448, -0.03072487935423851, -0.029151838272809982, -0.014295835979282856, 0.02163156494498253, -0.05214560404419899, -0.0274035707116127, 0.018235743045806885, -0.015007251873612404, 0.021447941660881042, 0.09874686598777771, -0.04768427461385727, -0.004931753966957331, -0.0011809788411483169, 0.07881279289722443, -0.04349806532263756, 0.059955283999443054, -0.05994945764541626, -0.0599602647125721, 0.09646390378475189, 0.046910032629966736, -0.03912091255187988, -0.011397229507565498, -0.020729631185531616, 0.013153035193681717, -0.039561763405799866, -0.001625630771741271, 0.010604227893054485, -0.019048526883125305, -0.017978304997086525, -0.00666642002761364, 0.0008640896994620562, -0.046686723828315735, 0.009982944466173649, 0.016302432864904404, 0.006551352795213461, 0.0746627151966095, 0.0033211628906428814, 0.0403333455324173, -0.03555944934487343, 0.0076132882386446, -0.006148459855467081, 0.055083636194467545, 0.021455388516187668, -0.016153883188962936, 0.007800145074725151, -0.020427506417036057, -0.0038863420486450195, -0.032703693956136703, -0.03889184817671776, 0.027076922357082367, -0.0008281060727313161, 0.05031000077724457, -0.00464666448533535, 0.024800235405564308, -0.03395136818289757, 0.04503283649682999, -0.016312135383486748, -0.02568601444363594, 0.0037497400771826506, -0.04911436140537262, 0.006415765266865492, -0.022261671721935272, -0.03239694610238075, 0.015300706028938293, -0.03215761482715607, 0.038748856633901596, -0.014150024391710758, -0.005584356840699911, -0.07302402704954147, -0.05144572630524635, -0.017625218257308006, -0.027751075103878975, 0.08297821879386902, 0.05212090536952019, -0.03160414472222328, -0.042734771966934204, 0.023098545148968697, -0.009336074814200401, 0.01251231413334608, -0.07678821682929993, -0.01672588661313057, 0.009197432547807693, -0.010439014993607998, -0.024220731109380722, 0.048804234713315964, 0.027001529932022095, -0.034633856266736984, -0.01627758890390396, 0.04134940728545189, -0.009174617007374763, 0.0747857615351677, -0.046179596334695816, 0.003551175119355321, -0.027669871225953102, 0.023499710485339165, 0.03300115838646889, -0.02853800356388092, 0.026700548827648163, -0.018217511475086212, -0.006683615036308765, -0.0023545899894088507, -0.08933531492948532, 0.05740419030189514, 0.0454949252307415, 0.013953293673694134, 0.026515096426010132, 0.013543124310672283, 0.05580947920680046, 0.013140436261892319, -0.028755217790603638, 0.028345610946416855, 0.012576157227158546, -0.06317576766014099, 0.06980615109205246, -0.02745901420712471, 0.022815626114606857, 0.02445257268846035, -0.0179249607026577, -0.052231092005968094, 0.009105668403208256, 0.027845047414302826, 0.028175214305520058, 0.0017383514204993844, 0.023914871737360954, -0.05655847117304802, -0.02129536122083664, 0.003639503847807646, 0.02737620286643505, 0.036239080131053925, -0.043417394161224365, 0.006589975673705339, 0.0232633538544178, -0.00943294633179903, -0.00978744588792324, -0.019242599606513977, 0.05515867844223976, 0.017138557508587837, 0.034167755395174026, 0.024405520409345627, -0.061480555683374405, -0.027404550462961197, -0.018473515287041664, -0.007885770872235298, -0.01920177973806858, -0.02497715689241886, -0.07377101480960846, -4.763089150536493e-33, 0.04683414846658707, 0.008490826934576035, 0.00324613181874156, -0.004092870280146599, -0.026161538437008858, 0.04569638893008232, -0.009191710501909256, -0.0038475992623716593, 0.0069779581390321255, -0.03731755167245865, 0.021095478907227516, -0.016912151128053665, 0.027422115206718445, -0.03291398286819458, 0.05027449131011963, 0.005600291304290295, 0.04426243156194687, -0.051059119403362274, 0.03836092725396156, 0.009801852516829967, 0.024394113570451736, 0.016505366191267967, 0.04058727249503136, -0.09320720285177231, -0.07067510485649109, 0.023288467898964882, 0.005791216157376766, -0.023021789267659187, 0.021656401455402374, -0.005886943079531193, -0.025469884276390076, -0.018311334773898125, 0.03916700929403305, 0.02541450597345829, -0.006178217940032482, 0.017246641218662262, -0.04688109830021858, -0.012213926762342453, -0.03492840752005577, 0.020219702273607254, -0.046569421887397766, -0.035745177417993546, 0.0026951152831315994, 0.026545001193881035, -0.07412762939929962, -0.009469138458371162, 0.027609089389443398, -0.0295275766402483, -0.010611564852297306, -0.030352134257555008, 0.021884970366954803, 0.01088955532759428, 0.0041642580181360245, -0.02374955452978611, -0.0065314495004713535, -0.03443291783332825, -0.02903219871222973, -0.03351283073425293, -0.06992868334054947, 0.032860174775123596, -0.03267759084701538, 0.004821044392883778, 0.004640388768166304, 0.04523313790559769, 0.019443748518824577, 0.03155363351106644, 0.007399215362966061, -0.021049577742815018, 0.011448729783296585, 0.0530768521130085, -0.0036036625970155, 0.10275227576494217, -0.01186390407383442, 0.03294903039932251, 0.06351342052221298, -0.02202734909951687, -0.096461221575737, 0.04363188520073891, 0.05346570163965225, 0.02824775129556656, -0.052542030811309814, 0.052679263055324554, -0.0349944606423378, 0.022207990288734436, 0.031082840636372566, 0.03965703025460243, -0.006406206637620926, -0.027411995455622673, -0.001667690696194768, 0.013765575364232063, -0.04766641929745674, 0.02348177693784237, 0.02944136969745159, -0.018430709838867188, 0.06081261858344078, 0.04711262881755829, 0.06781528145074844, -0.02388390526175499, 0.03978220745921135, -0.02213458903133869, -0.05566097050905228, -0.07220807671546936, -0.018119951710104942, 0.010956823825836182, -0.010985240340232849, 0.03055761754512787, 0.0015214714221656322, 0.05646856874227524, 0.07473859190940857, -0.016137558966875076, 0.0541599877178669, -0.03646382316946983, -0.016994468867778778, 0.07534952461719513, 0.05933207646012306, -0.05242691934108734, 0.010888515040278435, 0.09398028999567032, -0.042387451976537704, 0.0028348814230412245, -0.015260301530361176, -0.020026691257953644, 0.06812918186187744, 0.0035709987860172987, -0.02144976705312729, -0.009284520521759987, -0.08478091657161713, -0.01717095449566841, 0.012026959098875523, 0.00681664701551199, 0.005193904507905245, 0.009593886323273182, 2.4989407165776356e-07, -0.04054094851016998, -0.05123595520853996, -0.007724644150584936, -0.05656185746192932, 0.040280163288116455, 0.02529437094926834, 0.01362406462430954, 0.0469331257045269, -0.023686373606324196, 0.04258698597550392, 0.0643819198012352, -0.017399057745933533, 0.06060855835676193, -0.0005217443685978651, -0.007983045652508736, -0.00954620074480772, 0.02603616565465927, 0.05444168671965599, -0.08859547227621078, 0.014394675381481647, 0.030670499429106712, 0.0878940150141716, 0.020200684666633606, -0.005161324981600046, 0.058491140604019165, -0.06306969374418259, 0.0194462388753891, 0.007635171990841627, 0.005167480558156967, -0.06235508620738983, -0.002101166872307658, 0.02821556106209755, 0.004587395116686821, -0.05741359665989876, -0.05784018710255623, 0.024033255875110626, 0.0024169478565454483, 0.061635833233594894, -0.05260944366455078, -0.044294051826000214, -0.02437087893486023, 0.014945105649530888, 0.022540036588907242, 0.012906205840408802, 0.07399746030569077, -0.030429886654019356, -0.02506694756448269, -0.0337236225605011, 0.0013406738871708512, 0.04303678497672081, 0.02352728880941868, 0.030466072261333466, 0.020587878301739693, -0.030652325600385666, 0.033434733748435974, -0.059062764048576355, -0.04143203794956207, -0.04995901510119438, 0.0019047586247324944, -0.035138290375471115, -0.09962216019630432, 0.016036083921790123, -0.0038568107411265373, 0.009250245988368988, -0.0010154558112844825, 0.025052009150385857, -0.04113936051726341, 1.4344492130293362e-34, -0.062478795647621155, 0.01811904087662697, -0.022528592497110367, -0.027964532375335693, -0.062484338879585266, 0.01453975960612297, 0.018532095476984978, 0.023116551339626312, -0.019256215542554855, -0.018564919009804726, -0.011315268464386463]