Transactions of the Association for Computational Linguistics, vol. 6, pp. 529–541, 2018. Action Editor: Holger Schwenk.
Submission batch: 8/2017; Revision batch: 1/2018; Published 8/2018.
2018 Association for Computational Linguistics. Distributed under a CC-BY 4.0 Licence.
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NeuralLatticeLanguageModelsJacobBuckmanLanguageTechnologiesInstituteCarnegieMellonUniversityjacobbuckman@gmail.comGrahamNeubigLanguageTechnologiesInstituteCarnegieMellonUniversitygneubig@cs.cmu.eduAbstractInthiswork,weproposeanewlanguagemod-elingparadigmthathastheabilitytoperformbothpredictionandmoderationofinforma-tionflowatmultiplegranularities:neurallat-ticelanguagemodels.Thesemodelscon-structalatticeofpossiblepathsthroughasen-tenceandmarginalizeacrossthislatticetocal-culatesequenceprobabilitiesoroptimizepa-rameters.Thisapproachallowsustoseam-lesslyincorporatelinguisticintuitions–in-cludingpolysemyandtheexistenceofmulti-wordlexicalitems–intoourlanguagemodel.ExperimentsonmultiplelanguagemodelingtasksshowthatEnglishneurallatticelanguagemodelsthatutilizepolysemousembeddingsareabletoimproveperplexityby9.95%rela-tivetoaword-levelbaseline,andthataChi-nesemodelthathandlesmulti-characterto-kensisabletoimproveperplexityby20.94%relativetoacharacter-levelbaseline.1IntroductionNeuralnetworkmodelshaverecentlycontributedto-wardsagreatamountofprogressinnaturallanguageprocessing.Thesemodelstypicallyshareacommonbackbone:recurrentneuralnetworks(RNN),whichhaveproventhemselvestobecapableoftacklingavarietyofcorenaturallanguageprocessingtasks(HochreiterandSchmidhuber,1997;Elman,1990).Onesuchtaskislanguagemodeling,inwhichweestimateaprobabilitydistributionoversequencesoftokensthatcorrespondstoobservedsentences(§2).Neurallanguagemodels,particularlymodelscon-ditionedonaparticularinput,havemanyapplica-tionsincludinginmachinetranslation(Bahdanauetal.,2016),abstractivesummarization(Chopraetal.,2016),andspeechprocessing(Gravesetal.,2013).dogs chased the small cat dogs chased the smallcatdogs chased thesmalldogs chasedthethe_smallthe_small_cat small_catdogs_chasedchasedchased_thedogs_chased_thechased_the_smallFigure1:Latticedecompositionofasentenceanditscor-respondinglatticelanguagemodelprobabilitycalculationSimilarly,state-of-the-artlanguagemodelsareal-mostuniversallybasedonRNNs,particularlylongshort-termmemory(LSTM)réseaux(Jozefowiczetal.,2016;Inanetal.,2017;Merityetal.,2016).Whilepowerful,LSTMlanguagemodelsusuallydonotexplicitlymodelmanycommonly-acceptedlinguisticphenomena.Asaresult,standardmod-elslacklinguisticallyinformedinductivebiases,po-tentiallylimitingtheiraccuracy,particularlyinlow-datascenarios(Adamsetal.,2017;KoehnandKnowles,2017).Inthiswork,wepresentanovelmodificationtothestandardLSTMlanguagemod-elingframeworkthatallowsustoincorporatesomevarietiesoftheselinguisticintuitionsseamlessly:neurallatticelanguagemodels(§3.1).Neurallat-ticelanguagemodelsdefinealatticeoverpossi-blepathsthroughasentence,andmaximizethemarginalprobabilityoverallpathsthatleadtogen-eratingthereferencesentence,asshowninFig.1.Dependingonhowwedefinethesepaths,wecanin-corporatedifferentassumptionsabouthowlanguageshouldbemodeled.Intheparticularinstantiationsofneurallatticelanguagemodelscoveredbythispaper,wefocusontwopropertiesoflanguagethatcouldpotentiallybeofuseinlanguagemodeling:theexistenceofmulti-wordlexicalunits(Zgusta,1967)(§4.1)andpoly-
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semy(RavinandLeacock,2000)(§4.2).Neurallat-ticelanguagemodelsallowthemodeltoincorporatetheseaspectsinanend-to-endfashionbysimplyad-justingthestructureoftheunderlyinglattices.Werunexperimentstoexplorewhetherthesemodificationsimprovetheperformanceofthemodel(§5).En plus,weprovidequalitativevisualiza-tionsofthemodeltoattempttounderstandwhattypesofmulti-tokenphrasesandpolysemousem-beddingshavebeenlearned.2Background2.1LanguageModelsConsiderasequenceXforwhichwewanttocal-culateitsprobability.Assumewehaveavocabularyfromwhichwecanselectauniquelistof|X|tokensx1,x2,…,X|X|suchthatX=[x1;x2;…;X|X|],i.e.theconcatenationofthetokens(withanappro-priatedelimiter).Thesetokenscanbeeitheronthecharacterlevel(HwangandSung,2017;Lingetal.,2015)orwordlevel(Inanetal.,2017;Merityetal.,2016).Usingthechainrule,languagemodelsgen-erallyfactorizep(X)inthefollowingway:p(X)=p(x1,x2,…,X|X|)=|X|Yt=1p(xt|x1,x2,…,xt−1).(1)Notethatthisfactorizationisexactonlyinthecasewherethesegmentationisunique.Incharacter-levelmodels,itiseasytoseethatthispropertyismaintained,becauseeachtokenisuniqueandnon-overlapping.Inword-levelmodels,thisalsoholds,becausetokensaredelimitedbyspaces,andnowordcontainsaspace.2.2RecurrentNeuralNetworksRecurrentneuralnetworkshaveemergedasthestate-of-the-artapproachtoapproximatingp(X).Inparticular,theLSTMcell(HochreiterandSchmid-huber,1997)isaspecificRNNarchitecturewhichhasbeenshowntobeeffectiveonmanytasks,in-cludinglanguagemodeling(PressandWolf,2017;Jozefowiczetal.,2016;Merityetal.,2016;Inanetal.,2017).1LSTMlanguagemodelsrecursivelycal-1Inthiswork,weutilizeanLSTMwithlinkedinputandforgetgates,asproposedbyGreffetal.(2016).culatethehiddenandcellstates(htandctrespec-tively)giventheinputembeddinget−1correspond-ingtotokenxt−1:ht,ct=LSTM(ht−1,ct−1,et−1,θ),(2)thencalculatetheprobabilityofthenexttokengiventhehiddenstate,generallybyperforminganaffinetransformparameterizedbyWandb,followedbyasoftmax:p(xt|ht):=softmax(W∗ht+b).(3)3NeuralLatticeLanguageModels3.1LanguageModelswithAmbiguousSegmentationsToreiterate,thestandardformulationoflanguagemodelingintheprevioussectionrequiressplittingsentenceXintoauniquesetoftokensx1,…,X|X|.Ourproposedmethodgeneralizesthepreviousfor-mulationtoremovetherequirementofuniquenessofsegmentation,similartothatusedinnon-neuraln-gramlanguagemodelssuchasDupontandRosen-feld(1997)andGoldwateretal.(2007).D'abord,wedefinesometerminology.Weusetheterm“token”,designatedbyxi,todescribeanyin-divisibleiteminourvocabularythathasnoothervocabularyitemasitsconstituentpart.Weusetheterm“chunk”,designatedbykiorxji,todescribeasequenceofoneormoretokensthatrepresentsaportionofthefullstringX,containingtheunitto-kensxithroughxj:xji=[xi,xi+1;…;xj].Wealsorefertothe“tokenvocabulary”,whichisthesubsetofthevocabularycontainingonlytokens,andtothe“chunkvocabulary”,whichsimilarlycontainsallchunks.NotethatwecanfactorizetheprobabilityofanysequenceofchunksKusingthechainrule,inpre-ciselythesamewayassequencesoftokens:p(K)=p(k1,k2,…,k|K|)=|K|Yt=1p(kt|k1,k2,…,kt−1).(4)Wecanfactorizetheoverallprobabilityofato-kenlistXintermsofitschunksbyusingthechainrule,andmarginalizingoverallsegmentations.ForanyparticulartokenlistX,wedefineasetofvalid
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segmentationsS(X),suchthatforeverysequences∈S(X),X=[xs1−1s0;xs2−1s1;…;xs|s|s|s|−1].Thefactorizationis:p(X)=XSp(X,S)=XSp(X|S)p(S)=XS∈S(X)p(S)=XS∈S(X)|S|Yt=1p(xst−1st−1|xs1−1s0,xs2−1s1,…,xst−1−1st−2).(5)Notethat,bydefinition,thereexistsauniqueseg-mentationofXsuchthatx1,x2,…arealltokens,inwhichcase|S|=|X|.WhenonlythatoneuniquesegmentationisallowedperX,Scontainsonlythatoneelement,sosummationdropsout,andthereforeforstandardcharacter-levelandword-levelmodels,Eq.(5)reducestoEq.(4),asdesired.However,formodelsthatlicensemultiplesegmentationsperX,computingthismarginalizationdirectlyisgener-allyintractable.Forexample,considersegmentingasentenceusingavocabularycontainingallwordsandall2-wordexpressions.ThesizeofSwouldgrowexponentiallywiththenumberofwordsinX,meaningwewouldhavetomarginalizeovertril-lionsofuniquesegmentationsforevenmodestly-sizedsentences.3.2LatticeLanguageModelsToavoidthis,itispossibletore-organizethecom-putationsinalattice,whichallowsustodramati-callyreducethenumberofcomputationsrequired(DupontandRosenfeld,1997;Neubigetal.,2010).AllsegmentationsofXcanbeexpressedastheedgesofpathsthroughalatticeovertoken-levelpre-fixesofX:X<1,x<2,...,X.Theinfimumistheemptyprefixx<1;thesupremumisX;anedgefromprefixx
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4.2.2ModelingStrategyForourpolysemyexperiments,theunderlyinglat-ticesaremulti-lattices:latticeswhicharealsomulti-graphs,andcanhaveanynumberofedgesbetweenanygivenpairofnodes(Fig.2,d).Latticessetupinthismannerallowustoincorporatemultipleem-beddingsforeachword.Withinasinglesentence,anypairofnodescorrespondstothestartandendofaparticularsubsequenceofthefullsentence,andisthusassociatedwithaspecifictoken.Eachedgebetweenthemisauniqueembeddingforthatto-ken.Whilemanystrategiesforchoosingthenum-berofembeddingsexistintheliterature(Neelakan-tanetal.,2014),inthiswork,wechooseanumberofembeddingsEandassignthatmanyembeddingstoeachword.Thisensuresthatthemaximumin-degreeofanynodeinthelatticeD,isnogreaterthanE,givingusthetimeboundO(E|X|).Inthiswork,wedonotexploremodelsthatin-cludebothchunkvocabulariesandmultipleembed-dings.However,combiningthesetwotechniques,aswellasexploringother,morecomplexlatticestruc-tures,isaninterestingavenueforfuturework.5Experiments5.1DataWeperformexperimentsontwolanguages:EnglishandChinese,whichprovideaninterestingcontrastinlinguisticfeatures.4InEnglish,themostcommonbenchmarkforlanguagemodelingrecentlyisthePennTree-bank,specificallytheversionpreprocessedbyTom´aˇsMikolov(2010).Cependant,thiscorpusislim-itedbybeingrelativelysmall,onlycontainingap-proximately45,000sentences,whichwefoundtobeinsufficienttoeffectivelytrainlatticelanguagemod-els.5Thus,weinsteadusedtheBillionWordCorpus(Chelbaetal.,2014).PastexperimentsontheBWCtypicallymodeledeverywordwithoutrestrictingthevocabulary,whichresultsinanumberofchallengesregardingthemodelingofopenvocabulariesthatareorthogonaltothiswork.Thus,wecreateapre-4Codetoreproducedatasetsandexperimentsisavailableat:http://github.com/jbuckman/neural-lattice-language-models5Experimentsusingmulti-wordunitsresultedinoverfitting,regardlessofnormalizationandhyperparametersettings.processedversionofthedatainthesamemannerasMikolov,lowercasingthewords,replacingnum-berswith
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Figure3:Segmentationofthreesentencesrandomlysampledfromthetestcorpus,usingL=2.Greennumbersshowprobabilityassignedtotokensizes.Forexample,thefirstthreewordsinthefirstsentencehavea59%and41%chanceofbeing“pleaseletme”or“pleaseletme”respectively.Boxesaroundwordsshowgreedysegmentation.Table4:Comparisonofrandomly-selectedcontextsofseveralwordsselectedfromthevocabularyoftheBillionWordCorpus,inwhichthemodelpreferredoneembeddingovertheother.rock1rock2…atthe
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textinwhichtheyappear.Insomecases,likeprofileandedition,oneofthetwoembeddingssimplycap-turesanidiosyncrasyofthetrainingdata.Additionally,forsomewords,suchasrodhaminTable4,thesystemalwaysprefersoneembedding.Thisispromising,becauseitmeansthatinfutureworkitmaybepossibletofurtherimproveaccu-racyandtrainingefficiencybyassigningmoreem-beddingstopolysemouswords,insteadofassigningthesamenumberofembeddingstoallwords.6RelatedWorkPastworkthatutilizedlatticesinneuralmodelsfornaturallanguageprocessingcentersaroundus-ingtheselatticesintheencoderportionofmachinetranslation.Suetal.(2016)utilizedavariationoftheGatedRecurrentUnit(GRU)thatoperatedoverlattices,andpreprocessedlatticesoverChi-nesecharactersthatallowedittoeffectivelyencodemultiplesegmentations.Additionally,Sperberetal.(2017)proposedavariationoftheTreeLSTMwiththegoalofcreatinganencoderoverspeechlatticesinspeech-to-text.Ourworktackleslanguagemod-elingratherthanencoding,andthusaddressestheissueofmarginalizationoverthelattice.AnotherrecentworkwhichmarginalizedovermultiplepathsthroughasentenceisLingetal.(2016).Theauthorstackletheproblemofcodegen-eration,wheresomecomponentsofthecodecanbecopiedfromtheinput,viaaneuralnetwork.Ourworkexpandsonthisbyhandlingmulti-wordtokensasinputtotheneuralnetwork,ratherthanpassinginonetokenatatime.Neurallatticelanguagemodelsimproveaccuracybyhelpingthegradientflowoversmallerpaths,pre-ventingvanishinggradients.Manyhierarchicalneu-rallanguagemodelshavebeenproposedwithasim-ilarobjective(Koutniketal.,2014;Zhouetal.,2017).Ourworkisdistinguishedfromthesebytheuseoflatenttoken-levelsegmentationsthatcap-turemeaningdirectly,ratherthansimplybeinghigh-levelmechanismstoencouragegradientflow.Chanetal.(2017)proposeamodelforpredict-ingcharactersatmultiplegranularitiesinthede-codersegmentofamachinetranslationsystem.Ourworkexpandsontheirsbyconsideringtheentirelat-ticeatonce,ratherthanconsideringaonlyasin-glepaththroughthelatticeviaancestralsampling.Thisallowsustotrainend-to-endwithoutthemodelcollapsingtoalocalminimum,withnoexplorationbonusneeded.Additionally,weproposeamorebroadclassofmodels,includingthoseincorporat-ingpolysemouswords,andapplyourmodeltothetaskofword-levellanguagemodeling,ratherthancharacter-leveltranscription.Concurrentlytothiswork,vanMerri¨enboeretal.(2017)haveproposedaneurallanguagemodelthatcansimilarlyhandlemultiplescales.Ourworkisdifferentiatedinthatitismoregeneral:utilizinganopenmulti-tokenvocabulary,proposingmultipletechniquesforhiddenstatecalculation,andhandlingpolysemyusingmulti-embeddinglattices.7FutureWorkInthefuture,wewouldliketoexperimentwithuti-lizingneurallatticelanguagemodelsinextrinsicevaluation,suchasmachinetranslationandspeechrecognition.Additionally,inthecurrentmodel,thenon-compositionalembeddingsmustbeselectedapriori,andmaybesuboptimal.Weareexploringtechniquestostorefixedembeddingsdynamically,sothatthenon-compositionalphrasescanbese-lectedaspartoftheend-to-endtraining.8ConclusionInthiswork,wehaveintroducedtheideaofaneurallatticelanguagemodel,whichallowsustomarginal-izeoverallsegmentationsofasentenceinanend-to-endfashion.InourexperimentsontheBillionWordCorpusandChineseGigaWordcorpus,wedemonstratedthattheneurallatticelanguagemodelbeatsanLSTM-basedbaselineatthetaskoflan-guagemodeling,bothwhenitisusedtoincorpo-ratemultiple-wordphrasesandmultiple-embeddingwords.Qualitatively,weobservedthatthelatentsegmentationsgeneratedbythemodelcorrespondwelltohumanintuitionaboutmulti-wordphrases,andthatthevaryingusageofwordswithmultipleembeddingsseemstoalsobesensible.AcknowledgementsTheauthorswouldliketothankHolgerSchwenk,KristinaToutanova,CindyRobinson,andallthere-viewersofthisworkfortheirinvaluablefeedback.
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