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RNN Review & Hierarchical Attention Networks SHANG GAO
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  • RNN Review&HierarchicalAttentionNetworksSHANGGAO

  • Overview◦ ReviewofRecurrentNeuralNetworks◦ AdvancedRNNArchitectures

    ◦ Long-Short-Term-Memory◦ GatedRecurrentUnits

    ◦ RNNsforNaturalLanguageProcessing◦ WordEmbeddings◦ NLPApplications

    ◦ AttentionMechanisms◦ HierarchicalAttentionNetworks

  • FeedforwardNeuralNetworksInaregularfeedforwardnetwork,eachneurontakesininputsfromtheneuronsinthepreviouslayer,andthenpassitsoutputtotheneuronsinthenextlayer

    Theneuronsattheendmakeaclassificationbasedonlyonthedatafromthecurrentinput

  • RecurrentNeuralNetworksInarecurrentneuralnetwork,eachneurontakesindatafromthepreviouslayerANDitsownoutputfromtheprevioustimestep

    TheneuronsattheendmakeaclassificationdecisionbasedonNOTONLYtheinputatthecurrenttimestepBUTALSOtheinputfromalltimestepsbeforeit

    Recurrentneuralnetworkscanthuscapturepatternsovertime(e.g.weather,stockmarketdata,speechaudio,naturallanguage)

  • RecurrentNeuralNetworksIntheexamplebelow,theneuronatthefirsttimesteptakesinaninputandgeneratesanoutput

    TheneuronatthesecondtimesteptakesinaninputANDALSO theoutputfromthefirsttimesteptomakeitsdecision

    Theneuronatthethirdtimesteptakesinaninputandalsotheoutputfromthesecondtimestep(whichaccountedfordatafromthefirsttimestep),soitsoutputisaffectedbydatafromboththefirstandsecondtimestep

  • RecurrentNeuralNetworksTraditional Neuron: output=sigmoid(weights*input+bias)

    Recurrent Neuron:output=sigmoid(weights1*input+weights2*previous_output + bias)oroutput=sigmoid(weights*concat(input,previous_output)+bias)

  • Toy RNN ExampleAddingBinary

    Ateachtimestep,RNNtakesintwovaluesrepresentingbinaryinput

    Ateachtimestep,RNNoutputsthesumofthetwobinaryvaluestakingintoaccountanycarryoverfromprevioustimestep

  • ProblemswithBasicRNNsInabasicRNN,newdataiswrittenintoeachcellateverytimestep

    Datafromtimestepsveryearlyongetdilutedbecausetheyarewrittenoversomanytimes

    Intheexamplebelow,datafromthefirsttimestepisreadintotheRNN

    Ateachsubsequenttimestep,theRNNfactorsindatafromthecurrenttimestep

    BytheendoftheRNN,thedatafromthefirsttimestephasverylittleimpactontheoutputoftheRNN

  • ProblemswithBasicRNNsBasicRNNcellscan’tretaininformationacrossalargenumberoftimesteps

    Dependingontheproblem,RNNscanlosedatainasfewas3-5timesteps

    Thisiscausesproblemsontaskswhereinformationneedstoberetainedoveralongtime

    Forexample,innaturallanguageprocessing,themeaningofapronounmaydependonwhatwasstatedinaprevioussentence

  • LongShortTermMemoryLongShortTermMemorycellsareadvancedRNNcellsthataddresstheproblemoflong-termdependencies

    Insteadofalwayswritingtoeachcellateverytimestep,eachunithasaninternal‘memory’thatcanbewrittentoselectively

  • LongShortTermMemoryInputfromthecurrenttimestepiswrittentotheinternalmemorybasedonhowrelevantitistotheproblem(relevanceislearnedduringtrainingthroughbackpropagation)

    Iftheinputisn’trelevant,nodataiswrittenintothecell

    Thiswaydatacanbepreservedovermanytimestepsandberetrievedwhenitisneeded

  • LongShortTermMemoryMovementofdataintoandoutofanLSTMcelliscontrolledby“gates”

    The“forgetgate”outputsavaluebetween0(delete)and1(keep)andcontrolshowmuchoftheinternalmemorytokeepfromtheprevioustimestep

    Forexample,attheendofasentence,whena‘.’isencountered,wemaywanttoresettheinternalmemoryofthecell

  • LongShortTermMemoryThe“candidatevalue”istheprocessedinputvaluefromthecurrenttimestepthatmaybeaddedtomemory◦ Notethattanh activationisusedforthe“candidatevalue”toallowfornegativevaluestosubtractfrommemory

    The“inputgate”outputsavaluebetween0(delete)and1(keep)andcontrolshowmuchofthecandidatevalueaddtomemory

  • LongShortTermMemoryCombined,the“inputgate”and“candidatevalue”determinewhatnewdatagetswrittenintomemory

    The“forgetgate”determineshowmuchofthepreviousmemorytoretain

    ThenewmemoryoftheLSTMcellisthe“forgetgate”*thepreviousmemorystate+the“inputgate”*the“candidatevalue”fromthecurrenttimestep

  • LongShortTermMemoryTheLSTMcelldoesnotoutputthecontentsofitsmemorytothenextlayer◦ Storeddatainmemorymightnotberelevantforcurrenttimestep,e.g.,acellcanstoreapronounreferenceandonlyoutputwhenthepronounappears

    Instead,an“output”gateoutputsavaluebetween0and1thatdetermineshowmuchofthememorytooutput

    Thememorygoesthroughafinaltanh activationbeforebeingpassedtothenextlayer

  • GatedRecurrentUnitsGatedRecurrentUnitsareverysimilartoLSTMsbutusetwogatesinsteadofthree

    The“updategate”determineshowmuchofthepreviousmemorytokeep

    The“resetgate”determineshowtocombinethenewinputwiththepreviousmemory

    Theentireinternalmemoryisoutputwithoutanadditionalactivation

  • LSTMsvsGRUsGreff,etal.(2015) comparedLSTMsandGRUsandfoundtheyperformaboutthesame

    Jozefowicz,etal.(2015) generatedmorethantenthousandvariantsofRNNsanddeterminedthatdependingonthetask,somemayperformbetterthanLSTMs

    GRUstrainfasterthanLSTMsbecausetheyarelesscomplex

    Generallyspeaking,tuninghyperparameters(e.g.numberofunits,sizeofweights)willprobablyaffectperformancemorethanpickingbetweenGRUandLSTM

  • RNNsforNaturalLanguageProcessingThenaturalinputforaneuralnetworkisavectorofnumericvalues(e.g.pixeldensitiesforimagingoraudiofrequencyforspeechrecognition)

    Howdoyoufeedlanguageasinputintoaneuralnetwork?

    Themostbasicsolutionisonehotencoding◦ Alongvector(equaltothelengthofyourvocabulary)whereeachindexrepresentsonewordinthevocabulary

    ◦ Foreachword,theindexcorrespondingtothatwordissetto1,andeverythingelseissetto0

  • OneHotEncodingLSTMExampleTrainedLSTMtopredictthenextcharactergivenasequenceofcharacters

    Trainingcorpus:AllbooksinHitchhiker’sGuidetotheGalaxyseries

    One-hotencodingusedtoconverteachcharacterintoavector

    72possiblecharacters– lowercaseletters,uppercaseletters,numbers,andpunctuation

    Inputvectorisfedintoalayerof256LSTMnodes

    LSTMoutputfedintoasoftmax layerthatpredictsthefollowingcharacter

    Thecharacterwiththehighestsoftmax probabilityischosenasthenextcharacter

  • GeneratedSamples700iterations:aeae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae ae aeae ae ae ae ae

    4200iterations:thesandandthesaidthesandandthesaidthesandandthesaidthesandandthesaidthesandandthesaidthe

    36000iterations:searedtobealittlewasasmallbeachoftheshipwasasmallbeachoftheshipwasasmallbeachoftheship

    100000iterations:thesecondthestarsisthestarstothestarsinthestarsthathehadbeensotheshiphadbeensotheshiphadbeen

    290000iterations:startedtorunacomputertothecomputertotakeabitofaproblemofftheshipandthesunandtheairwasthesound

    500000iterations:"IthinktheGalaxywillbealotofthingsthatthesecondmanwhocouldnotbecontinuallyandthesoundofthestars

  • OneHotEncodingShortcomingsOne-hotencodingislackingbecauseitfailstocapturesemanticsimilaritybetweenwords,i.e.,theinherentmeaningofword

    Forexample,thewords“happy”,“joyful”,and“pleased”allhavesimilarmeanings,butunderone-hotencodingtheyarethreedistinctandunrelatedentities

    Whatifwecouldcapturethemeaningofwordswithinanumericalcontext?

  • WordEmbeddingsWordembeddingsarevectorrepresentationsofwordsthatattempttocapturesemanticmeaningEachwordisrepresentedasavectorofnumericalvaluesEachindexinthevectorrepresentssomeabstract“concept”◦ Theseconceptsareunlabeledandlearnedduringtraining

    Wordsthataresimilarwillhavesimilarvectors

    Masculinity Royality Youth Intelligence

    King 0.95 0.95 -0.1 0.6

    Queen -0.95 0.95 -0.1 0.6

    Prince 0.8 0.8 0.7 0.4

    Woman -0.95 0.01 -0.1 0.2

    Peasant 0.1 -0.95 0.1 -0.3

    Doctor 0.12 0.1 -0.2 0.95

  • Word2VecWordsthatappearinthesamecontextaremorelikelytohavethesamemeaning◦ Iamexcited toseeyoutoday!◦ Iamecstatic toseeyoutoday!

    Word2Vecisanalgorithmthatusesafunnel-shapedsinglehiddenlayerneuralnetwork(similartoautoencoder)tocreatewordembeddings

    Givenaword(inone-hotencodedformat),ittriestopredicttheneighborsofthatword(alsoinone-hotencodedformat),orviceversa

    Wordsthatappearinthesamecontextwillhavesimilarembeddings

  • Word2VecThemodelistrainedonalargecorpusoftextusingregularbackpropagation

    Foreachwordinthecorpus,predictthe5wordstotheleftandright(orviceversa)

    Oncethemodelistrained,theembeddingforaparticularwordistherowoftheweightmatrixassociatedwiththatword

    Manypretrainedvectors(e.g.Google)canbedownloadedonline

  • Word2Vecon20Newsgroups

  • BasicDeepLearningNLPPipelineGenerateWordEmbeddings◦ Pythongensim package

    FeedwordembeddingsintoLSTMorGRUlayer

    FeedoutputofLSTMorGRUlayerintosoftmax classifier

  • NLPApplicationsforRNNsLanguageModels◦ Givenaseriesofwords,predictthenextword◦ Understandtheinherentpatternsinagivenlanguage◦ Usefulforautocompletionandmachinetranslation

    SentimentAnalysis◦ Givenasentenceordocument,classifyifitispositiveornegative◦ Usefulforanalyzingthesuccessofaproductlaunchorautomatedstocktradingbasedoffnews

    Otherformstextclassification◦ Cancerpathologyreportclassification

  • AdvancedApplicationsQuestionAnswering◦ Readadocumentandthenanswerquestions◦ ManymodelsuseRNNsastheirfoundation

    AutomatedImageCaptioning◦ Givenanimage,automaticallygenerateacaption

    ◦ ManymodelsusebothCNNsandRNNs

    MachineTranslation◦ Automaticallytranslatetextfromonelanguagetoanother

    ◦ Manymodels(includingGoogleTranslate)useRNNsastheirfoundation

  • LSTM ImprovementsBi-directionalLSTMsSometimes,importantcontextforawordcomesaftertheword(especiallyimportanttranslation)◦ Isawacrane flyingacrossthesky◦ Isawacrane liftingalargeboulder

    Solution- usetwoLSTMlayers,onethatreadstheinputforwardandonethatreadstheinputbackwards,andconcatenatetheiroutputs

  • LSTM ImprovementsAttentionMechanismsSometimesonlyafewwordsinasentenceordocumentareimportantandtherestdonotcontributeasmuchmeaning◦ Forexample,whenclassifyingcancerlocationfromcancerpathologyreports,wemayonlycareaboutcertainkeywordslike“rightupperlung”or“ovarian”

    InatraditionalRNN,weusuallytaketheoutputatthelasttimestep

    Bythelasttimestep,informationfromtheimportantwordsmayhavebeendiluted,evenwithLSTMsandGRUsunits

    Howcanwecapturetheinformationatthemostimportantwords?

  • LSTM ImprovementsAttentionMechanismsNaïvesolution:topreventinformationloss,insteadofusingtheLSTMoutputatthelasttimestep,taketheLSTMoutputateverytimestepandusetheaverage

    Bettersolution:findtheimportanttimesteps,andweighttheoutputatthosetimestepsmuchhigherwhendoingtheaverage

  • LSTM ImprovementsAttentionMechanismsAnattentionmechanismcalculateshowimportanttheLSTMoutputateachtimestepis

    It’sasimplefeedforwardnetworkwithasingle(tanh)hiddenlayerandasoftmax output

    Ateachtimestep,feedtheoutputfromtheLSTM/GRUintotheattentionmechanism

  • LSTM ImprovementsAttentionMechanisms

    Oncetheattentionmechanismhasallthetimesteps,itcalculatesasoftmaxoverallthetimesteps◦ softmax alwaysaddsto1

    Thesoftmax tellsushowtoweighttheoutputateachtimestep,i.e.,howimportanteachtimestepis

    Multiplytheoutputateachtimestepwithitscorrespondingsoftmax weightandaddtocreateaweightedaverage

  • LSTM ImprovementsAttentionMechanisms

    Attentionmechanismscantakeintoaccount“context”todeterminewhat’simportant

    Rememberdotproductisameasureofsimilarity– twovectorsthataresimilarwillhavelargerdotproduct

    Innormalsoftmax,dotproductinputwithrandomlyinitializedweightsbeforeapplyingsoftmax function

  • LSTM ImprovementsAttentionMechanisms

    Instead,wecandotproductwithavectorthatrepresents“context”tofindwordsmostsimilar/relevanttothatcontext:◦ Forquestionanswering,canrepresentaquestionbeingasked

    ◦ Formachinetranslation,canrepresentthepreviousword

    ◦ Forclassification,canbeinitializedrandomlyandlearnedduringtraining

  • LSTM ImprovementsAttentionMechanisms

    Withattention,youcanvisualizehowimportanteachtimestepisforaparticulartask

  • LSTM ImprovementsAttentionMechanisms

    Withattention,youcanvisualizehowimportanteachtimestepisforaparticulartask

  • CNNsforTextClassificationStartwithWordEmbeddings◦ Ifyouhave10words,andyourembeddingsizeis300,you’llhavea10x300matrix

    3ParallelConvolutionLayers◦ Takeinwordembeddings◦ Slidingwindowthatprocesses3,4,and5wordsatatime(1Dconv)

    ◦ Filtersizesare3x300x100,4x300x100,and5x300x100(width,in-channels,out-channels)

    ◦ Eachconvlayeroutputs10x100matrix

  • CNNsforTextClassificationMaxpool andConcatenate◦ Foreachfilterchannel,maxpoolacrosstheentirewidthofsentence

    ◦ Thisislikepickingthe‘mostimportant’wordinthesentenceforeachchannel

    ◦ Alsoensureseverysentence,nomatterhowlong,isrepresentedbysamelengthvector

    ◦ Foreachofthethree10x100matrices,returns1x100matrix

    ◦ Concatenatethethree1x100matricesintoa1x300matrix

    DenseandSoftmax

  • HierarchicalAttentionNetworks

  • ProblemOverviewNationalCancerInstitutehasaskedOakRidgeNationalLabtodevelopaprogramthatcanautomaticallyclassifycancerpathologyreports

    Pathologyreportsarewhatdoctorswriteupwhentheydiagnosecancer,andNCIusesthemtocalculatenationalstatisticsandtrackhealthtrends

    Challenges:◦ Differentdoctorsusedifferentterminologytolabelthesametypesofcancer◦ Somediagnosesmayreferenceothertypesofcancerorotherorgansthatarenottheactualcancerbeingdiagnosed

    ◦ Typos

    Task:givenapathologyreport,teachaprogramtofindthetypeofcancer,locationofcancer,histologicalgrade,etc

  • ApproachTheperformanceofvariousdifferentclassifiersweretested:◦ Traditionalmachinelearningclassifiers:NaiveBayes,LogisticRegression,SupportVectorMachines,RandomForests,andXG-Boost

    ◦ Traditionalmachinelearningclassifiersrequiremanuallydefinedfeatures,suchn-gramsandtf-idf

    ◦ Deeplearningmethods:recurrentneuralnetworks,convolutionalneuralnetworks,andhierarchicalattentionnetworks

    ◦ Givenenoughdata,deeplearningmethodscanlearntheirownfeatures,suchaswhichwordsorphrasesareimportant

    TheHierarchicalAttentionNetworkisarelativelynewdeeplearningmodelthatcameoutlastyearandisoneofthetopperformers

  • HANArchitectureTheHierarchicalAttentionNetwork(HAN)isadeeplearningmodelfordocumentclassification

    BuiltfrombidirectionalRNNscomposedofGRUs/LSTMswithattentionmechanisms

    Composedof“hierarchies”wheretheoutputsofthelowerhierarchiesbecometheinputstotheupperhierarchies

  • HANArchitectureBeforefeedingadocumentintotheHAN,wefirstbreakitdownintosentences(orinourcase,lines)

    Thewordhierarchyisresponsibleforcreatingsentenceembeddings◦ Thishierarchyreadsinonefullsentenceatime,intheformofwordembeddings

    ◦ Theattentionmechanismselectsthemostimportantwords

    ◦ Theoutputisasentenceembeddingthatcapturesthesemanticcontentofthesentencebasedonthemostimportantwords

  • HANArchitectureThesentencehierarchyisresponsibleforcreatingthefinaldocumentembedding◦ Identicalstructurewiththewordhierarchy◦ Readsinthesentenceembeddingsoutputfromthewordhierarchy

    ◦ Theattentionmechanismselectsthemostimportantsentence

    ◦ Theoutputisadocumentembeddingrepresentingthemeaningoftheentiredocument

    Thefinaldocumentembeddingisusedforclassification

  • ExperimentalSetup945cancerpathologyreports,allcasesofbreastandlungcancer

    10– foldcrossvalidationused,30epochsperfold

    Hyperparameteroptimizationappliedonmodelstofindoptimalparameters

    Twomaintasks– primarysiteclassificationandhistologicalgradeclassification◦ Unevenclassdistribution,somewithonly~10occurrencesindataset◦ F-scoreusedforperformancemetric◦ MicroF-scoreisweightedF-scoreaveragebasedonclasssize◦ MacroF-scoreisunweightedF-scoreaverageacrossallclasses

  • HAN PerformancePrimarySite12possiblecancersubsitelocations◦ 5lungsubsites◦ 7breastsubsites

    DeeplearningmethodsoutperformedalltraditionalMLmethodsexceptforXGBoost

    HANhadbestperformance,pretrainingimprovedperformanceevenfurther

    TraditionalMachineLearningClassifiers

    Classifier PrimarySiteMicroF-Score

    PrimarySiteMacroF-Score

    NaiveBayes .554(.521,.586)

    .161(.152,.170)

    LogisticRegression .621(.589,.652)

    .222(.207,.237)

    SupportVectorMachine(C=1,gamma=1)

    .616(.585,.646)

    .220(.205,.234)

    RandomForest(numtrees=100)

    .628(.597,.661)

    .258(.236,.283)

    XGBoost(maxdepth=5,nestimators=300)

    .709(.681,.738)

    .441(.404,.474)

    DeepLearningClassifiers

    RecurrentNeuralNetwork(withattentionmechanism)

    .694(.666,.722)

    .468(.432,.502)

    ConvolutionalNeuralNetwork .712(.680,.736)

    .398(.359,.434)

    HierarchicalAttentionNetwork(nopretraining)

    .784(.759,.810)

    .566(.525,.607)

    HierarchicalAttentionNetwork(withpretraining)

    .800(.776,.825)

    .594(.553,.636)

  • HAN PerformanceHistologicalGrade4possiblehistologicalgrades◦ 1-4,indicatinghowabnormaltumorcellsandtumortissueslookunderamicroscopewith4beingmostabnormal

    ◦ Indicateshowquicklyatumorislikelytogrowandspread

    OtherthanRNNs,deeplearningmodelsgenerallyoutperformtraditionalMLmodels

    HANhadbestperformance,butpretrainingdidnothelpperformance

    TraditionalMachineLearningClassifiers

    Classifier HistologicalGradeMicroF-Score

    HistologicalGradeMacroF-Score

    NaiveBayes .481(.442,.519)

    .264(.244,.283)

    LogisticRegression .540(.499,.576)

    .340(.309,.371)

    SupportVectorMachine(C=1,gamma=1)

    .520(.482,.558)

    .330(.301,.357)

    RandomForest(numtrees=100)

    .597(.558,.636)

    .412(.364,.476)

    XGBoost(maxdepth=5,nestimators=300)

    .673(.634,.709)

    .593(.516,.662)

    DeepLearningClassifiers

    RecurrentNeuralNetwork(withattentionmechanism)

    .580(.541,.617)

    .474(.416,.536)

    ConvolutionalNeuralNetwork .716(.681,.750)

    .521(.493,.548)

    HierarchicalAttentionNetwork(nopretraining)

    .916(.895,.936)

    .841(.778,.895)

    HierarchicalAttentionNetwork(withpretraining)

    .904(.881,.927)

    .822(.744,.883)

  • TFIDFDocumentEmbeddings

    TFIDF-weightedWord2Vecembeddingsreducedto2dimensionsviaPCAfor(A.)primarysitetrainreports,(B.)histologicalgradetrainreports,(C.)primarysitetestreports,and(D.)histologicalgradetrainreports.

  • TFIDFDocumentEmbeddings

    HANdocumentembeddingsreducedto2dimensionsviaPCAfor(A.)primarysitetrainreports,(B.)histologicalgradetrainreports,(C.)primarysitetestreports,and(D.)histologicalgradetrainreports.

  • PretrainingWehaveaccesstomoreunlabeleddatathanlabeleddata(approximately1500unlabeled,1000labeled)

    Toutilizedunlabeleddata,wetrainedourHANtocreatedocumentembeddingsthatmatchedthecorrespondingTF-IDFweightedwordembeddingsforthatdocument

    HANtrainingandvalidationaccuracywithandwithoutpretrainingfor(A.)primarysitetaskand(B.)histologicalgradetask

  • HANDocumentAnnotations

  • MostImportantWordsperTaskWecanalsousetheHAN’sattentionweightstofindthewordsthatcontributemosttowardstheclassificationtaskathand:

    PrimarySite HistologicalGrademainstemadenocalullowerbreast

    carinacusauppermiddlerul

    buttocktemporalupperretrosputum

    poorlyg2highiiidlr

    Undifferentiatedg3iiig1

    moderatelyintermediatewellarising2

  • ScalingRelativetoothermodels,HANisveryslowtotrain◦ OnCPU,HANtakesapproximately4hourstogothrough30epochs◦ Incomparison,CNNtakesaround40minutestogothrough30epochs,andtraditionalmachinelearningclassifierstakelessthanaminute

    ◦ TheHANisslowduetoitscomplexarchitectureanduseofRNNs,sogradientsareveryexpensivetocompute

    WearecurrentworkingtoscaletheHANtorunonmultipleGPUs◦ OnTensorflow,RNNsonGPUrunslowerthanonCPU◦ WeareconsideringexploringaPyTorch implementationtogetaroundthisproblem

    WehavesuccessfullydevelopedadistributedCPU-onlyHANthatrunsonTITANusingMPI,with4xspeedupon8nodes

  • AttentionisAllYouNeedNewpaperthatcameoutJune2017fromGoogleBrain,inwhichtheyshowedtheycouldgetcompetitiveresultsinmachinetranslationwithonlyattentionmechanismsandnoRNNs

    WeappliedthesamearchitecturetoreplacetheRNNsinourHAN

    Becauseattentionmechanismsarejustmatrixmultiplications,itrunsabout10xfasterthantheHANwithRNNs

    ThisnewmodelperformsalmostaswellastheHANwithRNNs– 0.77micro-Fonprimarysite(comparedto0.78inoriginalHAN),and0.86micro-Fonhistologicalgrade(comparedto0.91inoriginalHAN)

    BecausenoRNNsareutilized,thismodelismucheasiertoscaleontheGPU

  • OtherFutureWorkMultitaskLearning◦ Predicthistologicalgrade,primarysite,andothertaskssimultaneouslywithinthesamemodel◦ Hopefullyboosttheperformanceofalltasksbysharinginformationacrosstasks

    Semi-SupervisedLearning◦ Utilizeunlabeleddataduringtrainingratherthaninpretrainingwiththegoalofimprovingclassificationperformance

    ◦ Thistaskischallengingbecauseinmostsemi-supervisedtasks,weknowallthelabelswithinthedataset.Inourcase,weonlyhaveasubsetofthelabels.

  • Questions?