Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe...

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Word Embeddings Wei Xu (many slides from Greg Durrett)

Transcript of Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe...

Page 1: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

WordEmbeddings

WeiXu(many slides from Greg Durrett)

Page 2: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Administrivia

‣ Homework2duenextTuesday

‣ ChangeofOfficeHourthisweek:5:00-5:45pmThursday

‣ Reading:Eisenstein3.3.4,14.5,14.6,J+M6

Page 3: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Recall:FeedforwardNNs

V

nfeatures

dhiddenunits

dxnmatrix num_classesxdmatrix

soSmaxWf(x)

z

nonlinearity(tanh,relu,…)

g P(y

|x)

P (y|x) = softmax(Wg(V f(x)))num_classesprobs

Page 4: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Recall:BackpropagaXon

V

dhiddenunits

soSmaxWf(x)

zg P

(y|x)

P (y|x) = softmax(Wg(V f(x)))

@L@W err(root)@z

@Verr(z)

zf(x)

Page 5: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

ThisLecture

‣ Training

‣WordrepresentaXons

‣ word2vec/GloVe

‣ EvaluaXngwordembeddings

Page 6: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

TrainingTips

Page 7: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Batching

‣ BatchingdatagivesspeedupsduetomoreefficientmatrixoperaXons

‣ NeedtomakethecomputaXongraphprocessabatchatthesameXme

probs = ffnn.forward(input) # [batch_size, num_classes]loss = torch.sum(torch.neg(torch.log(probs)).dot(gold_label))

...

‣ Batchsizesfrom1-100oSenworkwell

def make_update(input, gold_label)

# input is [batch_size, num_feats] # gold_label is [batch_size, num_classes]

...

Page 8: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

TrainingBasics‣ Basicformula:computegradientsonbatch,usefirst-orderopXmizaXonmethod(SGD,Adagrad,etc.)

‣ HowtoiniXalize?Howtoregularize?WhatopXmizertouse?

‣ Thislecture:somepracXcaltricks.TakedeeplearningoropXmizaXoncoursestounderstandthisfurther

Page 9: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

HowdoesiniXalizaXonaffectlearning?

V

nfeatures

dhiddenunits

dxnmatrix mxdmatrix

soSmaxWf(x)

z

nonlinearity(tanh,relu,…)

g P(y

|x)

P (y|x) = softmax(Wg(V f(x)))

‣ HowdoweiniXalizeVandW?Whatconsequencesdoesthishave?

‣ Nonconvexproblem,soiniXalizaXonmaders!

Page 10: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

‣ Nonlinearmodel…howdoesthisaffectthings?

‣ Tanh:IfcellacXvaXonsaretoolargeinabsolutevalue,gradientsaresmall

‣ ReLU:largerdynamicrange(allposiXvenumbers),butcanproducebigvalues,andcanbreakdownifeverythingistoonegaXve(“dead”ReLU)

HowdoesiniXalizaXonaffectlearning?

Krizhevskyetal.(2012)

http://cs231n.github.io/neural-networks-1/
Page 11: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

IniXalizaXon1)Can’tusezeroesforparameterstoproducehiddenlayers:allvaluesinthathiddenlayerarealways0andhavegradientsof0,neverchange

‣ Candorandomuniform/normaliniXalizaXonwithappropriatescale

U

"�r

6

fan-in + fan-out,+

r6

fan-in + fan-out

#‣ XavieriniXalizer:

‣Wantvarianceofinputsandgradientsforeachlayertobethesame

‣ BatchnormalizaXon(IoffeandSzegedy,2015):periodicallyshiS+rescaleeachlayertohavemean0andvariance1overabatch(usefulifnetisdeep)

2)IniXalizetoolargeandcellsaresaturated

Page 12: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Dropout‣ ProbabilisXcallyzerooutpartsofthenetworkduringtrainingtopreventoverfimng,usewholenetworkattestXme

Srivastavaetal.(2014)

‣ Similartobenefitsofensembling:networkneedstoberobusttomissingsignals,soithasredundancy

‣ FormofstochasXcregularizaXon

‣ OnelineinPytorch/Tensorflow

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�13

OpImizer‣ Adam(KingmaandBa,ICLR2015):verywidelyused.AdapIvestepsize+momentum

‣Wilsonetal.NIPS2017:adapIvemethodscanactuallyperformbadlyattestIme(Adamisinpink,SGDinblack)

‣ Onemoretrick:gradientclipping(setamaxvalueforyourgradients)

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‣Model:feedforward,RNNs,CNNscanbedefinedinauniformframework

‣ ObjecXve:manylossfuncXonslooksimilar,justchangesthelastlayeroftheneuralnetwork

‣ Inference:definethenetwork,yourlibraryofchoicetakescareofit(mostly…)

‣ Training:lotsofchoicesforopXmizaXon/hyperparameters

FourElementsofNNs

Page 15: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

WordRepresentaXons

Page 16: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

WordRepresentaXons

‣ ConXnuousmodel<->expectsconXnuoussemanXcsfrominput

‣ “Youshallknowawordbythecompanyitkeeps”Firth(1957)

‣ NeuralnetworksworkverywellatconXnuousdata,butwordsarediscrete

slidecredit:DanKlein

Page 17: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

DiscreteWordRepresentaXons

good

enjoyablegreat

0

fishcat

‣ Brownclusters:hierarchicalagglomeraXvehardclustering(eachwordhasonecluster,notsomeposteriordistribuXonlikeinmixturemodels)

‣Maximize

‣ UsefulfeaturesfortaskslikeNER,notsuitableforNNs

dog…

isgo

0

0 1 1

11

1

1

0

0

P (wi|wi�1) = P (ci|ci�1)P (wi|ci)

Brownetal.(1992)

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WordEmbeddings

Bothaetal.(2017)

…

Fedraisesinterestratesinorderto…

f(x)?? emb(raises)

‣Wordembeddingsforeachwordforminput

emb(interest)

emb(rates)

previousword

currword

nextword

otherwords,feats,etc.

‣ Part-of-speechtaggingwithFFNNs

‣WhatproperXesshouldthesevectorshave?

Page 19: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

SenXmentAnalysis‣ DeepAveragingNetworks:feedforwardneuralnetworkonaverageofwordembeddingsfrominput

Iyyeretal.(2015)

Page 20: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

goodenjoyable

bad

dog

great

is

‣Wantavectorspacewheresimilarwordshavesimilarembeddings

themoviewasgreat

themoviewasgood

~~

WordEmbeddings

‣ Goal:comeupwithawaytoproducetheseembeddings

‣ Foreachword,want“medium”dimensionalvector(50-300dims)represenXngit.

Page 21: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

word2vec/GloVe

Page 22: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

NeuralProbabilisXcLanguageModel

�22 Bengioetal.(2003)

Page 23: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

word2vec:ConXnuousBag-of-Words‣ Predictwordfromcontext

thedogbittheman

‣ Parameters:dx|V|(oned-lengthcontextvectorpervocword),|V|xdoutputparameters(W)

dog

the

+

sized

soSmax

goldlabel=bit,nomanuallabelingrequired!

Mikolovetal.(2013)

d-dimensional wordembeddings

P (w|w�1, w+1) = softmax (W (c(w�1) + c(w+1)))

size|V|xd

W

size|V|

Page 24: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

word2vec:Skip-Gram

thedogbittheman‣ Predictonewordofcontextfromword

bit

soSmax

goldlabel=dog

‣ Parameters:dx|V|vectors,|V|xdoutputparameters(W)(alsousableasvectors!)

‣ Anothertrainingexample:bit->the

P (w0|w) = softmax(We(w))

Mikolovetal.(2013)

W

d-dimensional wordembeddings

size|V|xd

Page 25: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

HierarchicalSoSmax

‣Matmul+soSmaxover|V|isveryslowtocomputeforCBOWandSG

‣ HierarchicalsoSmax:

P (w|w�1, w+1) = softmax (W (c(w�1) + c(w+1)))

‣ StandardsoSmax: O(|V|)dotproductsofsized-pertraininginstancepercontextword

O(log(|V|))dotproductsofsized,

…

…

thea

‣ Huffmanencodevocabulary,usebinaryclassifierstodecidewhichbranchtotake

|V|xdparametersMikolovetal.(2013)

P (w0|w) = softmax(We(w))

‣ log(|V|)binarydecisions

http://building-babylon.net/2017/08/01/hierarchical-softmax/

http://building-babylon.net/2017/08/01/hierarchical-softmax/
Page 26: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Skip-GramwithNegaXveSampling

‣ dx|V|vectors,dx|V|contextvectors(same#ofparamsasbefore)

Mikolovetal.(2013)

(bit,the)=>+1(bit,cat)=>-1

(bit,a)=>-1(bit,fish)=>-1

‣ Take(word,context)pairsandclassifythemas“real”ornot.CreaterandomnegaXveexamplesbysamplingfromunigramdistribuXon

wordsinsimilarcontextsselectforsimilarcvectors

P (y = 1|w, c) = ew·c

ew·c + 1

‣ ObjecXve= logP (y = 1|w, c)� 1

k

nX

i=1

logP (y = 0|wi, c)sampled

thedogbittheman

logP (y = 1|w, c)� 1

k

nX

i=1

logP (y = 0|wi, c)

Page 27: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

ConnecXonswithMatrixFactorizaXon

Levyetal.(2014)

‣ Skip-grammodellooksatword-wordco-occurrencesandproducestwotypesofvectors

wordpaircounts

|V|

|V| |V|

d

d

|V|

contextvecsword vecs

‣ LooksalmostlikeamatrixfactorizaXon…canweinterpretitthisway?

Page 28: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Skip-GramasMatrixFactorizaXon

Levyetal.(2014)

|V|

|V|Mij = PMI(wi, cj)� log k

PMI(wi, cj) =P (wi, cj)

P (wi)P (cj)=

count(wi,cj)D

count(wi)D

count(cj)D

‣ IfwesamplenegaXveexamplesfromtheuniformdistribuXonoverwords

numnegaXvesamples

‣ …andit’saweightedfactorizaXonproblem(weightedbywordfreq)

Skip-gramobjecXveexactlycorrespondstofactoringthismatrix:

Page 29: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

GloVe(GlobalVectors)

Penningtonetal.(2014)

X

i,j

f(count(wi, cj))�w>

i cj + ai + bj � log count(wi, cj))�2‣ Loss=

‣ Alsooperatesoncountsmatrix,weighted regressiononthelogco-occurrencematrix

‣ Constantinthedatasetsize(justneedcounts),quadraXcinvocsize

‣ Byfarthemostcommonwordvectorsusedtoday(10000+citaXons)

wordpaircounts

|V|

|V|

Page 30: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Preview:Context-dependentEmbeddings

Petersetal.(2018)

‣ Trainaneurallanguagemodeltopredictthenextwordgivenpreviouswordsinthesentence,useitsinternalrepresentaXonsaswordvectors

‣ Context-sensiCvewordembeddings:dependonrestofthesentence

‣ HugeimprovementsacrossnearlyallNLPtasksoverword2vec&GloVe

they hit the ballsthey dance at balls

‣ Howtohandledifferentwordsenses?Onevectorforballs

Page 31: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

EvaluaXon

Page 32: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

EvaluaXngWordEmbeddings

‣WhatproperXesoflanguageshouldwordembeddingscapture?

goodenjoyable

bad

dog

great

is

cat

wolf

Cger

was

‣ Similarity:similarwordsareclosetoeachother

‣ Analogy:

ParisistoFranceasTokyoisto???

goodistobestassmartisto???

Page 33: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Similarity

Levyetal.(2015)

‣ SVD=singularvaluedecomposiXononPMImatrix

‣ GloVedoesnotappeartobethebestwhenexperimentsarecarefullycontrolled,butitdependsonhyperparameters+thesedisXncXonsdon’tmaderinpracXce

Page 34: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

HypernymyDetecXon

‣ Hypernyms:detecXveisaperson,dogisaanimal

‣ word2vec(SGNS)worksbarelybederthanrandomguessinghere

‣ DowordvectorsencodetheserelaXonships?

Changetal.(2017)

Page 35: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Analogies

queen

king

woman

man

(king-man)+woman=queen

‣Whywouldthisbe?

‣ woman-mancapturesthedifferenceinthecontextsthattheseoccurin

king+(woman-man)=queen

‣ Dominantchange:more“he”withmanand“she”withwoman—similartodifferencebetweenkingandqueen

Page 36: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Analogies

Levyetal.(2015)

‣ Thesemethodscanperformwellonanalogiesontwodifferentdatasetsusingtwodifferentmethods

cos(b, a2 � a1 + b1)Maximizingforb:Add= Mul=cos(b2, a2) cos(b2, b1)

cos(b2, a1) + ✏

Page 37: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

UsingSemanXcKnowledge

Faruquietal.(2015)

‣ StructurederivedfromaresourcelikeWordNet

Originalvectorforfalse

Adaptedvectorforfalse

‣ Doesn’thelpmostproblems

Page 38: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

UsingWordEmbeddings

‣ Approach1:learnembeddingsasparametersfromyourdata

‣ Approach2:iniXalizeusingGloVe/word2vec/ELMo,keepfixed

‣ Approach3:iniXalizeusingGloVe,fine-tune‣ Fasterbecausenoneedtoupdatetheseparameters

‣Worksbestforsometasks,notusedforELMo,oSenusedforBERT

‣ OSenworkspredywell

Page 39: Word Embeddings - Wei Xu · ‣ Huge improvements across nearly all NLP tasks over word2vec & GloVe they dance at balls they hit the balls ‣ How to handle different word senses?

Takeaways

‣ Lotstotunewithneuralnetworks

‣Wordvectors:learningword->contextmappingshasgivenwaytomatrixfactorizaXonapproaches(constantindatasetsize)

‣ Training:opXmizer,iniXalizer,regularizaXon(dropout),…

‣ Hyperparameters:dimensionalityofwordembeddings,layers,…

‣ NextXme:RNNsandCNNs

‣ LotsofpretrainedembeddingsworkwellinpracXce,theycapturesomedesirableproperXes

‣ Evenbeder:context-sensiXvewordembeddings(ELMo/BERT)


Tutorial: word2vec Yang-de Chen yongde0108@gmail.com.

Tutorial: word2vec Yang-de Chen [email protected].

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¡¡Balls, balls, Balls!!

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