Answer with content missing: (formulas in selection): Pseudo-perplexity is perplexity where conditional joint probability is approximated.
ABSTRACTIVE
The goal of an language model is to assign meaningful probabilities to a sequence of words. Given a set of tokens $\mathbf {X}=(x_1,....,x_T)$, where $T$ is the length of a sequence, our task is to estimate the joint conditional probability $P(\mathbf {X})$ which is were $(x_{1}, \ldots , x_{i-1})$ is the context. An Intrinsic evaluation of the performance of Language Models is perplexity (PPL) which is defined as the inverse probability of the set of the tokens and taking the $T^{th}$ root were $T$ is the number of tokens BERT's bi-directional context poses a problem for us to calculate an auto-regressive joint probability. A simple fix could be that we mask all the tokens $\mathbf {x}_{>i}$ and we calculate the conditional factors as we do for an unidirectional model. By doing so though, we loose upon the advantage of bi-directional context the BERT model enables. We propose an approximation of the joint probability as, This type of approximations has been previously explored with Bi-directional RNN LM's BIBREF9 but not for deep transformer models. We therefore, define a pseudo-perplexity score from the above approximated joint probability.
2003.11562
Introduction </s> Language Ġmodeling Ġis Ġa Ġprob abil istic Ġdescription Ġof Ġlanguage Ġphenomenon . ĠIt Ġprovides Ġessential Ġcontext Ġto Ġdistinguish Ġwords Ġwhich Ġsound Ġsimilar Ġand Ġtherefore Ġhas Ġone Ġof Ġthe Ġmost Ġuseful Ġapplications Ġin ĠNatural ĠLanguage ĠProcessing Ġ( N LP ) Ġespecially Ġin Ġdownstream ing Ġtasks Ġlike ĠAutomatic ĠSpeech ĠRecogn ition Ġ( AS R ). ĠRec urrent ĠNeural ĠNetworks Ġ( R NN ) Ġespecially ĠLong ĠShort ĠTerm ĠMemory Ġ( L ST M ) Ġnetworks ĠB IB REF 0 Ġhave Ġbeen Ġthe Ġtypical Ġsolution Ġto Ġlanguage Ġmodeling Ġwhich Ġdo Ġachieve Ġstrong Ġresults . ĠIn Ġspite Ġof Ġthese Ġresults , Ġtheir Ġfundamental Ġsequential Ġcomputation Ġconstraint Ġhas Ġrestricted Ġtheir Ġuse Ġin Ġthe Ġmodeling Ġof Ġlong - term Ġdependencies Ġin Ġsequential Ġdata . ĠTo Ġaddress Ġthese Ġissues ĠTrans former Ġarchitecture Ġwas Ġintroduced . ĠTransformers Ġrelies Ġcompletely Ġon Ġan Ġattention Ġmechanism Ġto Ġform Ġglobal Ġdependencies Ġbetween Ġinput Ġand Ġoutput . ĠIt Ġalso Ġoffers Ġmore Ġparallel ization Ġand Ġhas Ġachieved ĠS OTA Ġresults Ġin Ġlanguage Ġmodeling Ġoutper forming ĠL ST M Ġmodels ĠB IB REF 1 . </s> In Ġrecent Ġyears , we Ġhave Ġseen Ġa Ġlot Ġof Ġdevelopment Ġbased Ġon Ġthis Ġstandard Ġtransformer Ġmodels Ġparticularly Ġon Ġun super vised Ġpre - training ( BI B REF 2 , ĠB IB REF 3 , ĠB IB REF 4 , ĠB IB REF 5 , ĠB IB REF 6 , ĠB IB REF 7 Ġwhich Ġhave Ġset Ġstate - of - the Ġart Ġresults Ġon Ġmultiple ĠN LP Ġbenchmarks . ĠOne Ġsuch Ġmodel Ġarchitecture Ġhas Ġbeen Ġthe ĠBid irection al ĠEnc oder ĠRepresent ations Ġfrom ĠTransformers Ġ( BER T ) Ġmodel Ġwhich Ġuses Ġa Ġdeep Ġbid irection al Ġtransformer Ġarchitecture . </s> Another Ġarchitecture Ġof Ġinterest Ġwould Ġbe Ġthe ĠTrans former - XL , Ġwhich Ġintroduces Ġthe Ġnotion Ġof Ġrec urrence Ġin Ġa Ġself - att ention Ġmodel . </s> The Ġprimary Ġresearch Ġfocus Ġthough Ġhas Ġbeen Ġmostly Ġon ĠEnglish Ġlanguage Ġfor Ġwhich Ġabundant Ġdata Ġis Ġpresent . ĠIt Ġis Ġinteresting Ġto Ġsee Ġthe Ġperformance Ġof Ġthese Ġmodels Ġfor Ġan Ġagg l ut in ative Ġlanguage Ġlike ĠFinnish , Ġwhich Ġis Ġmorph ologically Ġricher Ġthan ĠEnglish . </s> In Ġthis Ġproject , Ġwe Ġexplore Ġthe Ġimplementation Ġof ĠTrans former - based Ġmodels Ġ( BER T Ġand ĠTrans former - XL ) Ġin Ġlanguage Ġmodeling Ġfor ĠFinnish . ĠWe Ġwill Ġuse Ġthe Ġsame Ġtraining Ġdata Ġas Ġin ĠB IB REF 8 Ġso Ġthat Ġwe Ġcan Ġdo Ġfair Ġcomparisons Ġwith Ġthe Ġperformance Ġof Ġthe ĠL ST M Ġmodels . ĠAlso , Ġas Ġthe ĠB ERT Ġmodel Ġis Ġa Ġbi - direction al Ġtransformer , Ġwe Ġwill Ġhave Ġto Ġapproximate Ġthe Ġconditional Ġprobabilities Ġgiven Ġa Ġsequence Ġof Ġwords . ĠWe Ġalso Ġexperiment Ġwith Ġusing Ġsub - word Ġunits Ġwith ĠTrans former - XL Ġto Ġcope Ġwith Ġthe Ġlarge Ġvocabulary Ġproblems Ġassociated Ġwith Ġthe ĠFinnish ĠLanguage . ĠWith Ġsmaller Ġunits , Ġthe Ġmodeled Ġsequences Ġare Ġlonger , Ġand Ġwe Ġhope Ġthat Ġthe Ġrecursive ĠXL Ġarchitecture Ġcan Ġallow Ġus Ġto Ġstill Ġmodel Ġlong Ġterm Ġeffects . ĠTo Ġthe Ġbest Ġof Ġour Ġknowledge Ġthis Ġis Ġthe Ġfirst Ġwork Ġwith Ġthe ĠFinnish Ġlanguage Ġto Ġuse Ġthe Ġfollowing : </s> App rox imation Ġof Ġperplex ity Ġusing Ġa ĠB ERT Ġarchitecture </s> Using ĠTrans former - XL Ġarchitecture Ġwith Ġsub - word Ġunits . </s> Compar ison Ġof ĠTrans former Ġand ĠL ST M Ġmodels Ġas Ġlanguage Ġmodels Ġin Ġthe Ġsame Ġcomparable Ġsettings Ġwith Ġan Ġagg l ut in ative Ġlanguage . </s> Background Ġ& ĠMethods </s> The Ġgoal Ġof Ġan Ġlanguage Ġmodel Ġis Ġto Ġassign Ġmeaningful Ġprobabilities Ġto Ġa Ġsequence Ġof Ġwords . ĠGiven Ġa Ġset Ġof Ġtokens Ġ$\ math bf Ġ{ X } =( x _ 1 , .... , x _ T ) $, Ġwhere Ġ$ T $ Ġis Ġthe Ġlength Ġof Ġa Ġsequence , Ġour Ġtask Ġis Ġto Ġestimate Ġthe Ġjoint Ġconditional Ġprobability Ġ$ P (\ math bf Ġ{ X }) $ Ġwhich Ġis </s> were Ġ$( x _{ 1 }, Ġ\ ld ots Ġ, Ġx _{ i - 1 }) $ Ġis Ġthe Ġcontext . ĠAn ĠInt r ins ic Ġevaluation Ġof Ġthe Ġperformance Ġof ĠLanguage ĠModels Ġis Ġperplex ity Ġ( P PL ) Ġwhich Ġis Ġdefined Ġas Ġthe Ġinverse Ġprobability Ġof Ġthe Ġset Ġof Ġthe Ġtokens Ġand Ġtaking Ġthe Ġ$ T ^{ th } $ Ġroot Ġwere Ġ$ T $ Ġis Ġthe Ġnumber Ġof Ġtokens </s> In Ġour Ġtwo Ġapproaches Ġwe Ġuse Ġtransformer Ġbased Ġarchitectures : ĠB ERT Ġand ĠTrans former - XL Ġas Ġmentioned Ġbefore . ĠCalcul ating Ġthe Ġauto - reg ressive Ġ$ P (\ math bf Ġ{ X }) $ Ġfor Ġthe Ġtransformer - XL Ġis Ġquite Ġstraight - forward Ġas Ġthe Ġmodel Ġis Ġun id irection al Ġbut Ġit Ġdoesn 't Ġfactor ize Ġthe Ġsame Ġway Ġfor Ġa Ġbi - direction al Ġmodel Ġlike ĠB ERT . </s> BER T 's Ġbi - direction al Ġcontext Ġposes Ġa Ġproblem Ġfor Ġus Ġto Ġcalculate Ġan Ġauto - reg ressive Ġjoint Ġprobability . ĠA Ġsimple Ġfix Ġcould Ġbe Ġthat Ġwe Ġmask Ġall Ġthe Ġtokens Ġ$\ math bf Ġ{ x } _{ > i } $ Ġand Ġwe Ġcalculate Ġthe Ġconditional Ġfactors Ġas Ġwe Ġdo Ġfor Ġan Ġun id irection al Ġmodel . ĠBy Ġdoing Ġso Ġthough , Ġwe Ġloose Ġupon Ġthe Ġadvantage Ġof Ġbi - direction al Ġcontext Ġthe ĠB ERT Ġmodel Ġenables . ĠWe Ġpropose Ġan Ġapproximation Ġof Ġthe Ġjoint Ġprobability Ġas , </s> This Ġtype Ġof Ġapprox im ations Ġhas Ġbeen Ġpreviously Ġexplored Ġwith ĠBi - direction al ĠR NN ĠLM 's ĠB IB REF 9 Ġbut Ġnot Ġfor Ġdeep Ġtransformer Ġmodels . ĠWe Ġtherefore , Ġdefine Ġa Ġpseudo - per plex ity Ġscore Ġfrom Ġthe Ġabove Ġapprox imated Ġjoint Ġprobability . </s> The Ġoriginal ĠB ERT Ġhas Ġtwo Ġtraining Ġobjectives : Ġ' Mask ed Ġlanguage Ġmodelling ', Ġin Ġwhich Ġyou Ġmask Ġinput Ġtokens Ġrandomly Ġand Ġthen Ġpredict Ġthe Ġmasked Ġtokens Ġusing Ġthe Ġleft Ġand Ġright Ġcontext . ĠAdditionally , Ġthere Ġis Ġthe Ġ' next Ġsentence Ġprediction ' Ġtask Ġthat Ġjointly Ġtrains Ġtext - pair Ġrepresentations . ĠFor Ġtraining Ġthe ĠMask ed Ġlanguage Ġmodel Ġthe Ġoriginal ĠB ERT Ġused ĠByte ĠPair ĠEnc oding Ġ( B PE ) ĠB IB REF 10 Ġfor Ġsub word Ġtoken ization ĠB IB REF 11 . For Ġexample Ġthe Ġrare Ġword Ġ" un aff able " Ġto Ġbe Ġsplit Ġup Ġinto Ġmore Ġfrequent Ġsub words Ġsuch Ġas Ġ[" un ", Ġ" ## aff ", Ġ" ## able " ]. ĠTo Ġremain Ġconsistent Ġwith Ġexperiments Ġperformed Ġwith ĠL ST M 's Ġwe Ġuse Ġthe Ġmor f essor Ġfor Ġthe Ġsub word Ġtoken ization Ġin Ġthe ĠFinnish ĠLanguage . ĠIn ĠAdd ition , Ġwe Ġalso Ġapply Ġboundary Ġmarkers Ġas Ġin Ġ( Table ĠT AB REF 7 ) Ġand Ġtrain Ġtwo Ġseparate Ġmodels Ġusing Ġthis Ġdistinction . ĠWe Ġtrain Ġwith Ġleft - marked Ġmarkings Ġas Ġthe Ġoriginal ĠB ERT Ġwas Ġtrained Ġwith Ġsuch Ġa Ġscheme Ġand Ġthe Ġleft + right - marked Ġas Ġit Ġwas Ġthe Ġprevious ĠS OTA Ġwith Ġthe ĠFinnish ĠLanguage . ĠFor Ġthe Ġtransformer - XL Ġexperiments , Ġwe Ġjust Ġtrain Ġwith Ġthe Ġleft + right Ġmarked Ġscheme . </s> The ĠNext ĠSent ence ĠPrediction Ġ( N SP ) Ġis Ġa Ġbinary Ġclassification Ġtask Ġwhich Ġpredicts Ġwhether Ġtwo Ġsegments Ġfollow Ġeach Ġother Ġin Ġthe Ġoriginal Ġtext . ĠThis Ġpre - training Ġtask Ġwas Ġproposed Ġto Ġfurther Ġimprove Ġthe Ġperformance Ġon Ġdownstream ing Ġtasks , Ġlike ĠNatural ĠLanguage ĠIn ference ( N LI ) Ġbut Ġin Ġreality Ġremoving Ġthe ĠN SP Ġloss Ġmatches Ġor Ġslightly Ġimproves Ġthe Ġdownstream Ġtask Ġperformance ĠB IB REF 12 . ĠIn Ġthis Ġpaper , Ġwe Ġhave Ġomitted Ġthe ĠN SP Ġtask Ġfrom Ġthe ĠB ERT Ġpre - training Ġprocedure Ġand Ġchanged Ġthe Ġinput Ġfrom Ġa ĠS EG MENT - PA IR Ġinput Ġto Ġa ĠS ING LE ĠS EG MENT Ġinput . ĠAs Ġseen Ġin Ġ( Fig ĠFIG REF 8 ) </s> Trans former - XL Ġintroduced Ġthe Ġnotion Ġof Ġrec urrence Ġin Ġself - att ention Ġby Ġcaching Ġthe Ġhidden Ġstate Ġsequence Ġto Ġcompute Ġthe Ġhidden Ġstates Ġof Ġa Ġnew Ġsegment . ĠIt Ġalso Ġintroduces Ġa Ġnovel Ġrelative Ġpositional Ġembed ding Ġscheme Ġand Ġboth Ġof Ġthem Ġcombined Ġaddress Ġthe Ġissue Ġof Ġfixed Ġcontext Ġlengths . ĠTrans former - XL Ġas Ġmentioned Ġis Ġa Ġun id irection al Ġdeep Ġtransformer Ġarchitecture , Ġtherefore Ġthe Ġperplex ity Ġcan Ġbe Ġcalculated Ġas Ġ( E q ĠDIS PLAY _ FORM 5 ). ĠThe Ġonly Ġchange Ġis Ġin Ġthe Ġinput Ġformat , Ġwere Ġwe Ġuse Ġsub - word Ġunits Ġrather Ġthan Ġwhole Ġword Ġunits Ġas ĠFinnish Ġis Ġmorph ologically Ġricher Ġthan ĠEnglish . </s> Data </s> The ĠFinnish Ġtext Ġdata Ġused Ġfor Ġthe Ġlanguage Ġmodeling Ġtask Ġis Ġprovided Ġby ĠB IB REF 13 . ĠThe Ġdataset Ġconsists Ġmainly Ġof Ġnewspapers Ġand Ġbooks Ġof Ġaround Ġ144 Ġmillion Ġword Ġtokens Ġand Ġ4 . 2 Ġmillion Ġunique Ġtokens . ĠWe Ġuse Ġa ĠMor f essor Ġ2 . 0 ĠB IB REF 14 Ġusing Ġthe Ġbasic Ġun super vised ĠMor f essor ĠBas eline Ġalgorithm ĠB IB REF 15 Ġwith Ġa Ġcorpus Ġweight Ġparameter Ġ($ \ alpha Ġ$ ) Ġof Ġ0 . 001 . ĠWe Ġhave Ġa Ġvocabulary Ġof Ġ34 K Ġsub word Ġtokens Ġfor Ġthe Ġleft + right - marked Ġ(+ m +) Ġmarkings Ġand Ġ19 K Ġsub word Ġtokens Ġfor Ġthe Ġleft - marked Ġ(+ m ) Ġmarkings . ĠWe Ġalso Ġpre - process Ġthe Ġdata Ġto Ġremove Ġany Ġpunct uation Ġmarks Ġsuch Ġthat Ġwe Ġcan Ġuse Ġthe Ġsame Ġdata Ġwith Ġan ĠAS R Ġsystem . ĠThe Ġinput Ġis Ġone Ġsentence Ġper Ġline Ġand Ġwe Ġshuffle Ġthe Ġsentences Ġat Ġeach Ġepoch . ĠThe Ġdata Ġis Ġrandomly Ġdivided Ġinto - Ġtraining Ġdataset Ġand Ġa Ġvalidation Ġdataset . ĠThe Ġtest Ġdataset Ġconsists Ġof Ġ28 50 ĠFinnish Ġnews Ġarticles Ġobtained Ġfrom Ġthe ĠFinnish Ġnational Ġbroadcaster ĠY LE . </s> Exper iments Ġ& ĠResults Ġ: :: ĠB ERT </s> All ĠB ERT Ġexperiments Ġwere Ġtrained Ġfor Ġ500 K Ġsteps . ĠThe Ġcode Ġwas Ġwritten Ġin ĠPython Ġand Ġwe Ġused Ġthe ĠT ensor flow Ġlibraries Ġto Ġcreate Ġthe Ġmodels . ĠThe Ġexperiments Ġwere Ġtrained Ġon Ġa Ġsingle ĠNVIDIA ĠTesla ĠV 100 Ġ32 ĠGB Ġgraphic Ġcard . ĠThe Ġdata Ġwas Ġfirst Ġprocessed Ġinto ĠT ensor flow Ġrecords Ġas Ġthe Ġinput Ġto Ġthe Ġmodel . ĠThe Ġset Ġof Ġhyper param eters Ġwhich Ġwe Ġfound Ġoptimal Ġafter Ġexperimenting Ġwith Ġdifferent Ġsets Ġare Ġin Ġ( Table ĠT AB REF 10 ). </s> This Ġset Ġof Ġparameters Ġwere Ġchosen Ġas Ġthere Ġtraining Ġperformances Ġwere Ġbetter Ġthan Ġsmaller Ġmodels Ġon Ġmodelling Ġthe Ġlong Ġsequences Ġof Ġsub - words . ĠWe Ġuse Ġthe ĠAdam Ġoptim izer ĠB IB REF 16 Ġsame Ġas Ġthe ĠEnglish ĠB ERT . ĠA Ġmaximum Ġsequence Ġlength Ġof Ġ300 Ġencompasses Ġ98 Ġpercent Ġof Ġthe Ġtraining Ġdata Ġand Ġalso Ġallows Ġus Ġto Ġfit Ġlarger Ġmodels Ġon Ġthe ĠGPU Ġcard . ĠHyper - param eter Ġoptimization Ġis Ġvery Ġdifficult Ġin Ġcase Ġof Ġthese Ġmodels Ġas Ġthey Ġtake Ġaround Ġ15 Ġdays Ġto Ġtrain Ġgiven Ġthe Ġresources . ĠThe Ġhyper param eter Ġchoices Ġwere Ġtherefore Ġmore Ġdepend ant Ġon Ġthe Ġoriginal ĠB ERT Ġwith Ġlittle Ġtweaks . ĠWe Ġassess Ġthe Ġtraining Ġperformance Ġof Ġthe Ġthe Ġmodel Ġin Ġthe Ġ( Table ĠT AB REF 11 ). </s> When Ġwe Ġtrain Ġthe ĠB ERT Ġmodel Ġwe Ġmask Ġsome Ġpercentage Ġof Ġthe Ġinput Ġtokens Ġat Ġrandom , Ġand Ġthen Ġpredict Ġthose Ġmasked Ġtokens , Ġthis Ġis Ġknown Ġas ĠMask ed ĠLM . ĠThe Ġmasked ĠLM Ġloss , Ġrefers Ġspecifically Ġto Ġthe Ġloss Ġwhen Ġthe Ġmasked Ġlanguage Ġmodel Ġpredicts Ġon Ġthe Ġmasked Ġtokens . ĠThe Ġmasked ĠLM Ġaccuracy Ġrefers Ġspecifically Ġto Ġthe Ġaccuracy Ġwith Ġwhich Ġthe Ġmodel Ġpredicts Ġon Ġthe Ġmasked Ġtokens . ĠThe Ġloss Ġfor Ġboth Ġthe Ġmodels Ġare Ġfar Ġoff Ġfrom Ġthe ĠMask ed ĠLM Ġloss Ġof Ġthe ĠEnglish ĠB ERT , Ġkey Ġdifference Ġbeing Ġthe Ġpre - training Ġdata Ġfor Ġboth Ġthe Ġlanguage Ġmodels Ġare Ġquite Ġdifferent . ĠGoogle Ġtraining Ġtheir Ġmodel Ġon Ġ3 . 3 ĠBillion Ġwords Ġfrom ĠBooks Corp us ĠB IB REF 17 Ġand Ġthe ĠEnglish ĠWikipedia Ġand Ġour Ġmodel Ġbeing Ġtrained Ġon Ġ144 Ġmillion Ġwords . ĠComp aring Ġthe Ġtwo ĠFinnish Ġmodels , Ġthe Ġleft - marked Ġmodel Ġhas Ġa Ġbetter Ġtraining Ġperformance Ġthan Ġleft + right - marked Ġmodel . </s> The Ġresults Ġof Ġthe Ġpseudo - per plex ity Ġdescribed Ġin Ġthe Ġprevious Ġsection Ġto Ġevaluate Ġthe Ġabove Ġmodels Ġon Ġthe Ġtest Ġdata - set Ġis Ġin Ġtable Ġ( Table ĠT AB REF 12 ). The Ġtest Ġdataset Ġis Ġof Ġa Ġdifferent Ġcontext Ġwhen Ġcompared Ġto Ġthe Ġtraining Ġdata , Ġand Ġinterestingly Ġboth Ġthe Ġmodels Ġare Ġquite Ġconfident Ġwhen Ġit Ġcomes Ġto Ġthe Ġtest Ġdataset . ĠThe Ġpseudo - per plex ity Ġvalues Ġof Ġleft - marked Ġare Ġlower Ġwhen Ġcompared Ġto Ġleft - right - marked Ġsign ifying Ġthat Ġit Ġis Ġmore Ġconfident . </s> We Ġcannot Ġdirectly Ġcompare Ġthe Ġperplex ity Ġscores ĠB ERT Ġmodel Ġwith Ġa Ġun id irection al ĠL ST M Ġmodel Ġas Ġboth Ġare Ġcalculated Ġin Ġa Ġdifferent Ġmanner . ĠWe Ġcan Ġexperiment Ġto Ġcompare Ġit Ġwith Ġa ĠBi - direction al ĠL ST M Ġor Ġuse Ġa Ġdownstream ing Ġtask Ġto Ġcompare Ġboth Ġthe Ġperformances . ĠWe Ġcould Ġalso Ġrandomly Ġmask Ġtokens Ġand Ġthen Ġcompare Ġthe Ġprediction Ġaccuracy Ġon Ġthe Ġmasked Ġtokens . </s> Exper iments Ġ& ĠResults Ġ: :: ĠTrans former - XL </s> All ĠTrans former - XL Ġexperiments Ġare Ġalso Ġtrained Ġequally Ġfor Ġ500 K Ġsteps . ĠThe Ġcode Ġwas Ġwritten Ġin ĠPython Ġand Ġwe Ġused Ġthe ĠPy Tor ch Ġlibraries Ġfor Ġmodel Ġcreation . ĠThe Ġexperiments Ġwere Ġtrained Ġon Ġa Ġsingle ĠNVIDIA ĠTesla ĠV 100 Ġ32 ĠGB Ġgraphic Ġcard . ĠTwo Ġsets Ġof Ġhyper param eters Ġwere Ġchosen Ġto Ġbe Ġcompared Ġafter Ġsome Ġinitial Ġoptimization Ġand Ġare Ġin Ġ( Table ĠT AB REF 14 ) </s> From Ġthe Ġabove Ġparameter Ġchoice , Ġwe Ġwanted Ġto Ġexperiment , Ġwhether Ġproviding Ġmore ĠSe gment Ġand ĠMemory Ġlength Ġis Ġadvantageous Ġ( long er Ġcontext ) Ġthan Ġa Ġlarger Ġmodel . ĠThese Ġparameters Ġwhere Ġchosen Ġafter Ġsome Ġhyper param eter Ġoptimization . ĠSame Ġas Ġfor ĠB ERT Ġwe Ġuse Ġthe ĠAdam Ġoptim izer , Ġbut Ġwe Ġalso Ġuse Ġa Ġcos ine Ġan ne aling Ġlearning Ġrate Ġsched uler Ġto Ġspeed - up Ġtraining ĠB IB REF 18 . ĠThe Ġtraining Ġperformance Ġresults Ġare Ġin Ġ( Table ĠT AB REF 15 ) </s> As Ġopposed Ġto ĠB ERT , Ġthe Ġleft + right - marked Ġmodels Ġhave Ġa Ġbetter Ġtraining Ġperformance Ġthan Ġtheir Ġcounterpart . ĠInterestingly Ġthe Ġlarger Ġmodel Ġtrains Ġmuch Ġbetter Ġwhen Ġcompared Ġto Ġproviding Ġlarger Ġcontexts . ĠThe Ġsame Ġset Ġof Ġparameters Ġfor Ġthe Ġ32 - 32 Ġmodel Ġcannot Ġbe Ġreplicated Ġfor Ġ150 - 150 Ġmodel Ġas Ġthe Ġlatter Ġtakes Ġa Ġlot Ġof Ġspace Ġon Ġthe ĠGPU Ġcard . ĠThe Ġtest Ġset Ġis Ġsame Ġas Ġthat Ġused Ġwith ĠB ERT Ġand Ġthe Ġresults Ġare Ġin Ġ( Table ĠT AB REF 16 ). ĠThe Ġtest Ġperformance Ġis Ġsimilar Ġto Ġthat Ġof Ġthe Ġtraining Ġperformance Ġwith Ġleft - right - marked Ġlarge Ġmodel ( 32 - 32 ) Ġperforming Ġthe Ġbest . ĠWe Ġcan Ġdirectly Ġcompare Ġthe Ġperplex ity Ġscores Ġwith Ġthe Ġprevious Ġbest ĠB IB REF 19 Ġas Ġboth Ġare Ġun id irection al Ġmodels , ĠTrans former - XL Ġmodel Ġhas Ġoutper formed Ġthe Ġlatter Ġby Ġ27 %. </s> Exper iments Ġ& ĠResults Ġ: :: ĠResult Ġcomparisons Ġfor ĠTrans former Ġarchitectures </s> Trans former - XL Ġand ĠB ERT Ġboth Ġhave Ġlow Ġperplex ity Ġand Ġpseudo - per plex ity Ġscores , Ġbut Ġboth Ġcannot Ġbe Ġdirectly Ġcompared Ġas Ġthey Ġare Ġcalculated Ġquite Ġdifferently Ġ( E q . DIS PLAY _ FORM 4 , ĠE q . DIS PLAY _ FORM 6 ). ĠThe Ġdramatically Ġlow Ġscores Ġof ĠB ERT Ġindicate Ġthat Ġper Ġword Ġpredicted Ġprobability Ġis Ġhigher Ġthan Ġthat Ġof Ġa Ġun i - direction al Ġmodel . ĠThus Ġthe Ġpredicted Ġword Ġprobability Ġdistribution Ġis Ġmuch Ġsharper Ġwhen Ġcompared Ġto Ġthe ĠXL Ġmodel Ġprobability Ġdistribution . ĠAt Ġthis Ġpoint , Ġwe Ġcannot Ġsay Ġwhich Ġmodel Ġarchitecture Ġhas Ġperformed Ġbetter - ĠB ERT Ġor ĠTrans former - XL , Ġdespite Ġboth Ġof Ġthem Ġachieving Ġgood Ġlow Ġperplex ity Ġscores . ĠWe Ġwould Ġneed Ġto Ġexperiment Ġwith Ġa Ġdownstream ing Ġtask Ġin - order Ġto Ġfairly Ġcompare Ġmodel Ġperformances . </s> Conclusion </s> Recent Ġmigration Ġto Ġtransformer Ġbased Ġarchitectures Ġin Ġlanguage Ġmodeling Ġfrom ĠL ST M Ġmodels Ġis Ġjustified Ġas ĠTrans former - XL Ġob tains Ġstrong Ġperplex ity Ġresults . ĠB ERT Ġmodel Ġalso Ġob tains Ġvery Ġlow Ġpseudo - per plex ity Ġscores Ġbut Ġit Ġis Ġinequ itable Ġto Ġthe Ġun id irection al Ġmodels . ĠOur Ġmajor Ġcontributions Ġin Ġthis Ġproject , Ġis Ġthe Ġuse Ġof ĠTrans former - XL Ġarchitectures Ġfor Ġthe ĠFinnish Ġlanguage Ġin Ġa Ġsub - word Ġsetting , Ġand Ġthe Ġformulation Ġof Ġpseudo Ġperplex ity Ġfor Ġthe ĠB ERT Ġmodel . ĠFurther Ġcomparisons Ġbetween Ġthe Ġtransformer Ġarchitectures Ġcan Ġbe Ġmade Ġby Ġdownstream ing Ġit Ġto Ġan ĠAS R Ġtask , Ġwhich Ġwill Ġbe Ġexplored Ġin Ġthe Ġfuture .
Introduction Language modeling is a probabilistic description of language phenomenon. It provides essential context to distinguish words which sound similar and therefore has one of the most useful applications in Natural Language Processing (NLP) especially in downstreaming tasks like Automatic Speech Recognition (ASR). Recurrent Neural Networks (RNN) especially Long Short Term Memory (LSTM) networks BIBREF0 have been the typical solution to language modeling which do achieve strong results. In spite of these results, their fundamental sequential computation constraint has restricted their use in the modeling of long-term dependencies in sequential data. To address these issues Transformer architecture was introduced. Transformers relies completely on an attention mechanism to form global dependencies between input and output. It also offers more parallelization and has achieved SOTA results in language modeling outperforming LSTM models BIBREF1. In recent years,we have seen a lot of development based on this standard transformer models particularly on unsupervised pre-training(BIBREF2, BIBREF3, BIBREF4, BIBREF5, BIBREF6, BIBREF7 which have set state-of-the art results on multiple NLP benchmarks. One such model architecture has been the Bidirectional Encoder Representations from Transformers (BERT) model which uses a deep bidirectional transformer architecture. Another architecture of interest would be the Transformer-XL, which introduces the notion of recurrence in a self-attention model. The primary research focus though has been mostly on English language for which abundant data is present. It is interesting to see the performance of these models for an agglutinative language like Finnish, which is morphologically richer than English. In this project, we explore the implementation of Transformer-based models (BERT and Transformer-XL) in language modeling for Finnish. We will use the same training data as in BIBREF8 so that we can do fair comparisons with the performance of the LSTM models. Also, as the BERT model is a bi-directional transformer, we will have to approximate the conditional probabilities given a sequence of words. We also experiment with using sub-word units with Transformer-XL to cope with the large vocabulary problems associated with the Finnish Language. With smaller units, the modeled sequences are longer, and we hope that the recursive XL architecture can allow us to still model long term effects. To the best of our knowledge this is the first work with the Finnish language to use the following: Approximation of perplexity using a BERT architecture Using Transformer-XL architecture with sub-word units. Comparison of Transformer and LSTM models as language models in the same comparable settings with an agglutinative language. Background & Methods The goal of an language model is to assign meaningful probabilities to a sequence of words. Given a set of tokens $\mathbf {X}=(x_1,....,x_T)$, where $T$ is the length of a sequence, our task is to estimate the joint conditional probability $P(\mathbf {X})$ which is were $(x_{1}, \ldots , x_{i-1})$ is the context. An Intrinsic evaluation of the performance of Language Models is perplexity (PPL) which is defined as the inverse probability of the set of the tokens and taking the $T^{th}$ root were $T$ is the number of tokens In our two approaches we use transformer based architectures: BERT and Transformer-XL as mentioned before. Calculating the auto-regressive $P(\mathbf {X})$ for the transformer-XL is quite straight-forward as the model is unidirectional but it doesn't factorize the same way for a bi-directional model like BERT. BERT's bi-directional context poses a problem for us to calculate an auto-regressive joint probability. A simple fix could be that we mask all the tokens $\mathbf {x}_{>i}$ and we calculate the conditional factors as we do for an unidirectional model. By doing so though, we loose upon the advantage of bi-directional context the BERT model enables. We propose an approximation of the joint probability as, This type of approximations has been previously explored with Bi-directional RNN LM's BIBREF9 but not for deep transformer models. We therefore, define a pseudo-perplexity score from the above approximated joint probability. The original BERT has two training objectives: 'Masked language modelling', in which you mask input tokens randomly and then predict the masked tokens using the left and right context. Additionally, there is the 'next sentence prediction' task that jointly trains text-pair representations. For training the Masked language model the original BERT used Byte Pair Encoding (BPE) BIBREF10 for subword tokenization BIBREF11.For example the rare word "unaffable" to be split up into more frequent subwords such as ["un", "##aff", "##able"]. To remain consistent with experiments performed with LSTM's we use the morfessor for the subword tokenization in the Finnish Language. In Addition, we also apply boundary markers as in (Table TABREF7) and train two separate models using this distinction. We train with left-marked markings as the original BERT was trained with such a scheme and the left+right-marked as it was the previous SOTA with the Finnish Language. For the transformer-XL experiments, we just train with the left+right marked scheme. The Next Sentence Prediction (NSP) is a binary classification task which predicts whether two segments follow each other in the original text. This pre-training task was proposed to further improve the performance on downstreaming tasks, like Natural Language Inference(NLI) but in reality removing the NSP loss matches or slightly improves the downstream task performance BIBREF12. In this paper, we have omitted the NSP task from the BERT pre-training procedure and changed the input from a SEGMENT-PAIR input to a SINGLE SEGMENT input. As seen in (Fig FIGREF8) Transformer-XL introduced the notion of recurrence in self-attention by caching the hidden state sequence to compute the hidden states of a new segment. It also introduces a novel relative positional embedding scheme and both of them combined address the issue of fixed context lengths. Transformer-XL as mentioned is a unidirectional deep transformer architecture, therefore the perplexity can be calculated as (Eq DISPLAY_FORM5). The only change is in the input format, were we use sub-word units rather than whole word units as Finnish is morphologically richer than English. Data The Finnish text data used for the language modeling task is provided by BIBREF13. The dataset consists mainly of newspapers and books of around 144 million word tokens and 4.2 million unique tokens. We use a Morfessor 2.0 BIBREF14 using the basic unsupervised Morfessor Baseline algorithm BIBREF15 with a corpus weight parameter ($\alpha $) of 0.001. We have a vocabulary of 34K subword tokens for the left+right-marked (+m+) markings and 19K subword tokens for the left-marked (+m) markings. We also pre-process the data to remove any punctuation marks such that we can use the same data with an ASR system. The input is one sentence per line and we shuffle the sentences at each epoch. The data is randomly divided into- training dataset and a validation dataset. The test dataset consists of 2850 Finnish news articles obtained from the Finnish national broadcaster YLE. Experiments & Results ::: BERT All BERT experiments were trained for 500K steps. The code was written in Python and we used the Tensorflow libraries to create the models. The experiments were trained on a single NVIDIA Tesla V100 32 GB graphic card. The data was first processed into Tensorflow records as the input to the model. The set of hyperparameters which we found optimal after experimenting with different sets are in (Table TABREF10). This set of parameters were chosen as there training performances were better than smaller models on modelling the long sequences of sub-words. We use the Adam optimizer BIBREF16 same as the English BERT. A maximum sequence length of 300 encompasses 98 percent of the training data and also allows us to fit larger models on the GPU card. Hyper-parameter optimization is very difficult in case of these models as they take around 15 days to train given the resources. The hyperparameter choices were therefore more dependant on the original BERT with little tweaks. We assess the training performance of the the model in the (Table TABREF11). When we train the BERT model we mask some percentage of the input tokens at random, and then predict those masked tokens, this is known as Masked LM. The masked LM loss, refers specifically to the loss when the masked language model predicts on the masked tokens. The masked LM accuracy refers specifically to the accuracy with which the model predicts on the masked tokens. The loss for both the models are far off from the Masked LM loss of the English BERT, key difference being the pre-training data for both the language models are quite different. Google training their model on 3.3 Billion words from BooksCorpus BIBREF17 and the English Wikipedia and our model being trained on 144 million words. Comparing the two Finnish models, the left-marked model has a better training performance than left+right-marked model. The results of the pseudo-perplexity described in the previous section to evaluate the above models on the test data-set is in table (Table TABREF12).The test dataset is of a different context when compared to the training data, and interestingly both the models are quite confident when it comes to the test dataset. The pseudo-perplexity values of left-marked are lower when compared to left-right-marked signifying that it is more confident. We cannot directly compare the perplexity scores BERT model with a unidirectional LSTM model as both are calculated in a different manner. We can experiment to compare it with a Bi-directional LSTM or use a downstreaming task to compare both the performances. We could also randomly mask tokens and then compare the prediction accuracy on the masked tokens. Experiments & Results ::: Transformer-XL All Transformer-XL experiments are also trained equally for 500K steps. The code was written in Python and we used the PyTorch libraries for model creation. The experiments were trained on a single NVIDIA Tesla V100 32 GB graphic card. Two sets of hyperparameters were chosen to be compared after some initial optimization and are in (Table TABREF14) From the above parameter choice, we wanted to experiment, whether providing more Segment and Memory length is advantageous (longer context) than a larger model. These parameters where chosen after some hyperparameter optimization. Same as for BERT we use the Adam optimizer, but we also use a cosine annealing learning rate scheduler to speed-up training BIBREF18. The training performance results are in (Table TABREF15) As opposed to BERT, the left+right-marked models have a better training performance than their counterpart. Interestingly the larger model trains much better when compared to providing larger contexts. The same set of parameters for the 32-32 model cannot be replicated for 150-150 model as the latter takes a lot of space on the GPU card. The test set is same as that used with BERT and the results are in (Table TABREF16). The test performance is similar to that of the training performance with left-right-marked large model(32-32) performing the best. We can directly compare the perplexity scores with the previous best BIBREF19 as both are unidirectional models, Transformer-XL model has outperformed the latter by 27%. Experiments & Results ::: Result comparisons for Transformer architectures Transformer-XL and BERT both have low perplexity and pseudo-perplexity scores, but both cannot be directly compared as they are calculated quite differently (Eq.DISPLAY_FORM4, Eq.DISPLAY_FORM6). The dramatically low scores of BERT indicate that per word predicted probability is higher than that of a uni-directional model. Thus the predicted word probability distribution is much sharper when compared to the XL model probability distribution. At this point, we cannot say which model architecture has performed better- BERT or Transformer-XL, despite both of them achieving good low perplexity scores. We would need to experiment with a downstreaming task in-order to fairly compare model performances. Conclusion Recent migration to transformer based architectures in language modeling from LSTM models is justified as Transformer-XL obtains strong perplexity results. BERT model also obtains very low pseudo-perplexity scores but it is inequitable to the unidirectional models. Our major contributions in this project, is the use of Transformer-XL architectures for the Finnish language in a sub-word setting, and the formulation of pseudo perplexity for the BERT model. Further comparisons between the transformer architectures can be made by downstreaming it to an ASR task, which will be explored in the future.
How is pseudo-perplexity defined?
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How Ġis Ġpseudo - per plex ity Ġdefined ?
Answer Ġwith Ġcontent Ġmissing : Ġ( form ulas Ġin Ġselection ): ĠPse udo - per plex ity Ġis Ġperplex ity Ġwhere Ġconditional Ġjoint Ġprobability Ġis Ġapprox imated .
<s> How Ġis Ġpseudo - per plex ity Ġdefined ? </s> Introduction </s> Language Ġmodeling Ġis Ġa Ġprob abil istic Ġdescription Ġof Ġlanguage Ġphenomenon . ĠIt Ġprovides Ġessential Ġcontext Ġto Ġdistinguish Ġwords Ġwhich Ġsound Ġsimilar Ġand Ġtherefore Ġhas Ġone Ġof Ġthe Ġmost Ġuseful Ġapplications Ġin ĠNatural ĠLanguage ĠProcessing Ġ( N LP ) Ġespecially Ġin Ġdownstream ing Ġtasks Ġlike ĠAutomatic ĠSpeech ĠRecogn ition Ġ( AS R ). ĠRec urrent ĠNeural ĠNetworks Ġ( R NN ) Ġespecially ĠLong ĠShort ĠTerm ĠMemory Ġ( L ST M ) Ġnetworks ĠB IB REF 0 Ġhave Ġbeen Ġthe Ġtypical Ġsolution Ġto Ġlanguage Ġmodeling Ġwhich Ġdo Ġachieve Ġstrong Ġresults . ĠIn Ġspite Ġof Ġthese Ġresults , Ġtheir Ġfundamental Ġsequential Ġcomputation Ġconstraint Ġhas Ġrestricted Ġtheir Ġuse Ġin Ġthe Ġmodeling Ġof Ġlong - term Ġdependencies Ġin Ġsequential Ġdata . ĠTo Ġaddress Ġthese Ġissues ĠTrans former Ġarchitecture Ġwas Ġintroduced . ĠTransformers Ġrelies Ġcompletely Ġon Ġan Ġattention Ġmechanism Ġto Ġform Ġglobal Ġdependencies Ġbetween Ġinput Ġand Ġoutput . ĠIt Ġalso Ġoffers Ġmore Ġparallel ization Ġand Ġhas Ġachieved ĠS OTA Ġresults Ġin Ġlanguage Ġmodeling Ġoutper forming ĠL ST M Ġmodels ĠB IB REF 1 . </s> In Ġrecent Ġyears , we Ġhave Ġseen Ġa Ġlot Ġof Ġdevelopment Ġbased Ġon Ġthis Ġstandard Ġtransformer Ġmodels Ġparticularly Ġon Ġun super vised Ġpre - training ( BI B REF 2 , ĠB IB REF 3 , ĠB IB REF 4 , ĠB IB REF 5 , ĠB IB REF 6 , ĠB IB REF 7 Ġwhich Ġhave Ġset Ġstate - of - the Ġart Ġresults Ġon Ġmultiple ĠN LP Ġbenchmarks . ĠOne Ġsuch Ġmodel Ġarchitecture Ġhas Ġbeen Ġthe ĠBid irection al ĠEnc oder ĠRepresent ations Ġfrom ĠTransformers Ġ( BER T ) Ġmodel Ġwhich Ġuses Ġa Ġdeep Ġbid irection al Ġtransformer Ġarchitecture . </s> Another Ġarchitecture Ġof Ġinterest Ġwould Ġbe Ġthe ĠTrans former - XL , Ġwhich Ġintroduces Ġthe Ġnotion Ġof Ġrec urrence Ġin Ġa Ġself - att ention Ġmodel . </s> The Ġprimary Ġresearch Ġfocus Ġthough Ġhas Ġbeen Ġmostly Ġon ĠEnglish Ġlanguage Ġfor Ġwhich Ġabundant Ġdata Ġis Ġpresent . ĠIt Ġis Ġinteresting Ġto Ġsee Ġthe Ġperformance Ġof Ġthese Ġmodels Ġfor Ġan Ġagg l ut in ative Ġlanguage Ġlike ĠFinnish , Ġwhich Ġis Ġmorph ologically Ġricher Ġthan ĠEnglish . </s> In Ġthis Ġproject , Ġwe Ġexplore Ġthe Ġimplementation Ġof ĠTrans former - based Ġmodels Ġ( BER T Ġand ĠTrans former - XL ) Ġin Ġlanguage Ġmodeling Ġfor ĠFinnish . ĠWe Ġwill Ġuse Ġthe Ġsame Ġtraining Ġdata Ġas Ġin ĠB IB REF 8 Ġso Ġthat Ġwe Ġcan Ġdo Ġfair Ġcomparisons Ġwith Ġthe Ġperformance Ġof Ġthe ĠL ST M Ġmodels . ĠAlso , Ġas Ġthe ĠB ERT Ġmodel Ġis Ġa Ġbi - direction al Ġtransformer , Ġwe Ġwill Ġhave Ġto Ġapproximate Ġthe Ġconditional Ġprobabilities Ġgiven Ġa Ġsequence Ġof Ġwords . ĠWe Ġalso Ġexperiment Ġwith Ġusing Ġsub - word Ġunits Ġwith ĠTrans former - XL Ġto Ġcope Ġwith Ġthe Ġlarge Ġvocabulary Ġproblems Ġassociated Ġwith Ġthe ĠFinnish ĠLanguage . ĠWith Ġsmaller Ġunits , Ġthe Ġmodeled Ġsequences Ġare Ġlonger , Ġand Ġwe Ġhope Ġthat Ġthe Ġrecursive ĠXL Ġarchitecture Ġcan Ġallow Ġus Ġto Ġstill Ġmodel Ġlong Ġterm Ġeffects . ĠTo Ġthe Ġbest Ġof Ġour Ġknowledge Ġthis Ġis Ġthe Ġfirst Ġwork Ġwith Ġthe ĠFinnish Ġlanguage Ġto Ġuse Ġthe Ġfollowing : </s> App rox imation Ġof Ġperplex ity Ġusing Ġa ĠB ERT Ġarchitecture </s> Using ĠTrans former - XL Ġarchitecture Ġwith Ġsub - word Ġunits . </s> Compar ison Ġof ĠTrans former Ġand ĠL ST M Ġmodels Ġas Ġlanguage Ġmodels Ġin Ġthe Ġsame Ġcomparable Ġsettings Ġwith Ġan Ġagg l ut in ative Ġlanguage . </s> Background Ġ& ĠMethods </s> The Ġgoal Ġof Ġan Ġlanguage Ġmodel Ġis Ġto Ġassign Ġmeaningful Ġprobabilities Ġto Ġa Ġsequence Ġof Ġwords . ĠGiven Ġa Ġset Ġof Ġtokens Ġ$\ math bf Ġ{ X } =( x _ 1 , .... , x _ T ) $, Ġwhere Ġ$ T $ Ġis Ġthe Ġlength Ġof Ġa Ġsequence , Ġour Ġtask Ġis Ġto Ġestimate Ġthe Ġjoint Ġconditional Ġprobability Ġ$ P (\ math bf Ġ{ X }) $ Ġwhich Ġis </s> were Ġ$( x _{ 1 }, Ġ\ ld ots Ġ, Ġx _{ i - 1 }) $ Ġis Ġthe Ġcontext . ĠAn ĠInt r ins ic Ġevaluation Ġof Ġthe Ġperformance Ġof ĠLanguage ĠModels Ġis Ġperplex ity Ġ( P PL ) Ġwhich Ġis Ġdefined Ġas Ġthe Ġinverse Ġprobability Ġof Ġthe Ġset Ġof Ġthe Ġtokens Ġand Ġtaking Ġthe Ġ$ T ^{ th } $ Ġroot Ġwere Ġ$ T $ Ġis Ġthe Ġnumber Ġof Ġtokens </s> In Ġour Ġtwo Ġapproaches Ġwe Ġuse Ġtransformer Ġbased Ġarchitectures : ĠB ERT Ġand ĠTrans former - XL Ġas Ġmentioned Ġbefore . ĠCalcul ating Ġthe Ġauto - reg ressive Ġ$ P (\ math bf Ġ{ X }) $ Ġfor Ġthe Ġtransformer - XL Ġis Ġquite Ġstraight - forward Ġas Ġthe Ġmodel Ġis Ġun id irection al Ġbut Ġit Ġdoesn 't Ġfactor ize Ġthe Ġsame Ġway Ġfor Ġa Ġbi - direction al Ġmodel Ġlike ĠB ERT . </s> BER T 's Ġbi - direction al Ġcontext Ġposes Ġa Ġproblem Ġfor Ġus Ġto Ġcalculate Ġan Ġauto - reg ressive Ġjoint Ġprobability . ĠA Ġsimple Ġfix Ġcould Ġbe Ġthat Ġwe Ġmask Ġall Ġthe Ġtokens Ġ$\ math bf Ġ{ x } _{ > i } $ Ġand Ġwe Ġcalculate Ġthe Ġconditional Ġfactors Ġas Ġwe Ġdo Ġfor Ġan Ġun id irection al Ġmodel . ĠBy Ġdoing Ġso Ġthough , Ġwe Ġloose Ġupon Ġthe Ġadvantage Ġof Ġbi - direction al Ġcontext Ġthe ĠB ERT Ġmodel Ġenables . ĠWe Ġpropose Ġan Ġapproximation Ġof Ġthe Ġjoint Ġprobability Ġas , </s> This Ġtype Ġof Ġapprox im ations Ġhas Ġbeen Ġpreviously Ġexplored Ġwith ĠBi - direction al ĠR NN ĠLM 's ĠB IB REF 9 Ġbut Ġnot Ġfor Ġdeep Ġtransformer Ġmodels . ĠWe Ġtherefore , Ġdefine Ġa Ġpseudo - per plex ity Ġscore Ġfrom Ġthe Ġabove Ġapprox imated Ġjoint Ġprobability . </s> The Ġoriginal ĠB ERT Ġhas Ġtwo Ġtraining Ġobjectives : Ġ' Mask ed Ġlanguage Ġmodelling ', Ġin Ġwhich Ġyou Ġmask Ġinput Ġtokens Ġrandomly Ġand Ġthen Ġpredict Ġthe Ġmasked Ġtokens Ġusing Ġthe Ġleft Ġand Ġright Ġcontext . ĠAdditionally , Ġthere Ġis Ġthe Ġ' next Ġsentence Ġprediction ' Ġtask Ġthat Ġjointly Ġtrains Ġtext - pair Ġrepresentations . ĠFor Ġtraining Ġthe ĠMask ed Ġlanguage Ġmodel Ġthe Ġoriginal ĠB ERT Ġused ĠByte ĠPair ĠEnc oding Ġ( B PE ) ĠB IB REF 10 Ġfor Ġsub word Ġtoken ization ĠB IB REF 11 . For Ġexample Ġthe Ġrare Ġword Ġ" un aff able " Ġto Ġbe Ġsplit Ġup Ġinto Ġmore Ġfrequent Ġsub words Ġsuch Ġas Ġ[" un ", Ġ" ## aff ", Ġ" ## able " ]. ĠTo Ġremain Ġconsistent Ġwith Ġexperiments Ġperformed Ġwith ĠL ST M 's Ġwe Ġuse Ġthe Ġmor f essor Ġfor Ġthe Ġsub word Ġtoken ization Ġin Ġthe ĠFinnish ĠLanguage . ĠIn ĠAdd ition , Ġwe Ġalso Ġapply Ġboundary Ġmarkers Ġas Ġin Ġ( Table ĠT AB REF 7 ) Ġand Ġtrain Ġtwo Ġseparate Ġmodels Ġusing Ġthis Ġdistinction . ĠWe Ġtrain Ġwith Ġleft - marked Ġmarkings Ġas Ġthe Ġoriginal ĠB ERT Ġwas Ġtrained Ġwith Ġsuch Ġa Ġscheme Ġand Ġthe Ġleft + right - marked Ġas Ġit Ġwas Ġthe Ġprevious ĠS OTA Ġwith Ġthe ĠFinnish ĠLanguage . ĠFor Ġthe Ġtransformer - XL Ġexperiments , Ġwe Ġjust Ġtrain Ġwith Ġthe Ġleft + right Ġmarked Ġscheme . </s> The ĠNext ĠSent ence ĠPrediction Ġ( N SP ) Ġis Ġa Ġbinary Ġclassification Ġtask Ġwhich Ġpredicts Ġwhether Ġtwo Ġsegments Ġfollow Ġeach Ġother Ġin Ġthe Ġoriginal Ġtext . ĠThis Ġpre - training Ġtask Ġwas Ġproposed Ġto Ġfurther Ġimprove Ġthe Ġperformance Ġon Ġdownstream ing Ġtasks , Ġlike ĠNatural ĠLanguage ĠIn ference ( N LI ) Ġbut Ġin Ġreality Ġremoving Ġthe ĠN SP Ġloss Ġmatches Ġor Ġslightly Ġimproves Ġthe Ġdownstream Ġtask Ġperformance ĠB IB REF 12 . ĠIn Ġthis Ġpaper , Ġwe Ġhave Ġomitted Ġthe ĠN SP Ġtask Ġfrom Ġthe ĠB ERT Ġpre - training Ġprocedure Ġand Ġchanged Ġthe Ġinput Ġfrom Ġa ĠS EG MENT - PA IR Ġinput Ġto Ġa ĠS ING LE ĠS EG MENT Ġinput . ĠAs Ġseen Ġin Ġ( Fig ĠFIG REF 8 ) </s> Trans former - XL Ġintroduced Ġthe Ġnotion Ġof Ġrec urrence Ġin Ġself - att ention Ġby Ġcaching Ġthe Ġhidden Ġstate Ġsequence Ġto Ġcompute Ġthe Ġhidden Ġstates Ġof Ġa Ġnew Ġsegment . ĠIt Ġalso Ġintroduces Ġa Ġnovel Ġrelative Ġpositional Ġembed ding Ġscheme Ġand Ġboth Ġof Ġthem Ġcombined Ġaddress Ġthe Ġissue Ġof Ġfixed Ġcontext Ġlengths . ĠTrans former - XL Ġas Ġmentioned Ġis Ġa Ġun id irection al Ġdeep Ġtransformer Ġarchitecture , Ġtherefore Ġthe Ġperplex ity Ġcan Ġbe Ġcalculated Ġas Ġ( E q ĠDIS PLAY _ FORM 5 ). ĠThe Ġonly Ġchange Ġis Ġin Ġthe Ġinput Ġformat , Ġwere Ġwe Ġuse Ġsub - word Ġunits Ġrather Ġthan Ġwhole Ġword Ġunits Ġas ĠFinnish Ġis Ġmorph ologically Ġricher Ġthan ĠEnglish . </s> Data </s> The ĠFinnish Ġtext Ġdata Ġused Ġfor Ġthe Ġlanguage Ġmodeling Ġtask Ġis Ġprovided Ġby ĠB IB REF 13 . ĠThe Ġdataset Ġconsists Ġmainly Ġof Ġnewspapers Ġand Ġbooks Ġof Ġaround Ġ144 Ġmillion Ġword Ġtokens Ġand Ġ4 . 2 Ġmillion Ġunique Ġtokens . ĠWe Ġuse Ġa ĠMor f essor Ġ2 . 0 ĠB IB REF 14 Ġusing Ġthe Ġbasic Ġun super vised ĠMor f essor ĠBas eline Ġalgorithm ĠB IB REF 15 Ġwith Ġa Ġcorpus Ġweight Ġparameter Ġ($ \ alpha Ġ$ ) Ġof Ġ0 . 001 . ĠWe Ġhave Ġa Ġvocabulary Ġof Ġ34 K Ġsub word Ġtokens Ġfor Ġthe Ġleft + right - marked Ġ(+ m +) Ġmarkings Ġand Ġ19 K Ġsub word Ġtokens Ġfor Ġthe Ġleft - marked Ġ(+ m ) Ġmarkings . ĠWe Ġalso Ġpre - process Ġthe Ġdata Ġto Ġremove Ġany Ġpunct uation Ġmarks Ġsuch Ġthat Ġwe Ġcan Ġuse Ġthe Ġsame Ġdata Ġwith Ġan ĠAS R Ġsystem . ĠThe Ġinput Ġis Ġone Ġsentence Ġper Ġline Ġand Ġwe Ġshuffle Ġthe Ġsentences Ġat Ġeach Ġepoch . ĠThe Ġdata Ġis Ġrandomly Ġdivided Ġinto - Ġtraining Ġdataset Ġand Ġa Ġvalidation Ġdataset . ĠThe Ġtest Ġdataset Ġconsists Ġof Ġ28 50 ĠFinnish Ġnews Ġarticles Ġobtained Ġfrom Ġthe ĠFinnish Ġnational Ġbroadcaster ĠY LE . </s> Exper iments Ġ& ĠResults Ġ: :: ĠB ERT </s> All ĠB ERT Ġexperiments Ġwere Ġtrained Ġfor Ġ500 K Ġsteps . ĠThe Ġcode Ġwas Ġwritten Ġin ĠPython Ġand Ġwe Ġused Ġthe ĠT ensor flow Ġlibraries Ġto Ġcreate Ġthe Ġmodels . ĠThe Ġexperiments Ġwere Ġtrained Ġon Ġa Ġsingle ĠNVIDIA ĠTesla ĠV 100 Ġ32 ĠGB Ġgraphic Ġcard . ĠThe Ġdata Ġwas Ġfirst Ġprocessed Ġinto ĠT ensor flow Ġrecords Ġas Ġthe Ġinput Ġto Ġthe Ġmodel . ĠThe Ġset Ġof Ġhyper param eters Ġwhich Ġwe Ġfound Ġoptimal Ġafter Ġexperimenting Ġwith Ġdifferent Ġsets Ġare Ġin Ġ( Table ĠT AB REF 10 ). </s> This Ġset Ġof Ġparameters Ġwere Ġchosen Ġas Ġthere Ġtraining Ġperformances Ġwere Ġbetter Ġthan Ġsmaller Ġmodels Ġon Ġmodelling Ġthe Ġlong Ġsequences Ġof Ġsub - words . ĠWe Ġuse Ġthe ĠAdam Ġoptim izer ĠB IB REF 16 Ġsame Ġas Ġthe ĠEnglish ĠB ERT . ĠA Ġmaximum Ġsequence Ġlength Ġof Ġ300 Ġencompasses Ġ98 Ġpercent Ġof Ġthe Ġtraining Ġdata Ġand Ġalso Ġallows Ġus Ġto Ġfit Ġlarger Ġmodels Ġon Ġthe ĠGPU Ġcard . ĠHyper - param eter Ġoptimization Ġis Ġvery Ġdifficult Ġin Ġcase Ġof Ġthese Ġmodels Ġas Ġthey Ġtake Ġaround Ġ15 Ġdays Ġto Ġtrain Ġgiven Ġthe Ġresources . ĠThe Ġhyper param eter Ġchoices Ġwere Ġtherefore Ġmore Ġdepend ant Ġon Ġthe Ġoriginal ĠB ERT Ġwith Ġlittle Ġtweaks . ĠWe Ġassess Ġthe Ġtraining Ġperformance Ġof Ġthe Ġthe Ġmodel Ġin Ġthe Ġ( Table ĠT AB REF 11 ). </s> When Ġwe Ġtrain Ġthe ĠB ERT Ġmodel Ġwe Ġmask Ġsome Ġpercentage Ġof Ġthe Ġinput Ġtokens Ġat Ġrandom , Ġand Ġthen Ġpredict Ġthose Ġmasked Ġtokens , Ġthis Ġis Ġknown Ġas ĠMask ed ĠLM . ĠThe Ġmasked ĠLM Ġloss , Ġrefers Ġspecifically Ġto Ġthe Ġloss Ġwhen Ġthe Ġmasked Ġlanguage Ġmodel Ġpredicts Ġon Ġthe Ġmasked Ġtokens . ĠThe Ġmasked ĠLM Ġaccuracy Ġrefers Ġspecifically Ġto Ġthe Ġaccuracy Ġwith Ġwhich Ġthe Ġmodel Ġpredicts Ġon Ġthe Ġmasked Ġtokens . ĠThe Ġloss Ġfor Ġboth Ġthe Ġmodels Ġare Ġfar Ġoff Ġfrom Ġthe ĠMask ed ĠLM Ġloss Ġof Ġthe ĠEnglish ĠB ERT , Ġkey Ġdifference Ġbeing Ġthe Ġpre - training Ġdata Ġfor Ġboth Ġthe Ġlanguage Ġmodels Ġare Ġquite Ġdifferent . ĠGoogle Ġtraining Ġtheir Ġmodel Ġon Ġ3 . 3 ĠBillion Ġwords Ġfrom ĠBooks Corp us ĠB IB REF 17 Ġand Ġthe ĠEnglish ĠWikipedia Ġand Ġour Ġmodel Ġbeing Ġtrained Ġon Ġ144 Ġmillion Ġwords . ĠComp aring Ġthe Ġtwo ĠFinnish Ġmodels , Ġthe Ġleft - marked Ġmodel Ġhas Ġa Ġbetter Ġtraining Ġperformance Ġthan Ġleft + right - marked Ġmodel . </s> The Ġresults Ġof Ġthe Ġpseudo - per plex ity Ġdescribed Ġin Ġthe Ġprevious Ġsection Ġto Ġevaluate Ġthe Ġabove Ġmodels Ġon Ġthe Ġtest Ġdata - set Ġis Ġin Ġtable Ġ( Table ĠT AB REF 12 ). The Ġtest Ġdataset Ġis Ġof Ġa Ġdifferent Ġcontext Ġwhen Ġcompared Ġto Ġthe Ġtraining Ġdata , Ġand Ġinterestingly Ġboth Ġthe Ġmodels Ġare Ġquite Ġconfident Ġwhen Ġit Ġcomes Ġto Ġthe Ġtest Ġdataset . ĠThe Ġpseudo - per plex ity Ġvalues Ġof Ġleft - marked Ġare Ġlower Ġwhen Ġcompared Ġto Ġleft - right - marked Ġsign ifying Ġthat Ġit Ġis Ġmore Ġconfident . </s> We Ġcannot Ġdirectly Ġcompare Ġthe Ġperplex ity Ġscores ĠB ERT Ġmodel Ġwith Ġa Ġun id irection al ĠL ST M Ġmodel Ġas Ġboth Ġare Ġcalculated Ġin Ġa Ġdifferent Ġmanner . ĠWe Ġcan Ġexperiment Ġto Ġcompare Ġit Ġwith Ġa ĠBi - direction al ĠL ST M Ġor Ġuse Ġa Ġdownstream ing Ġtask Ġto Ġcompare Ġboth Ġthe Ġperformances . ĠWe Ġcould Ġalso Ġrandomly Ġmask Ġtokens Ġand Ġthen Ġcompare Ġthe Ġprediction Ġaccuracy Ġon Ġthe Ġmasked Ġtokens . </s> Exper iments Ġ& ĠResults Ġ: :: ĠTrans former - XL </s> All ĠTrans former - XL Ġexperiments Ġare Ġalso Ġtrained Ġequally Ġfor Ġ500 K Ġsteps . ĠThe Ġcode Ġwas Ġwritten Ġin ĠPython Ġand Ġwe Ġused Ġthe ĠPy Tor ch Ġlibraries Ġfor Ġmodel Ġcreation . ĠThe Ġexperiments Ġwere Ġtrained Ġon Ġa Ġsingle ĠNVIDIA ĠTesla ĠV 100 Ġ32 ĠGB Ġgraphic Ġcard . ĠTwo Ġsets Ġof Ġhyper param eters Ġwere Ġchosen Ġto Ġbe Ġcompared Ġafter Ġsome Ġinitial Ġoptimization Ġand Ġare Ġin Ġ( Table ĠT AB REF 14 ) </s> From Ġthe Ġabove Ġparameter Ġchoice , Ġwe Ġwanted Ġto Ġexperiment , Ġwhether Ġproviding Ġmore ĠSe gment Ġand ĠMemory Ġlength Ġis Ġadvantageous Ġ( long er Ġcontext ) Ġthan Ġa Ġlarger Ġmodel . ĠThese Ġparameters Ġwhere Ġchosen Ġafter Ġsome Ġhyper param eter Ġoptimization . ĠSame Ġas Ġfor ĠB ERT Ġwe Ġuse Ġthe ĠAdam Ġoptim izer , Ġbut Ġwe Ġalso Ġuse Ġa Ġcos ine Ġan ne aling Ġlearning Ġrate Ġsched uler Ġto Ġspeed - up Ġtraining ĠB IB REF 18 . ĠThe Ġtraining Ġperformance Ġresults Ġare Ġin Ġ( Table ĠT AB REF 15 ) </s> As Ġopposed Ġto ĠB ERT , Ġthe Ġleft + right - marked Ġmodels Ġhave Ġa Ġbetter Ġtraining Ġperformance Ġthan Ġtheir Ġcounterpart . ĠInterestingly Ġthe Ġlarger Ġmodel Ġtrains Ġmuch Ġbetter Ġwhen Ġcompared Ġto Ġproviding Ġlarger Ġcontexts . ĠThe Ġsame Ġset Ġof Ġparameters Ġfor Ġthe Ġ32 - 32 Ġmodel Ġcannot Ġbe Ġreplicated Ġfor Ġ150 - 150 Ġmodel Ġas Ġthe Ġlatter Ġtakes Ġa Ġlot Ġof Ġspace Ġon Ġthe ĠGPU Ġcard . ĠThe Ġtest Ġset Ġis Ġsame Ġas Ġthat Ġused Ġwith ĠB ERT Ġand Ġthe Ġresults Ġare Ġin Ġ( Table ĠT AB REF 16 ). ĠThe Ġtest Ġperformance Ġis Ġsimilar Ġto Ġthat Ġof Ġthe Ġtraining Ġperformance Ġwith Ġleft - right - marked Ġlarge Ġmodel ( 32 - 32 ) Ġperforming Ġthe Ġbest . ĠWe Ġcan Ġdirectly Ġcompare Ġthe Ġperplex ity Ġscores Ġwith Ġthe Ġprevious Ġbest ĠB IB REF 19 Ġas Ġboth Ġare Ġun id irection al Ġmodels , ĠTrans former - XL Ġmodel Ġhas Ġoutper formed Ġthe Ġlatter Ġby Ġ27 %. </s> Exper iments Ġ& ĠResults Ġ: :: ĠResult Ġcomparisons Ġfor ĠTrans former Ġarchitectures </s> Trans former - XL Ġand ĠB ERT Ġboth Ġhave Ġlow Ġperplex ity Ġand Ġpseudo - per plex ity Ġscores , Ġbut Ġboth Ġcannot Ġbe Ġdirectly Ġcompared Ġas Ġthey Ġare Ġcalculated Ġquite Ġdifferently Ġ( E q . DIS PLAY _ FORM 4 , ĠE q . DIS PLAY _ FORM 6 ). ĠThe Ġdramatically Ġlow Ġscores Ġof ĠB ERT Ġindicate Ġthat Ġper Ġword Ġpredicted Ġprobability Ġis Ġhigher Ġthan Ġthat Ġof Ġa Ġun i - direction al Ġmodel . ĠThus Ġthe Ġpredicted Ġword Ġprobability Ġdistribution Ġis Ġmuch Ġsharper Ġwhen Ġcompared Ġto Ġthe ĠXL Ġmodel Ġprobability Ġdistribution . ĠAt Ġthis Ġpoint , Ġwe Ġcannot Ġsay Ġwhich Ġmodel Ġarchitecture Ġhas Ġperformed Ġbetter - ĠB ERT Ġor ĠTrans former - XL , Ġdespite Ġboth Ġof Ġthem Ġachieving Ġgood Ġlow Ġperplex ity Ġscores . ĠWe Ġwould Ġneed Ġto Ġexperiment Ġwith Ġa Ġdownstream ing Ġtask Ġin - order Ġto Ġfairly Ġcompare Ġmodel Ġperformances . </s> Conclusion </s> Recent Ġmigration Ġto Ġtransformer Ġbased Ġarchitectures Ġin Ġlanguage Ġmodeling Ġfrom ĠL ST M Ġmodels Ġis Ġjustified Ġas ĠTrans former - XL Ġob tains Ġstrong Ġperplex ity Ġresults . ĠB ERT Ġmodel Ġalso Ġob tains Ġvery Ġlow Ġpseudo - per plex ity Ġscores Ġbut Ġit Ġis Ġinequ itable Ġto Ġthe Ġun id irection al Ġmodels . ĠOur Ġmajor Ġcontributions Ġin Ġthis Ġproject , Ġis Ġthe Ġuse Ġof ĠTrans former - XL Ġarchitectures Ġfor Ġthe ĠFinnish Ġlanguage Ġin Ġa Ġsub - word Ġsetting , Ġand Ġthe Ġformulation Ġof Ġpseudo Ġperplex ity Ġfor Ġthe ĠB ERT Ġmodel . ĠFurther Ġcomparisons Ġbetween Ġthe Ġtransformer Ġarchitectures Ġcan Ġbe Ġmade Ġby Ġdownstream ing Ġit Ġto Ġan ĠAS R Ġtask , Ġwhich Ġwill Ġbe Ġexplored Ġin Ġthe Ġfuture .