While there has been existing work on reducing NLP model vocabulary sizes BIBREF15, distillation techniques cannot utilize these, since they require the student and teacher models to share the same vocabulary and output space. This profoundly limits their potential to further reduce model sizes.
EXTRACTIVE
distillation techniques cannot utilize these, since they require the student and teacher models to share the same vocabulary and output space. This profoundly limits their potential to further reduce model sizes.
EXTRACTIVE
However, a significant bottleneck that has been overlooked by previous efforts is the input vocabulary size and its corresponding word embedding matrix, often accounting for a significant proportion of all model parameters. For instance, the embedding table of the BERTBASE model, comprising over 30K WordPiece tokens BIBREF14, accounts for over $21\%$ of the model size. While there has been existing work on reducing NLP model vocabulary sizes BIBREF15, distillation techniques cannot utilize these, since they require the student and teacher models to share the same vocabulary and output space. This profoundly limits their potential to further reduce model sizes.
However, a significant bottleneck that has been overlooked by previous efforts is the input vocabulary size and its corresponding word embedding matrix, often accounting for a significant proportion of all model parameters. For instance, the embedding table of the BERTBASE model, comprising over 30K WordPiece tokens BIBREF14, accounts for over $21\%$ of the model size. While there has been existing work on reducing NLP model vocabulary sizes BIBREF15, distillation techniques cannot utilize these, since they require the student and teacher models to share the same vocabulary and output space. This profoundly limits their potential to further reduce model sizes.
1909.11687
Introduction </s> Recently , Ġcontextual - aware Ġlanguage Ġmodels Ġsuch Ġas ĠEL Mo ĠB IB REF 0 , ĠG PT ĠB IB REF 1 , ĠB ERT ĠB IB REF 2 Ġand ĠXL Net ĠB IB REF 3 Ġhave Ġshown Ġto Ġgreatly Ġoutper form Ġtraditional Ġword Ġembed ding Ġmodels Ġincluding ĠWord 2 V ec ĠB IB REF 4 Ġand ĠGl o Ve ĠB IB REF 5 Ġin Ġa Ġvariety Ġof ĠN LP Ġtasks . ĠThese Ġpre - trained Ġlanguage Ġmodels , Ġwhen Ġfine - tun ed Ġon Ġdownstream Ġlanguage Ġunderstanding Ġtasks Ġsuch Ġas Ġsentiment Ġclassification ĠB IB REF 6 , Ġnatural Ġlanguage Ġinference ĠB IB REF 7 Ġand Ġreading Ġcomprehension ĠB IB REF 8 , ĠB IB REF 9 , Ġhave Ġachieved Ġstate - of - the - art Ġperformance . ĠHowever , Ġthe Ġlarge Ġnumber Ġof Ġparameters Ġin Ġthese Ġmodels , Ġoften Ġabove Ġhundreds Ġof Ġmillions , Ġmakes Ġit Ġimpossible Ġto Ġhost Ġthem Ġon Ġresource - con str ained Ġtasks Ġsuch Ġas Ġdoing Ġreal - time Ġinference Ġon Ġmobile Ġand Ġedge Ġdevices . </s> Besides Ġutilizing Ġmodel Ġquant ization Ġtechniques ĠB IB REF 10 , ĠB IB REF 11 Ġwhich Ġaim Ġto Ġreduce Ġthe Ġfloating - point Ġaccuracy Ġof Ġthe Ġparameters , Ġsignificant Ġrecent Ġresearch Ġhas Ġfocused Ġon Ġknowledge Ġdist illation ĠB IB REF 12 , ĠB IB REF 13 Ġtechniques . ĠHere , Ġthe Ġgoal Ġis Ġto Ġtrain Ġa Ġsmall - foot print Ġstudent Ġmodel Ġby Ġborrowing Ġknowledge , Ġsuch Ġas Ġthrough Ġa Ġsoft Ġpredicted Ġlabel Ġdistribution , Ġfrom Ġa Ġlarger Ġpre - trained Ġteacher Ġmodel . </s> However , Ġa Ġsignificant Ġbottleneck Ġthat Ġhas Ġbeen Ġoverlooked Ġby Ġprevious Ġefforts Ġis Ġthe Ġinput Ġvocabulary Ġsize Ġand Ġits Ġcorresponding Ġword Ġembed ding Ġmatrix , Ġoften Ġaccounting Ġfor Ġa Ġsignificant Ġproportion Ġof Ġall Ġmodel Ġparameters . ĠFor Ġinstance , Ġthe Ġembed ding Ġtable Ġof Ġthe ĠB ERT B ASE Ġmodel , Ġcomprising Ġover Ġ30 K ĠWord P iece Ġtokens ĠB IB REF 14 , Ġaccounts Ġfor Ġover Ġ$ 21 \ % $ Ġof Ġthe Ġmodel Ġsize . ĠWhile Ġthere Ġhas Ġbeen Ġexisting Ġwork Ġon Ġreducing ĠN LP Ġmodel Ġvocabulary Ġsizes ĠB IB REF 15 , Ġdist illation Ġtechniques Ġcannot Ġutilize Ġthese , Ġsince Ġthey Ġrequire Ġthe Ġstudent Ġand Ġteacher Ġmodels Ġto Ġshare Ġthe Ġsame Ġvocabulary Ġand Ġoutput Ġspace . ĠThis Ġprofoundly Ġlimits Ġtheir Ġpotential Ġto Ġfurther Ġreduce Ġmodel Ġsizes . </s> We Ġpresent Ġtwo Ġnovel Ġideas Ġto Ġimprove Ġthe Ġeffectiveness Ġof Ġknowledge Ġdist illation , Ġin Ġparticular Ġfor ĠB ERT , Ġwith Ġthe Ġfocus Ġon Ġbringing Ġdown Ġmodel Ġsizes Ġto Ġas Ġmuch Ġas Ġa Ġfew Ġmega - bytes . ĠOur Ġmodel Ġis Ġamong Ġthe Ġfirst Ġto Ġpropose Ġto Ġuse Ġa Ġsignificantly Ġsmaller Ġvocabulary Ġfor Ġthe Ġstudent Ġmodel Ġlearned Ġduring Ġdist illation . ĠIn Ġaddition , Ġinstead Ġof Ġdist illing Ġsolely Ġon Ġthe Ġteacher Ġmodel 's Ġfinal - layer Ġoutputs , Ġour Ġmodel Ġlever ages Ġlayer - wise Ġteacher Ġmodel Ġparameters Ġto Ġdirectly Ġoptimize Ġthe Ġparameters Ġof Ġthe Ġcorresponding Ġlayers Ġin Ġthe Ġstudent Ġmodel . ĠSpecifically , Ġour Ġcontributions Ġare : </s> [ left margin = * ] </s> Dual ĠTraining : ĠOur Ġteacher Ġand Ġstudent Ġmodels Ġhave Ġdifferent Ġvoc ab ular ies Ġand Ġincompatible Ġtoken izations Ġfor Ġthe Ġsame Ġsequence . ĠTo Ġaddress Ġthis Ġduring Ġdist illation , Ġwe Ġfeed Ġthe Ġteacher Ġmodel Ġa Ġmix Ġof Ġteacher Ġvocabulary - token ized Ġand Ġstudent Ġvocabulary - token ized Ġwords Ġwithin Ġa Ġsingle Ġsequence . ĠCou pled Ġwith Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask , Ġthis Ġencourages Ġan Ġimplicit Ġalignment Ġof Ġthe Ġteacher Ġand Ġstudent ĠWord P iece Ġembed d ings , Ġsince Ġthe Ġstudent Ġvocabulary Ġembed ding Ġmay Ġbe Ġused Ġas Ġcontext Ġto Ġpredict Ġa Ġword Ġtoken ized Ġby Ġthe Ġteacher Ġvocabulary Ġand Ġvice Ġversa . </s> Sh ared ĠVariable ĠProject ions : ĠTo Ġminimize Ġthe Ġloss Ġof Ġinformation Ġfrom Ġreducing Ġthe Ġhidden Ġstate Ġdimension , Ġwe Ġintroduce Ġa Ġseparate Ġloss Ġto Ġalign Ġthe Ġteacher Ġand Ġstudent Ġmodels ' Ġtrain able Ġvariables . ĠThis Ġallows Ġfor Ġmore Ġdirect Ġlayer - wise Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent Ġmodel . </s> Using Ġthe Ġcombination Ġof Ġdual Ġtraining Ġand Ġshared Ġvariable Ġprojections , Ġwe Ġtrain Ġa Ġ12 - layer Ġhighly - comp ressed Ġstudent ĠB ERT Ġmodel , Ġachieving Ġa Ġmaximum Ġcompression Ġratio Ġof Ġ$\ sim Ġ$ 61 . 94 x Ġ( with Ġ48 Ġdimension Ġsize ) Ġcompared Ġto Ġthe Ġteacher ĠB ERT B ASE Ġmodel . ĠWe Ġconduct Ġexperiments Ġfor Ġmeasuring Ġboth Ġgeneralized Ġlanguage Ġmodeling Ġperspective Ġand Ġfor Ġdownstream Ġtasks , Ġdemonstrating Ġcompetitive Ġperformance Ġwith Ġhigh Ġcompression Ġratios Ġfor Ġboth Ġfamilies Ġof Ġtasks . </s> Related ĠWork </s> Research Ġin Ġneural Ġnetwork Ġmodel Ġcompression Ġhas Ġbeen Ġcon com itant Ġwith Ġthe Ġrise Ġin Ġpopularity Ġof Ġneural Ġnetworks Ġthemselves , Ġsince Ġthese Ġmodels Ġhave Ġoften Ġbeen Ġmemory - intensive Ġfor Ġthe Ġhardware Ġof Ġtheir Ġtime . ĠWork Ġin Ġmodel Ġcompression Ġfor ĠN LP Ġapplications Ġfalls Ġbroadly Ġinto Ġfour Ġcategories : Ġmatrix Ġapproximation , Ġparameter Ġpr uning / sharing , Ġweight Ġquant ization Ġand Ġknowledge Ġdist illation . </s> A Ġfamily Ġof Ġapproaches ĠB IB REF 16 , ĠB IB REF 17 Ġseeks Ġto Ġcompress Ġthe Ġmatrix Ġparameters Ġof Ġthe Ġmodels Ġby Ġlow - rank Ġapproximation Ġi . e . Ġthe Ġfull - rank Ġmatrix Ġparameter Ġis Ġapprox imated Ġusing Ġmultiple Ġlow - rank Ġmat rices , Ġthereby Ġreducing Ġthe Ġeffective Ġnumber Ġof Ġmodel Ġparameters . ĠAnother Ġline Ġof Ġwork Ġexplores Ġparameter Ġpr uning Ġand Ġsharing - based Ġmethods ĠB IB REF 18 , ĠB IB REF 19 , ĠB IB REF 20 , ĠB IB REF 21 , Ġwhich Ġexplore Ġthe Ġredundancy Ġin Ġmodel Ġparameters Ġand Ġtry Ġto Ġremove Ġredundant Ġweights Ġas Ġwell Ġas Ġneurons , Ġfor Ġa Ġvariety Ġof Ġneural Ġnetwork Ġarchitectures . </s> Model Ġweight Ġquant ization Ġtechniques ĠB IB REF 22 , ĠB IB REF 23 , ĠB IB REF 24 , ĠB IB REF 25 Ġfocus Ġon Ġmapping Ġmodel Ġweights Ġto Ġlower - pre cision Ġintegers Ġand Ġfloating - point Ġnumbers . ĠThese Ġcan Ġbe Ġespecially Ġeffective Ġwith Ġhardware Ġsupporting Ġefficient Ġlow - pre cision Ġcalculations . ĠMore Ġrecently , ĠB IB REF 26 Ġapply Ġquant ization Ġto ĠB ERT - based Ġtransformer Ġmodels . </s> Know ledge Ġdist illation ĠB IB REF 12 , ĠB IB REF 13 Ġdiffers Ġfrom Ġthe Ġother Ġdiscussed Ġapproaches : Ġthe Ġsmaller Ġstudent Ġmodel Ġmay Ġbe Ġparam et ri zed Ġdifferently Ġfrom Ġthe Ġbigger Ġteacher Ġmodel , Ġaff ording Ġmore Ġmodeling Ġfreedom . ĠTeaching Ġa Ġstudent Ġmodel Ġto Ġmatch Ġthe Ġsoft Ġoutput Ġlabel Ġdistributions Ġfrom Ġa Ġlarger Ġmodel Ġalongside Ġthe Ġhard Ġground - truth Ġdistribution Ġworks Ġwell Ġfor Ġmany Ġtasks , Ġsuch Ġas Ġmachine Ġtranslation ĠB IB REF 27 Ġand Ġlanguage Ġmodeling ĠB IB REF 28 . </s> Not Ġlimited Ġto Ġthe Ġteacher Ġmodel Ġoutputs , Ġsome Ġapproaches Ġperform Ġknowledge Ġdist illation Ġvia Ġattention Ġtransfer ĠB IB REF 29 , Ġor Ġvia Ġfeature Ġmaps Ġor Ġintermediate Ġmodel Ġoutputs ĠB IB REF 30 , ĠB IB REF 31 , ĠB IB REF 32 . ĠMore Ġrelevant Ġto Ġcurrent Ġwork , ĠB IB REF 33 Ġand ĠB IB REF 34 Ġemploy Ġvariants Ġof Ġthese Ġtechniques Ġto ĠB ERT Ġmodel Ġcompression Ġby Ġreducing Ġthe Ġnumber Ġof Ġtransformer Ġlayers . ĠHowever , Ġas Ġexplained Ġbefore , Ġthese Ġapproaches Ġare Ġnot Ġimmediately Ġapplicable Ġto Ġour Ġsetting Ġdue Ġto Ġincompatible Ġteacher Ġand Ġstudent Ġmodel Ġvoc ab ular ies , Ġand Ġdo Ġnot Ġfocus Ġsufficiently Ġon Ġthe Ġembed ding Ġmatrix Ġsize ĠB IB REF 35 . </s> Method ology </s> Our Ġknowledge Ġdist illation Ġapproach Ġis Ġcentered Ġaround Ġreducing Ġthe Ġnumber Ġof ĠWord P iece Ġtokens Ġin Ġthe Ġmodel Ġvocabulary . ĠIn Ġthis Ġsection , Ġwe Ġfirst Ġdiscuss Ġthe Ġrationale Ġbehind Ġthis Ġreduction Ġand Ġthe Ġchallenges Ġit Ġintroduces , Ġfollowed Ġby Ġour Ġtechniques , Ġnamely Ġdual Ġtraining Ġand Ġshared Ġprojection . </s> Method ology Ġ: :: ĠOpt imal ĠSub word ĠEmb edd ings Ġvia ĠKnowledge ĠDist illation </s> We Ġfollow Ġthe Ġgeneral Ġknowledge Ġdist illation Ġparadigm Ġof Ġtraining Ġa Ġsmall Ġstudent Ġmodel Ġfrom Ġa Ġlarge Ġteacher Ġmodel . ĠOur Ġteacher Ġmodel Ġis Ġa Ġ12 - layer Ġunc ased ĠB ERT B ASE , Ġtrained Ġwith Ġ305 22 ĠWord P iece Ġtokens Ġand Ġ768 - dimensional Ġembed d ings Ġand Ġhidden Ġstates . ĠWe Ġdenote Ġthe Ġteacher Ġmodel Ġparameters Ġby Ġ$\ the ta Ġ_ { t } $. ĠOur Ġstudent Ġmodel Ġconsists Ġof Ġan Ġequal Ġnumber Ġof Ġtransformer Ġlayers Ġwith Ġparameters Ġden oted Ġby Ġ$\ the ta Ġ_ { s } $, Ġbut Ġwith Ġa Ġsmaller Ġvocabulary Ġas Ġwell Ġas Ġembed ding / hidden Ġdimensions , Ġillustrated Ġin ĠFigure ĠFIG REF 4 . ĠUsing Ġthe Ġsame ĠWord P iece Ġalgorithm Ġand Ġtraining Ġcorpus Ġas ĠB ERT , Ġwe Ġobtain Ġa Ġvocabulary Ġof Ġ49 28 ĠWord Pie ces , Ġwhich Ġwe Ġuse Ġfor Ġthe Ġstudent Ġmodel . </s> Word P iece Ġtokens ĠB IB REF 14 Ġare Ġsub - word Ġunits Ġobtained Ġby Ġapplying Ġa Ġgreedy Ġsegment ation Ġalgorithm Ġto Ġthe Ġtraining Ġcorpus : Ġa Ġdesired Ġnumber Ġ( say , Ġ$ D $ ) Ġof ĠWord Pie ces Ġare Ġchosen Ġsuch Ġthat Ġthe Ġsegment ed Ġcorpus Ġis Ġminimal Ġin Ġthe Ġnumber Ġof ĠWord Pie ces Ġused . ĠA Ġcurs ory Ġlook Ġat Ġboth Ġvoc ab ular ies Ġreveals Ġthat Ġ$ 93 . 9 \ % $ Ġof Ġthe ĠWord Pie ces Ġin Ġthe Ġstudent Ġvocabulary Ġalso Ġexist Ġin Ġthe Ġteacher Ġvocabulary , Ġsuggesting Ġroom Ġfor Ġa Ġreduction Ġin Ġthe ĠWord P iece Ġvocabulary Ġsize Ġfrom Ġ30 K Ġtokens . </s> Since Ġwe Ġseek Ġto Ġtrain Ġa Ġgeneral - purpose Ġstudent Ġlanguage Ġmodel , Ġwe Ġelect Ġto Ġreuse Ġthe Ġteacher Ġmodel 's Ġoriginal Ġtraining Ġobjective Ġto Ġoptimize Ġthe Ġstudent Ġmodel , Ġi . e ., Ġmasked Ġlanguage Ġmodeling Ġand Ġnext Ġsentence Ġprediction , Ġbefore Ġany Ġfine - tun ing . ĠIn Ġthe Ġformer Ġtask , Ġwords Ġin Ġcontext Ġare Ġrandomly Ġmasked , Ġand Ġthe Ġlanguage Ġmodel Ġneeds Ġto Ġpredict Ġthose Ġwords Ġgiven Ġthe Ġmasked Ġcontext . ĠIn Ġthe Ġlatter Ġtask , Ġgiven Ġa Ġpair Ġof Ġsentences , Ġthe Ġlanguage Ġmodel Ġpredicts Ġwhether Ġthe Ġpair Ġis Ġconsistent . </s> However , Ġsince Ġthe Ġstudent Ġvocabulary Ġis Ġnot Ġa Ġcomplete Ġsubset Ġof Ġthe Ġteacher Ġvocabulary , Ġthe Ġtwo Ġvoc ab ular ies Ġmay Ġtoken ize Ġthe Ġsame Ġwords Ġdifferently . ĠAs Ġa Ġresult , Ġthe Ġoutputs Ġof Ġthe Ġteacher Ġand Ġstudent Ġmodel Ġfor Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask Ġmay Ġnot Ġalign . ĠEven Ġwith Ġthe Ġhigh Ġoverlap Ġbetween Ġthe Ġtwo Ġvoc ab ular ies , Ġthe Ġneed Ġto Ġtrain Ġthe Ġstudent Ġembed ding Ġfrom Ġscratch , Ġand Ġthe Ġchange Ġin Ġembed ding Ġdimension Ġpre cludes Ġexisting Ġknowledge Ġdist illation Ġtechniques , Ġwhich Ġrely Ġon Ġthe Ġalignment Ġof Ġboth Ġmodels ' Ġoutput Ġspaces . ĠAs Ġa Ġresult , Ġwe Ġexplore Ġtwo Ġalternative Ġapproaches Ġthat Ġenable Ġimplicit Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent Ġmodel , Ġwhich Ġwe Ġdescribe Ġbelow . </s> Method ology Ġ: :: ĠDual ĠTraining </s> During Ġdist illation , Ġfor Ġa Ġgiven Ġtraining Ġsequence Ġinput Ġto Ġthe Ġteacher Ġmodel , Ġwe Ġpropose Ġto Ġmix Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies Ġby Ġrandomly Ġselecting Ġ( with Ġa Ġprobability Ġ$ p _{ DT } $, Ġa Ġhyper param eter ) Ġtokens Ġfrom Ġthe Ġsequence Ġto Ġsegment Ġusing Ġthe Ġstudent Ġvocabulary , Ġwith Ġthe Ġother Ġtokens Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary . ĠAs Ġillustrated Ġin ĠFigure ĠFIG REF 4 , Ġgiven Ġthe Ġinput Ġcontext Ġ[ Ġ` I ', Ġ` like ', Ġ` machine ', Ġ` learning ' ], Ġthe Ġwords Ġ` I ' Ġand Ġ` machine ' Ġare Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary Ġ( in Ġgreen ), Ġwhile Ġ` like ' Ġand Ġ` learning ' Ġare Ġsegment ed Ġusing Ġthe Ġstudent Ġvocabulary Ġ( in Ġblue ). ĠSimilar Ġto Ġcross - ling ual Ġtraining Ġin ĠB IB REF 36 , Ġthis Ġencourages Ġalignment Ġof Ġthe Ġrepresentations Ġfor Ġthe Ġsame Ġword Ġas Ġper Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies . ĠThis Ġis Ġeffected Ġthrough Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask : Ġthe Ġmodel Ġnow Ġneeds Ġto Ġlearn Ġto Ġpredict Ġwords Ġfrom Ġthe Ġstudent Ġvocabulary Ġusing Ġcontext Ġwords Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary , Ġand Ġvice Ġversa . </s> The Ġexpectation Ġis Ġthat Ġthe Ġstudent Ġembed d ings Ġcan Ġbe Ġlearned Ġeffectively Ġthis Ġway Ġfrom Ġthe Ġteacher Ġembed d ings Ġas Ġwell Ġas Ġmodel Ġparameters Ġ$\ the ta Ġ_ { t } $. ĠNote Ġthat Ġwe Ġperform Ġdual Ġtraining Ġonly Ġfor Ġthe Ġteacher Ġmodel Ġinputs : Ġthe Ġstudent Ġmodel Ġreceives Ġwords Ġsegment ed Ġexclusively Ġusing Ġthe Ġstudent Ġvocabulary . ĠAlso , Ġduring Ġmasked Ġlanguage Ġmodeling , Ġthe Ġmodel Ġuses Ġdifferent Ġsoft max Ġlayers Ġfor Ġthe Ġteacher Ġand Ġthe Ġstudent Ġvoc ab ular ies Ġdepending Ġon Ġwhich Ġone Ġwas Ġused Ġto Ġsegment Ġthe Ġword Ġin Ġquestion . </s> Method ology Ġ: :: ĠShared ĠProject ions </s> Re lying Ġsolely Ġon Ġteacher Ġmodel Ġoutputs Ġto Ġtrain Ġthe Ġstudent Ġmodel Ġmay Ġnot Ġgeneral ize Ġwell ĠB IB REF 34 . ĠTherefore , Ġsome Ġapproaches Ġutilize Ġand Ġtry Ġto Ġalign Ġthe Ġstudent Ġmodel 's Ġintermediate Ġpredictions Ġto Ġthose Ġof Ġthe Ġteacher ĠB IB REF 30 . ĠIn Ġour Ġsetting , Ġhowever , Ġsince Ġthe Ġstudent Ġand Ġteacher Ġmodel Ġoutput Ġspaces Ġare Ġnot Ġidentical , Ġintermediate Ġmodel Ġoutputs Ġmay Ġprove Ġhard Ġto Ġalign . ĠInstead , Ġwe Ġseek Ġto Ġdirectly Ġminimize Ġthe Ġloss Ġof Ġinformation Ġfrom Ġthe Ġteacher Ġmodel Ġparameters Ġ$\ the ta Ġ_ { t } $ Ġto Ġthe Ġstudent Ġparameters Ġ$\ the ta Ġ_ { s } $ Ġwith Ġsmaller Ġdimensions . ĠWe Ġachieve Ġthis Ġby Ġprojecting Ġthe Ġmodel Ġparameters Ġinto Ġthe Ġsame Ġspace , Ġto Ġencourage Ġalignment . </s> More Ġspecifically , Ġas Ġin ĠFigure ĠFIG REF 4 , Ġwe Ġproject Ġeach Ġtrain able Ġvariable Ġin Ġ$\ the ta Ġ_ { t } $ Ġto Ġthe Ġsame Ġshape Ġas Ġthe Ġcorresponding Ġvariable Ġin Ġ$\ the ta Ġ_ { s } $. ĠFor Ġexample , Ġfor Ġall Ġthe Ġtrain able Ġvariables Ġ$\ the ta Ġ_ { t } $ Ġwith Ġshape Ġ$ 768 \ times Ġ768 $, Ġwe Ġlearn Ġtwo Ġprojection Ġmat rices Ġ$\ math bf Ġ{ U }\ in Ġ\ math bb Ġ{ R } ^{ d \ times Ġ768 } $ Ġand Ġ$\ math bf Ġ{ V }\ in Ġ\ math bb Ġ{ R } ^{ 768 \ times Ġd } $ Ġto Ġproject Ġthem Ġinto Ġthe Ġcorresponding Ġspace Ġof Ġthe Ġstudent Ġmodel Ġvariable Ġ$\ the ta Ġ_ { t } ^ \ prime Ġ$ , Ġwhere Ġ$ d $ Ġis Ġthe Ġstudent Ġmodel 's Ġhidden Ġdimension . Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġare Ġcommon Ġto Ġall ĠB ERT Ġmodel Ġparameters Ġof Ġthat Ġdimension ality ; Ġin Ġaddition , Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġare Ġnot Ġneeded Ġfor Ġfine - tun ing Ġor Ġinference Ġafter Ġdist illation . ĠIn Ġorder Ġto Ġalign Ġthe Ġstudent Ġvariable Ġand Ġthe Ġteacher Ġvariable 's Ġprojection , Ġwe Ġintroduce Ġa Ġseparate Ġmean Ġsquare Ġerror Ġloss Ġdefined Ġin ĠEqu ation ĠDIS PLAY _ FORM 7 , Ġwhere Ġ$\ down arrow Ġ$ Ġstands Ġfor Ġdown Ġprojection Ġ( since Ġthe Ġprojection Ġis Ġto Ġa Ġlower Ġdimension ). </s> The Ġabove Ġloss Ġfunction Ġalign s Ġthe Ġtrain able Ġvariables Ġin Ġthe Ġstudent Ġspace . ĠAlternatively , Ġwe Ġcan Ġproject Ġtrain able Ġvariables Ġin Ġ$\ the ta Ġ_ { s } $ Ġto Ġthe Ġsame Ġshape Ġas Ġin Ġ$\ the ta Ġ_ { t } $. ĠThis Ġway , Ġthe Ġloss Ġfunction Ġin ĠEqu ation ĠDIS PLAY _ FORM 8 , Ġ($ \ up arrow Ġ$ Ġdenotes Ġup Ġprojection ) Ġcan Ġcompare Ġthe Ġtrain able Ġvariables Ġin Ġthe Ġteacher Ġspace . </s> Method ology Ġ: :: ĠOptim ization ĠObjective </s> Our Ġfinal Ġloss Ġfunction Ġincludes , Ġin Ġaddition Ġto Ġan Ġoptional Ġprojection Ġloss , Ġmasked Ġlanguage Ġmodeling Ġcross - ent ropy Ġlosses Ġfor Ġthe Ġstudent Ġas Ġwell Ġas Ġthe Ġteacher Ġmodels , Ġsince Ġthe Ġteacher Ġmodel Ġis Ġtrained Ġwith Ġdual - voc abulary Ġinputs Ġand Ġis Ġnot Ġstatic . Ġ$ P ( y _ i = c | \ the ta Ġ_ { s }) $ Ġand Ġ$ P ( y _ i = c | \ the ta Ġ_ { t }) $ Ġdenote Ġthe Ġstudent Ġand Ġteacher Ġmodel Ġprediction Ġprobabilities Ġfor Ġclass Ġc Ġrespectively , Ġand Ġ$\ math bb Ġ{ 1 } $ Ġdenotes Ġan Ġindicator Ġfunction . ĠEqu ations ĠDIS PLAY _ FORM 10 Ġand Ġbelow Ġdefine Ġthe Ġfinal Ġloss Ġ$ L _{ final } $, Ġwhere Ġ$\ ep sil on Ġ$ Ġis Ġa Ġhyper param eter . </s> Exper iments </s> To Ġevaluate Ġour Ġknowledge Ġdist illation Ġapproach , Ġwe Ġdesign Ġtwo Ġclasses Ġof Ġexperiments . ĠFirst , Ġwe Ġevaluate Ġthe Ġdistilled Ġstudent Ġlanguage Ġmodels Ġusing Ġthe Ġmasked Ġword Ġprediction Ġtask Ġon Ġan Ġunseen Ġevaluation Ġcorpus , Ġfor Ġan Ġexplicit Ġevaluation Ġof Ġthe Ġlanguage Ġmodel . ĠSecond , Ġwe Ġfine - t une Ġthe Ġlanguage Ġmodel Ġby Ġadding Ġa Ġtask - specific Ġaff ine Ġlayer Ġon Ġtop Ġof Ġthe Ġstudent Ġlanguage Ġmodel Ġoutputs , Ġon Ġa Ġsuite Ġof Ġdownstream Ġsentence Ġand Ġsentence Ġpair Ġclassification Ġtasks . ĠThis Ġis Ġmeant Ġto Ġbe Ġan Ġimplicit Ġevaluation Ġof Ġthe Ġquality Ġof Ġthe Ġrepresentations Ġlearned Ġby Ġthe Ġstudent Ġlanguage Ġmodel . ĠWe Ġdescribe Ġthese Ġexperiments , Ġalong Ġwith Ġdetails Ġon Ġtraining , Ġimplementation Ġand Ġour Ġbas elines Ġbelow . </s> Exper iments Ġ: :: ĠLanguage ĠModel ĠTraining </s> During Ġthe Ġdist illation Ġof Ġthe Ġteacher ĠB ERT Ġmodel Ġto Ġtrain Ġthe Ġstudent ĠB ERT Ġlanguage Ġmodel , Ġwe Ġutilize Ġthe Ġsame Ġcorpus Ġas Ġwas Ġused Ġto Ġtrain Ġthe Ġteacher Ġi . e . ĠBooks Corp us ĠB IB REF 37 Ġand ĠEnglish ĠWikipedia , Ġwith Ġwhites paces Ġused Ġtoken ize Ġthe Ġtext Ġinto Ġwords . ĠWe Ġonly Ġuse Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask Ġto Ġcalculate Ġthe Ġoverall Ġdist illation Ġloss Ġfrom ĠSection ĠSEC REF 6 , Ġsince Ġthe Ġnext Ġsentence Ġprediction Ġloss Ġhurt Ġperformance Ġslightly . ĠDual Ġtraining Ġis Ġenabled Ġfor Ġteacher Ġmodel Ġinputs , Ġwith Ġ$ p _{ DT } $, Ġthe Ġprobability Ġof Ġsegment ing Ġa Ġteacher Ġmodel Ġinput Ġword Ġusing Ġthe Ġstudent Ġvocabulary , Ġset Ġto Ġ0 . 5 . ĠFor Ġexperiments Ġincluding Ġshared Ġprojection , Ġthe Ġprojection Ġmat rices Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġutilized ĠXavier Ġinitialization ĠB IB REF 38 . ĠThe Ġloss Ġweight Ġcoefficient Ġ$\ ep sil on Ġ$ Ġis Ġset Ġto Ġ1 Ġafter Ġtuning . </s> It Ġis Ġworth Ġnoting Ġthat Ġin Ġcontrast Ġto Ġa Ġnumber Ġof Ġexisting Ġapproaches , Ġwe Ġdirectly Ġdist ill Ġthe Ġteacher ĠB ERT Ġlanguage Ġmodel , Ġnot Ġyet Ġfine - tun ed Ġon Ġa Ġdownstream Ġtask , Ġto Ġobtain Ġa Ġstudent Ġlanguage Ġmodel Ġthat Ġis Ġtask - agn ostic . ĠFor Ġdownstream Ġtasks , Ġwe Ġfine - t une Ġthis Ġdistilled Ġstudent Ġlanguage Ġmodel . </s> Dist illation Ġis Ġcarried Ġout Ġon ĠCloud ĠT PU s Ġin Ġa Ġ4 x 4 Ġpod Ġconfiguration Ġ( 32 ĠT PU Ġcores Ġoverall ). ĠWe Ġoptimized Ġthe Ġloss Ġusing ĠL AM B ĠB IB REF 39 Ġfor Ġ250 K Ġsteps , Ġwith Ġa Ġlearning Ġrate Ġof Ġ0 . 00 125 Ġand Ġbatch Ġsize Ġof Ġ4096 . ĠDepending Ġon Ġthe Ġstudent Ġmodel Ġdimension , Ġtraining Ġtook Ġbetween Ġ2 - 4 Ġdays . </s> Exper iments Ġ: :: ĠModels Ġand ĠBas elines </s> We Ġevaluate Ġthree Ġvariants Ġof Ġour Ġdistilled Ġstudent Ġmodels : Ġwith Ġonly Ġdual Ġtraining Ġof Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies Ġ( Dual Train ) Ġand Ġwith Ġdual Ġtraining Ġalong Ġwith Ġdown - project ion Ġ( Dual Train Ġ+ ĠShared Pro j Down ) Ġor Ġup - project ion Ġ( Dual Train Ġ+ ĠShared Pro j Up ) Ġof Ġthe Ġteacher Ġmodel Ġparameters . ĠFor Ġeach Ġof Ġthese Ġconfigurations , Ġwe Ġtrain Ġstudent Ġmodels Ġwith Ġembed ding Ġand Ġhidden Ġdimensions Ġ48 , Ġ96 Ġand Ġ192 , Ġfor Ġ9 Ġtotal Ġvariants , Ġeach Ġusing Ġa Ġcompact Ġ5 K - Word P iece Ġvocabulary . ĠTable ĠT AB REF 14 Ġpresents Ġsome Ġstatistics Ġon Ġthese Ġmodels ' Ġsizes : Ġour Ġsmallest Ġmodel Ġcontains Ġtwo Ġorders Ġof Ġmagnitude Ġfewer Ġparameters , Ġand Ġrequires Ġonly Ġ1 % Ġfloating - point Ġoperations Ġwhen Ġcompared Ġto Ġthe ĠB ERT B ASE Ġmodel . </s> For Ġthe Ġlanguage Ġmodeling Ġevaluation , Ġwe Ġalso Ġevaluate Ġa Ġbaseline Ġwithout Ġknowledge Ġdist illation Ġ( ter med ĠNo K D ), Ġwith Ġa Ġmodel Ġparameter ized Ġident ically Ġto Ġthe Ġdistilled Ġstudent Ġmodels Ġbut Ġtrained Ġdirectly Ġon Ġthe Ġteacher Ġmodel Ġobjective Ġfrom Ġscratch . ĠFor Ġdownstream Ġtasks , Ġwe Ġcompare Ġwith ĠNo K D Ġas Ġwell Ġas ĠPatient ĠKnowledge ĠDist illation Ġ( PK D ) Ġfrom ĠB IB REF 34 , Ġwho Ġdist ill Ġthe Ġ12 - layer ĠB ERT B ASE Ġmodel Ġinto Ġ3 Ġand Ġ6 - layer ĠB ERT Ġmodels Ġby Ġusing Ġthe Ġteacher Ġmodel 's Ġhidden Ġstates . </s> Exper iments Ġ: :: ĠEvaluation ĠT asks Ġand ĠDat as ets </s> For Ġexplicit Ġevaluation Ġof Ġthe Ġgeneralized Ġlanguage Ġperspective Ġof Ġthe Ġdistilled Ġstudent Ġlanguage Ġmodels , Ġwe Ġuse Ġthe ĠReddit Ġdataset ĠB IB REF 40 Ġto Ġmeasure Ġword Ġmask Ġprediction Ġaccuracy Ġof Ġthe Ġstudent Ġmodels , Ġsince Ġthe Ġlanguage Ġused Ġon ĠReddit Ġis Ġdifferent Ġfrom Ġthat Ġin Ġthe Ġtraining Ġcorpor a . ĠThe Ġdataset Ġis Ġpre process ed Ġsimilarly Ġto Ġthe Ġtraining Ġcorpor a , Ġexcept Ġwe Ġdo Ġnot Ġneed Ġto Ġtoken ize Ġit Ġusing Ġthe Ġteacher Ġvocabulary , Ġsince Ġwe Ġonly Ġrun Ġand Ġevaluate Ġthe Ġstudent Ġmodels . </s> For Ġimplicit Ġevaluation Ġon Ġdownstream Ġlanguage Ġunderstanding Ġtasks , Ġwe Ġfine - t une Ġand Ġevaluate Ġthe Ġdistilled Ġstudent Ġmodels Ġon Ġthree Ġtasks Ġfrom Ġthe ĠGL UE Ġbenchmark ĠB IB REF 41 : </s> [ left margin = *, top se p = 0 pt ] </s> Stan ford ĠSent iment ĠTree bank Ġ( S ST - 2 ) ĠB IB REF 6 , Ġa Ġtwo - way Ġsentence Ġsentiment Ġclassification Ġtask Ġwith Ġ67 K Ġtraining Ġinstances , </s> Microsoft ĠResearch ĠPar aph rase ĠCorpus Ġ( MR PC ) ĠB IB REF 42 , Ġa Ġtwo - way Ġsentence Ġpair Ġclassification Ġtask Ġto Ġidentify Ġparaph r ases , Ġwith Ġ3 . 7 K Ġtraining Ġinstances , Ġand </s> Multi - Gen re ĠNatural ĠLanguage ĠIn ference Ġ( MN LI ) ĠB IB REF 7 , Ġa Ġthree - way Ġsentence Ġpair Ġclassification Ġtask Ġwith Ġ39 3 K Ġtraining Ġinstances , Ġto Ġidentify Ġpremise - hyp ot hesis Ġrelations . ĠThere Ġare Ġseparate Ġdevelopment Ġand Ġtest Ġsets Ġfor Ġgenre - matched Ġand Ġgenre - m ism atched Ġpremise - hyp ot hesis Ġpairs ; Ġwe Ġtune Ġour Ġmodels Ġsolely Ġon Ġthe Ġgenre - matched Ġdevelopment Ġset . </s> For Ġall Ġdownstream Ġtask Ġevaluations , Ġwe Ġfine - t une Ġfor Ġ10 Ġepoch s Ġusing ĠL AM B Ġwith Ġa Ġlearning Ġrate Ġof Ġ0 . 0002 Ġand Ġbatch Ġsize Ġof Ġ32 . ĠSince Ġour Ġlanguage Ġmodels Ġare Ġtrained Ġwith Ġa Ġmaximum Ġsequence Ġlength Ġof Ġ128 Ġtokens , Ġwe Ġdo Ġnot Ġevaluate Ġon Ġreading Ġcomprehension Ġdatasets Ġsuch Ġas ĠS Qu AD ĠB IB REF 8 Ġor ĠR ACE ĠB IB REF 9 , Ġwhich Ġrequire Ġmodels Ġsupporting Ġlonger Ġsequences . </s> Results </s> Table ĠT AB REF 20 Ġcontains Ġmasked Ġword Ġprediction Ġaccuracy Ġfigures Ġfor Ġthe Ġdifferent Ġmodels Ġand Ġthe ĠNo K D Ġbaseline . ĠWe Ġobserve Ġthat Ġdual Ġtraining Ġsignificantly Ġimproves Ġover Ġthe Ġbaseline Ġfor Ġall Ġmodel Ġdimensions , Ġand Ġthat Ġboth Ġshared Ġprojection Ġlosses Ġadded Ġto Ġdual Ġtraining Ġfurther Ġimprove Ġthe Ġword Ġprediction Ġaccuracy . ĠIt Ġis Ġinteresting Ġto Ġnote Ġthat Ġfor Ġall Ġmodel Ġdimensions , ĠShared Pro j Up Ġprojecting Ġinto Ġthe Ġteacher Ġspace Ġoutper forms ĠShared Pro j Down , Ġsignificantly Ġso Ġfor Ġdimension Ġ48 . ĠEx pected ly , Ġthere Ġis Ġa Ġnoticeable Ġperformance Ġdrop Ġgoing Ġfrom Ġ192 Ġto Ġ96 Ġto Ġ48 - dimensional Ġhidden Ġstate Ġmodels . ĠNote Ġthat Ġbecause Ġof Ġthe Ġdiffering Ġteacher Ġand Ġstudent Ġmodel Ġvoc ab ular ies , Ġmasked Ġword Ġprediction Ġaccuracy Ġfor Ġthe Ġteacher ĠB ERT B ASE Ġmodel Ġis Ġnot Ġdirectly Ġcomparable Ġwith Ġthe Ġstudent Ġmodels . </s> Table ĠT AB REF 21 Ġshows Ġresults Ġon Ġthe Ġdownstream Ġlanguage Ġunderstanding Ġtasks , Ġas Ġwell Ġas Ġmodel Ġsizes , Ġfor Ġour Ġapproaches , Ġthe ĠB ERT B ASE Ġteacher Ġmodel , Ġand Ġthe ĠPK D Ġand ĠNo K D Ġbas elines . ĠWe Ġnote Ġthat Ġmodels Ġtrained Ġwith Ġour Ġproposed Ġapproaches Ġperform Ġstrongly Ġand Ġconsistently Ġimprove Ġupon Ġthe Ġident ically Ġparam et ri zed ĠNo K D Ġbas elines , Ġindicating Ġthat Ġthe Ġdual Ġtraining Ġand Ġshared Ġprojection Ġtechniques Ġare Ġeffective , Ġwithout Ġinc urring Ġsignificant Ġlosses Ġagainst Ġthe ĠB ERT B ASE Ġteacher Ġmodel . ĠComp aring Ġwith Ġthe ĠPK D Ġbaseline , Ġour Ġ192 - dimensional Ġmodels , Ġachieving Ġa Ġhigher Ġcompression Ġrate Ġthan Ġeither Ġof Ġthe ĠPK D Ġmodels , Ġperform Ġbetter Ġthan Ġthe Ġ3 - layer ĠPK D Ġbaseline Ġand Ġare Ġcompetitive Ġwith Ġthe Ġlarger Ġ6 - layer Ġbaseline Ġon Ġtask Ġaccuracy Ġwhile Ġbeing Ġnearly Ġ5 Ġtimes Ġas Ġsmall . </s> Another Ġobservation Ġwe Ġmake Ġis Ġthat Ġthe Ġperformance Ġdrop Ġfrom Ġ192 - dimensional Ġto Ġ96 - dimensional Ġmodels Ġis Ġminimal Ġ( less Ġthan Ġ2 % Ġfor Ġmost Ġtasks ). ĠFor Ġthe ĠMR PC Ġtask , Ġin Ġfact , Ġthe Ġ96 - dimensional Ġmodel Ġtrained Ġwith Ġdual Ġtraining Ġachieves Ġan Ġaccuracy Ġof Ġ80 . 5 %, Ġwhich Ġis Ġhigher Ġthan Ġeven Ġthe ĠPK D Ġ6 - layer Ġbaseline Ġwith Ġnearly Ġ12 Ġtimes Ġas Ġmany Ġparameters . ĠFinally , Ġour Ġhighly - comp ressed Ġ48 - dimensional Ġmodels Ġalso Ġperform Ġrespect ably : Ġthe Ġbest Ġ48 - dimensional Ġmodels Ġare Ġin Ġa Ġsimilar Ġperformance Ġbracket Ġas Ġthe Ġ3 - layer ĠPK D Ġmodel , Ġa Ġmodel Ġ25 Ġtimes Ġlarger Ġby Ġmemory Ġfootprint . </s> Discussion </s> Sh ared Ġprojections Ġand Ġmodel Ġperformance : ĠWe Ġsee Ġthat Ġfor Ġdownstream Ġtask Ġperformance , Ġdual Ġtraining Ġstill Ġconsistently Ġimproves Ġupon Ġthe Ġdirect Ġfine - tun ing Ġapproach Ġfor Ġvirtually Ġall Ġexperiments . ĠThe Ġeffect Ġof Ġshared Ġvariable Ġprojection , Ġhowever , Ġis Ġless Ġpronounced , Ġwith Ġconsistent Ġimprovements Ġvisible Ġonly Ġfor ĠMR PC Ġand Ġfor Ġthe Ġ48 - dimensional Ġmodels Ġi . e . Ġthe Ġsmallest Ġdataset Ġand Ġmodels Ġrespectively Ġin Ġour Ġexperiments . ĠThis Ġalign s Ġwith Ġour Ġintuition Ġfor Ġvariable Ġprojection Ġas Ġa Ġmore Ġdirect Ġway Ġto Ġprovide Ġa Ġtraining Ġsignal Ġfrom Ġthe Ġteacher Ġmodel Ġintern als , Ġwhich Ġcan Ġassume Ġmore Ġimportance Ġfor Ġa Ġlow - data Ġor Ġsmall - model Ġscenario . ĠHowever , Ġfor Ġlarger Ġmodels Ġand Ġmore Ġdata , Ġthe Ġlinear Ġprojection Ġof Ġparameters Ġmay Ġbe Ġreducing Ġthe Ġdegrees Ġof Ġfreedom Ġavailable Ġto Ġthe Ġmodel , Ġsince Ġlinear Ġprojection Ġis Ġa Ġfairly Ġsimple Ġfunction Ġto Ġalign Ġthe Ġteacher Ġand Ġstudent Ġparameter Ġspaces . </s> A Ġrelated Ġcomparison Ġof Ġinterest Ġis Ġbetween Ġup - project ion Ġand Ġdown - project ion Ġof Ġthe Ġmodel Ġvariables : Ġwe Ġnote Ġup - project ion Ġdoes Ġvisibly Ġbetter Ġon Ġthe Ġlanguage Ġmodeling Ġtask Ġand Ġslightly Ġbetter Ġon Ġthe Ġdownstream Ġtasks . ĠThe Ġparameters Ġof Ġa Ġwell - trained Ġteacher Ġmodel Ġrepresent Ġa Ġhigh - quality Ġlocal Ġminimum Ġin Ġthe Ġteacher Ġspace , Ġwhich Ġmay Ġbe Ġeasier Ġto Ġsearch Ġfor Ġduring Ġup - project ion . </s> V oc abulary Ġsize Ġtrade offs : ĠIssues Ġwith Ġinput Ġvocabulary Ġsize Ġare Ġpeculiar Ġto Ġproblems Ġin Ġnatural Ġlanguage Ġprocessing : Ġthey Ġdo Ġnot Ġalways Ġapply Ġto Ġother Ġareas Ġsuch Ġas Ġcomputer Ġvision , Ġwhere Ġa Ġsmall Ġfixed Ġnumber Ġof Ġsymbols Ġcan Ġencode Ġmost Ġinputs . ĠThere Ġhas Ġbeen Ġsome Ġwork Ġon Ġreducing Ġinput Ġvocabulary Ġsizes Ġfor ĠN LP , Ġbut Ġtypically Ġnot Ġtargeting Ġmodel Ġcompression . ĠOne Ġconcern Ġwith Ġreducing Ġthe Ġvoc ab ular ies Ġof ĠN LP Ġmodels Ġis Ġit Ġpushes Ġthe Ġaverage Ġtoken ized Ġsequence Ġlengths Ġup , Ġmaking Ġmodel Ġtraining Ġharder . ĠIn Ġthis Ġwork , Ġhowever , Ġwe Ġconsider Ġclassification Ġtasks Ġon Ġshorter Ġtexts , Ġwhich Ġare Ġnot Ġas Ġaffected Ġby Ġinput Ġsequence Ġlengths Ġas , Ġsay , Ġtasks Ġsuch Ġas Ġmachine Ġtranslation Ġare . ĠFurthermore , Ġmany Ġreal - world Ġapplications Ġrev olve Ġaround Ġshort Ġtext Ġinputs , Ġwhich Ġis Ġwhy Ġa Ġbetter Ġtrade - off Ġbetween Ġvocabulary Ġsize Ġand Ġsequence Ġlengths Ġmay Ġbe Ġworthwhile Ġfor Ġsuch Ġapplications . </s> Order Ġof Ġdist illation Ġand Ġfine - tun ing : ĠMost Ġof Ġthe Ġexisting Ġwork Ġon Ġdist illing Ġlanguage Ġmodels Ġsuch Ġas ĠB ERT Ġand Ġreporting Ġresults Ġon Ġdownstream Ġtasks , Ġincluding Ġsome Ġof Ġthe Ġbas elines Ġin Ġthis Ġwork , Ġfirst Ġfine - t une Ġa Ġteacher Ġmodel Ġon Ġthe Ġdownstream Ġtasks , Ġand Ġthen Ġdist ill Ġthis Ġmodel . ĠOur Ġgoal Ġin Ġthis Ġwork , Ġhowever , Ġis Ġto Ġexplore Ġthe Ġlimits Ġto Ġwhich ĠB ERT 's Ġlanguage Ġmodeling Ġcapacity Ġitself , Ġand Ġhow Ġmuch Ġof Ġit Ġis Ġdriven Ġby Ġits Ġlarge ĠWord P iece Ġvocabulary . ĠWe Ġleave Ġexperiments Ġon Ġdist illing Ġfine - tun ed Ġteacher Ġmodels , Ġpotentially Ġyielding Ġbetter Ġresults Ġon Ġdownstream Ġtasks , Ġto Ġfuture Ġwork . </s> Conclusion </s> We Ġproposed Ġtwo Ġnovel Ġideas Ġto Ġimprove Ġthe Ġeffectiveness Ġof Ġknowledge Ġdist illation Ġfor ĠB ERT , Ġfocusing Ġon Ġusing Ġa Ġsignificantly Ġsmaller Ġvocabulary , Ġas Ġwell Ġas Ġsmaller Ġembed ding Ġand Ġhidden Ġdimensions Ġfor Ġthe Ġstudent ĠB ERT Ġlanguage Ġmodels . ĠOur Ġdual Ġtraining Ġmechanism Ġencourages Ġimplicit Ġalignment Ġof Ġthe Ġteacher Ġand Ġstudent ĠWord P iece Ġembed d ings , Ġand Ġshared Ġvariable Ġprojection Ġallows Ġfor Ġthe Ġfaster Ġand Ġdirect Ġlayer - wise Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent ĠB ERT Ġmodel . ĠComb ining Ġthe Ġtwo Ġtechniques , Ġwe Ġtrained Ġa Ġseries Ġof Ġhighly - comp ressed Ġ12 - layer Ġstudent ĠB ERT Ġmodels . ĠExper iments Ġon Ġthese Ġmodels , Ġto Ġevaluate Ġboth Ġgeneralized Ġlanguage Ġperspective Ġand Ġfour Ġstandardized Ġdownstream Ġtasks , Ġdemonstrate Ġthe Ġeffectiveness Ġof Ġour Ġproposed Ġmethods Ġon Ġboth Ġmodel Ġaccuracy Ġand Ġcompression Ġefficiency . </s> One Ġfuture Ġdirection Ġof Ġinterest Ġis Ġto Ġcombine Ġour Ġapproach Ġwith Ġexisting Ġwork Ġto Ġreduce Ġthe Ġnumber Ġof Ġlayers Ġin Ġthe Ġstudent Ġmodels Ġand Ġexplore Ġother Ġapproaches Ġsuch Ġas Ġlow - rank Ġmatrix Ġfactor ization Ġto Ġtransfer Ġmodel Ġparameters Ġfrom Ġthe Ġteacher Ġspace Ġto Ġthe Ġstudent Ġspace . ĠIn Ġaddition , Ġtaking Ġinto Ġaccount Ġthe Ġfrequency Ġdistribution Ġof Ġthe ĠWord P iece Ġtokens Ġwhile Ġtraining Ġembed d ings Ġmay Ġhelp Ġoptimize Ġthe Ġmodel Ġsize Ġfurther .
Introduction Recently, contextual-aware language models such as ELMo BIBREF0, GPT BIBREF1, BERT BIBREF2 and XLNet BIBREF3 have shown to greatly outperform traditional word embedding models including Word2Vec BIBREF4 and GloVe BIBREF5 in a variety of NLP tasks. These pre-trained language models, when fine-tuned on downstream language understanding tasks such as sentiment classification BIBREF6, natural language inference BIBREF7 and reading comprehension BIBREF8, BIBREF9, have achieved state-of-the-art performance. However, the large number of parameters in these models, often above hundreds of millions, makes it impossible to host them on resource-constrained tasks such as doing real-time inference on mobile and edge devices. Besides utilizing model quantization techniques BIBREF10, BIBREF11 which aim to reduce the floating-point accuracy of the parameters, significant recent research has focused on knowledge distillation BIBREF12, BIBREF13 techniques. Here, the goal is to train a small-footprint student model by borrowing knowledge, such as through a soft predicted label distribution, from a larger pre-trained teacher model. However, a significant bottleneck that has been overlooked by previous efforts is the input vocabulary size and its corresponding word embedding matrix, often accounting for a significant proportion of all model parameters. For instance, the embedding table of the BERTBASE model, comprising over 30K WordPiece tokens BIBREF14, accounts for over $21\%$ of the model size. While there has been existing work on reducing NLP model vocabulary sizes BIBREF15, distillation techniques cannot utilize these, since they require the student and teacher models to share the same vocabulary and output space. This profoundly limits their potential to further reduce model sizes. We present two novel ideas to improve the effectiveness of knowledge distillation, in particular for BERT, with the focus on bringing down model sizes to as much as a few mega-bytes. Our model is among the first to propose to use a significantly smaller vocabulary for the student model learned during distillation. In addition, instead of distilling solely on the teacher model's final-layer outputs, our model leverages layer-wise teacher model parameters to directly optimize the parameters of the corresponding layers in the student model. Specifically, our contributions are: [leftmargin=*] Dual Training: Our teacher and student models have different vocabularies and incompatible tokenizations for the same sequence. To address this during distillation, we feed the teacher model a mix of teacher vocabulary-tokenized and student vocabulary-tokenized words within a single sequence. Coupled with the masked language modeling task, this encourages an implicit alignment of the teacher and student WordPiece embeddings, since the student vocabulary embedding may be used as context to predict a word tokenized by the teacher vocabulary and vice versa. Shared Variable Projections: To minimize the loss of information from reducing the hidden state dimension, we introduce a separate loss to align the teacher and student models' trainable variables. This allows for more direct layer-wise transfer of knowledge to the student model. Using the combination of dual training and shared variable projections, we train a 12-layer highly-compressed student BERT model, achieving a maximum compression ratio of $\sim $61.94x (with 48 dimension size) compared to the teacher BERTBASE model. We conduct experiments for measuring both generalized language modeling perspective and for downstream tasks, demonstrating competitive performance with high compression ratios for both families of tasks. Related Work Research in neural network model compression has been concomitant with the rise in popularity of neural networks themselves, since these models have often been memory-intensive for the hardware of their time. Work in model compression for NLP applications falls broadly into four categories: matrix approximation, parameter pruning/sharing, weight quantization and knowledge distillation. A family of approaches BIBREF16, BIBREF17 seeks to compress the matrix parameters of the models by low-rank approximation i.e. the full-rank matrix parameter is approximated using multiple low-rank matrices, thereby reducing the effective number of model parameters. Another line of work explores parameter pruning and sharing-based methods BIBREF18, BIBREF19, BIBREF20, BIBREF21, which explore the redundancy in model parameters and try to remove redundant weights as well as neurons, for a variety of neural network architectures. Model weight quantization techniques BIBREF22, BIBREF23, BIBREF24, BIBREF25 focus on mapping model weights to lower-precision integers and floating-point numbers. These can be especially effective with hardware supporting efficient low-precision calculations. More recently, BIBREF26 apply quantization to BERT-based transformer models. Knowledge distillation BIBREF12, BIBREF13 differs from the other discussed approaches: the smaller student model may be parametrized differently from the bigger teacher model, affording more modeling freedom. Teaching a student model to match the soft output label distributions from a larger model alongside the hard ground-truth distribution works well for many tasks, such as machine translation BIBREF27 and language modeling BIBREF28. Not limited to the teacher model outputs, some approaches perform knowledge distillation via attention transfer BIBREF29, or via feature maps or intermediate model outputs BIBREF30, BIBREF31, BIBREF32. More relevant to current work, BIBREF33 and BIBREF34 employ variants of these techniques to BERT model compression by reducing the number of transformer layers. However, as explained before, these approaches are not immediately applicable to our setting due to incompatible teacher and student model vocabularies, and do not focus sufficiently on the embedding matrix size BIBREF35. Methodology Our knowledge distillation approach is centered around reducing the number of WordPiece tokens in the model vocabulary. In this section, we first discuss the rationale behind this reduction and the challenges it introduces, followed by our techniques, namely dual training and shared projection. Methodology ::: Optimal Subword Embeddings via Knowledge Distillation We follow the general knowledge distillation paradigm of training a small student model from a large teacher model. Our teacher model is a 12-layer uncased BERTBASE, trained with 30522 WordPiece tokens and 768-dimensional embeddings and hidden states. We denote the teacher model parameters by $\theta _{t}$. Our student model consists of an equal number of transformer layers with parameters denoted by $\theta _{s}$, but with a smaller vocabulary as well as embedding/hidden dimensions, illustrated in Figure FIGREF4. Using the same WordPiece algorithm and training corpus as BERT, we obtain a vocabulary of 4928 WordPieces, which we use for the student model. WordPiece tokens BIBREF14 are sub-word units obtained by applying a greedy segmentation algorithm to the training corpus: a desired number (say, $D$) of WordPieces are chosen such that the segmented corpus is minimal in the number of WordPieces used. A cursory look at both vocabularies reveals that $93.9\%$ of the WordPieces in the student vocabulary also exist in the teacher vocabulary, suggesting room for a reduction in the WordPiece vocabulary size from 30K tokens. Since we seek to train a general-purpose student language model, we elect to reuse the teacher model's original training objective to optimize the student model, i.e., masked language modeling and next sentence prediction, before any fine-tuning. In the former task, words in context are randomly masked, and the language model needs to predict those words given the masked context. In the latter task, given a pair of sentences, the language model predicts whether the pair is consistent. However, since the student vocabulary is not a complete subset of the teacher vocabulary, the two vocabularies may tokenize the same words differently. As a result, the outputs of the teacher and student model for the masked language modeling task may not align. Even with the high overlap between the two vocabularies, the need to train the student embedding from scratch, and the change in embedding dimension precludes existing knowledge distillation techniques, which rely on the alignment of both models' output spaces. As a result, we explore two alternative approaches that enable implicit transfer of knowledge to the student model, which we describe below. Methodology ::: Dual Training During distillation, for a given training sequence input to the teacher model, we propose to mix the teacher and student vocabularies by randomly selecting (with a probability $p_{DT}$, a hyperparameter) tokens from the sequence to segment using the student vocabulary, with the other tokens segmented using the teacher vocabulary. As illustrated in Figure FIGREF4, given the input context [ `I', `like', `machine', `learning'], the words `I' and `machine' are segmented using the teacher vocabulary (in green), while `like' and `learning' are segmented using the student vocabulary (in blue). Similar to cross-lingual training in BIBREF36, this encourages alignment of the representations for the same word as per the teacher and student vocabularies. This is effected through the masked language modeling task: the model now needs to learn to predict words from the student vocabulary using context words segmented using the teacher vocabulary, and vice versa. The expectation is that the student embeddings can be learned effectively this way from the teacher embeddings as well as model parameters $\theta _{t}$. Note that we perform dual training only for the teacher model inputs: the student model receives words segmented exclusively using the student vocabulary. Also, during masked language modeling, the model uses different softmax layers for the teacher and the student vocabularies depending on which one was used to segment the word in question. Methodology ::: Shared Projections Relying solely on teacher model outputs to train the student model may not generalize well BIBREF34. Therefore, some approaches utilize and try to align the student model's intermediate predictions to those of the teacher BIBREF30. In our setting, however, since the student and teacher model output spaces are not identical, intermediate model outputs may prove hard to align. Instead, we seek to directly minimize the loss of information from the teacher model parameters $\theta _{t}$ to the student parameters $\theta _{s}$ with smaller dimensions. We achieve this by projecting the model parameters into the same space, to encourage alignment. More specifically, as in Figure FIGREF4, we project each trainable variable in $\theta _{t}$ to the same shape as the corresponding variable in $\theta _{s}$. For example, for all the trainable variables $\theta _{t}$ with shape $768\times 768$, we learn two projection matrices $\mathbf {U}\in \mathbb {R}^{d\times 768}$ and $\mathbf {V}\in \mathbb {R}^{768\times d}$ to project them into the corresponding space of the student model variable $\theta _{t}^\prime $, where $d$ is the student model's hidden dimension. $\mathbf {U}$ and $\mathbf {V}$ are common to all BERT model parameters of that dimensionality; in addition, $\mathbf {U}$ and $\mathbf {V}$ are not needed for fine-tuning or inference after distillation. In order to align the student variable and the teacher variable's projection, we introduce a separate mean square error loss defined in Equation DISPLAY_FORM7, where $\downarrow $ stands for down projection (since the projection is to a lower dimension). The above loss function aligns the trainable variables in the student space. Alternatively, we can project trainable variables in $\theta _{s}$ to the same shape as in $\theta _{t}$. This way, the loss function in Equation DISPLAY_FORM8, ($\uparrow $ denotes up projection) can compare the trainable variables in the teacher space. Methodology ::: Optimization Objective Our final loss function includes, in addition to an optional projection loss, masked language modeling cross-entropy losses for the student as well as the teacher models, since the teacher model is trained with dual-vocabulary inputs and is not static. $P(y_i=c|\theta _{s})$ and $P(y_i=c|\theta _{t})$ denote the student and teacher model prediction probabilities for class c respectively, and $\mathbb {1}$ denotes an indicator function. Equations DISPLAY_FORM10 and below define the final loss $L_{final}$, where $\epsilon $ is a hyperparameter. Experiments To evaluate our knowledge distillation approach, we design two classes of experiments. First, we evaluate the distilled student language models using the masked word prediction task on an unseen evaluation corpus, for an explicit evaluation of the language model. Second, we fine-tune the language model by adding a task-specific affine layer on top of the student language model outputs, on a suite of downstream sentence and sentence pair classification tasks. This is meant to be an implicit evaluation of the quality of the representations learned by the student language model. We describe these experiments, along with details on training, implementation and our baselines below. Experiments ::: Language Model Training During the distillation of the teacher BERT model to train the student BERT language model, we utilize the same corpus as was used to train the teacher i.e. BooksCorpus BIBREF37 and English Wikipedia, with whitespaces used tokenize the text into words. We only use the masked language modeling task to calculate the overall distillation loss from Section SECREF6, since the next sentence prediction loss hurt performance slightly. Dual training is enabled for teacher model inputs, with $p_{DT}$, the probability of segmenting a teacher model input word using the student vocabulary, set to 0.5. For experiments including shared projection, the projection matrices $\mathbf {U}$ and $\mathbf {V}$ utilized Xavier initialization BIBREF38. The loss weight coefficient $\epsilon $ is set to 1 after tuning. It is worth noting that in contrast to a number of existing approaches, we directly distill the teacher BERT language model, not yet fine-tuned on a downstream task, to obtain a student language model that is task-agnostic. For downstream tasks, we fine-tune this distilled student language model. Distillation is carried out on Cloud TPUs in a 4x4 pod configuration (32 TPU cores overall). We optimized the loss using LAMB BIBREF39 for 250K steps, with a learning rate of 0.00125 and batch size of 4096. Depending on the student model dimension, training took between 2-4 days. Experiments ::: Models and Baselines We evaluate three variants of our distilled student models: with only dual training of the teacher and student vocabularies (DualTrain) and with dual training along with down-projection (DualTrain + SharedProjDown) or up-projection (DualTrain + SharedProjUp) of the teacher model parameters. For each of these configurations, we train student models with embedding and hidden dimensions 48, 96 and 192, for 9 total variants, each using a compact 5K-WordPiece vocabulary. Table TABREF14 presents some statistics on these models' sizes: our smallest model contains two orders of magnitude fewer parameters, and requires only 1% floating-point operations when compared to the BERTBASE model. For the language modeling evaluation, we also evaluate a baseline without knowledge distillation (termed NoKD), with a model parameterized identically to the distilled student models but trained directly on the teacher model objective from scratch. For downstream tasks, we compare with NoKD as well as Patient Knowledge Distillation (PKD) from BIBREF34, who distill the 12-layer BERTBASE model into 3 and 6-layer BERT models by using the teacher model's hidden states. Experiments ::: Evaluation Tasks and Datasets For explicit evaluation of the generalized language perspective of the distilled student language models, we use the Reddit dataset BIBREF40 to measure word mask prediction accuracy of the student models, since the language used on Reddit is different from that in the training corpora. The dataset is preprocessed similarly to the training corpora, except we do not need to tokenize it using the teacher vocabulary, since we only run and evaluate the student models. For implicit evaluation on downstream language understanding tasks, we fine-tune and evaluate the distilled student models on three tasks from the GLUE benchmark BIBREF41: [leftmargin=*,topsep=0pt] Stanford Sentiment Treebank (SST-2) BIBREF6, a two-way sentence sentiment classification task with 67K training instances, Microsoft Research Paraphrase Corpus (MRPC) BIBREF42, a two-way sentence pair classification task to identify paraphrases, with 3.7K training instances, and Multi-Genre Natural Language Inference (MNLI) BIBREF7, a three-way sentence pair classification task with 393K training instances, to identify premise-hypothesis relations. There are separate development and test sets for genre-matched and genre-mismatched premise-hypothesis pairs; we tune our models solely on the genre-matched development set. For all downstream task evaluations, we fine-tune for 10 epochs using LAMB with a learning rate of 0.0002 and batch size of 32. Since our language models are trained with a maximum sequence length of 128 tokens, we do not evaluate on reading comprehension datasets such as SQuAD BIBREF8 or RACE BIBREF9, which require models supporting longer sequences. Results Table TABREF20 contains masked word prediction accuracy figures for the different models and the NoKD baseline. We observe that dual training significantly improves over the baseline for all model dimensions, and that both shared projection losses added to dual training further improve the word prediction accuracy. It is interesting to note that for all model dimensions, SharedProjUp projecting into the teacher space outperforms SharedProjDown, significantly so for dimension 48. Expectedly, there is a noticeable performance drop going from 192 to 96 to 48-dimensional hidden state models. Note that because of the differing teacher and student model vocabularies, masked word prediction accuracy for the teacher BERTBASE model is not directly comparable with the student models. Table TABREF21 shows results on the downstream language understanding tasks, as well as model sizes, for our approaches, the BERTBASE teacher model, and the PKD and NoKD baselines. We note that models trained with our proposed approaches perform strongly and consistently improve upon the identically parametrized NoKD baselines, indicating that the dual training and shared projection techniques are effective, without incurring significant losses against the BERTBASE teacher model. Comparing with the PKD baseline, our 192-dimensional models, achieving a higher compression rate than either of the PKD models, perform better than the 3-layer PKD baseline and are competitive with the larger 6-layer baseline on task accuracy while being nearly 5 times as small. Another observation we make is that the performance drop from 192-dimensional to 96-dimensional models is minimal (less than 2% for most tasks). For the MRPC task, in fact, the 96-dimensional model trained with dual training achieves an accuracy of 80.5%, which is higher than even the PKD 6-layer baseline with nearly 12 times as many parameters. Finally, our highly-compressed 48-dimensional models also perform respectably: the best 48-dimensional models are in a similar performance bracket as the 3-layer PKD model, a model 25 times larger by memory footprint. Discussion Shared projections and model performance: We see that for downstream task performance, dual training still consistently improves upon the direct fine-tuning approach for virtually all experiments. The effect of shared variable projection, however, is less pronounced, with consistent improvements visible only for MRPC and for the 48-dimensional models i.e. the smallest dataset and models respectively in our experiments. This aligns with our intuition for variable projection as a more direct way to provide a training signal from the teacher model internals, which can assume more importance for a low-data or small-model scenario. However, for larger models and more data, the linear projection of parameters may be reducing the degrees of freedom available to the model, since linear projection is a fairly simple function to align the teacher and student parameter spaces. A related comparison of interest is between up-projection and down-projection of the model variables: we note up-projection does visibly better on the language modeling task and slightly better on the downstream tasks. The parameters of a well-trained teacher model represent a high-quality local minimum in the teacher space, which may be easier to search for during up-projection. Vocabulary size tradeoffs: Issues with input vocabulary size are peculiar to problems in natural language processing: they do not always apply to other areas such as computer vision, where a small fixed number of symbols can encode most inputs. There has been some work on reducing input vocabulary sizes for NLP, but typically not targeting model compression. One concern with reducing the vocabularies of NLP models is it pushes the average tokenized sequence lengths up, making model training harder. In this work, however, we consider classification tasks on shorter texts, which are not as affected by input sequence lengths as, say, tasks such as machine translation are. Furthermore, many real-world applications revolve around short text inputs, which is why a better trade-off between vocabulary size and sequence lengths may be worthwhile for such applications. Order of distillation and fine-tuning: Most of the existing work on distilling language models such as BERT and reporting results on downstream tasks, including some of the baselines in this work, first fine-tune a teacher model on the downstream tasks, and then distill this model. Our goal in this work, however, is to explore the limits to which BERT's language modeling capacity itself, and how much of it is driven by its large WordPiece vocabulary. We leave experiments on distilling fine-tuned teacher models, potentially yielding better results on downstream tasks, to future work. Conclusion We proposed two novel ideas to improve the effectiveness of knowledge distillation for BERT, focusing on using a significantly smaller vocabulary, as well as smaller embedding and hidden dimensions for the student BERT language models. Our dual training mechanism encourages implicit alignment of the teacher and student WordPiece embeddings, and shared variable projection allows for the faster and direct layer-wise transfer of knowledge to the student BERT model. Combining the two techniques, we trained a series of highly-compressed 12-layer student BERT models. Experiments on these models, to evaluate both generalized language perspective and four standardized downstream tasks, demonstrate the effectiveness of our proposed methods on both model accuracy and compression efficiency. One future direction of interest is to combine our approach with existing work to reduce the number of layers in the student models and explore other approaches such as low-rank matrix factorization to transfer model parameters from the teacher space to the student space. In addition, taking into account the frequency distribution of the WordPiece tokens while training embeddings may help optimize the model size further.
Why are prior knowledge distillation techniques models are ineffective in producing student models with vocabularies different from the original teacher models?  
d087539e6a38c42f0a521ff2173ef42c0733878e
Why Ġare Ġprior Ġknowledge Ġdist illation Ġtechniques Ġmodels Ġare Ġineffective Ġin Ġproducing Ġstudent Ġmodels Ġwith Ġvoc ab ular ies Ġdifferent Ġfrom Ġthe Ġoriginal Ġteacher Ġmodels ? Ġ Ġ
While Ġthere Ġhas Ġbeen Ġexisting Ġwork Ġon Ġreducing ĠN LP Ġmodel Ġvocabulary Ġsizes ĠB IB REF 15 , Ġdist illation Ġtechniques Ġcannot Ġutilize Ġthese , Ġsince Ġthey Ġrequire Ġthe Ġstudent Ġand Ġteacher Ġmodels Ġto Ġshare Ġthe Ġsame Ġvocabulary Ġand Ġoutput Ġspace . ĠThis Ġprofoundly Ġlimits Ġtheir Ġpotential Ġto Ġfurther Ġreduce Ġmodel Ġsizes .
<s> Why Ġare Ġprior Ġknowledge Ġdist illation Ġtechniques Ġmodels Ġare Ġineffective Ġin Ġproducing Ġstudent Ġmodels Ġwith Ġvoc ab ular ies Ġdifferent Ġfrom Ġthe Ġoriginal Ġteacher Ġmodels ? Ġ Ġ </s> Introduction </s> Recently , Ġcontextual - aware Ġlanguage Ġmodels Ġsuch Ġas ĠEL Mo ĠB IB REF 0 , ĠG PT ĠB IB REF 1 , ĠB ERT ĠB IB REF 2 Ġand ĠXL Net ĠB IB REF 3 Ġhave Ġshown Ġto Ġgreatly Ġoutper form Ġtraditional Ġword Ġembed ding Ġmodels Ġincluding ĠWord 2 V ec ĠB IB REF 4 Ġand ĠGl o Ve ĠB IB REF 5 Ġin Ġa Ġvariety Ġof ĠN LP Ġtasks . ĠThese Ġpre - trained Ġlanguage Ġmodels , Ġwhen Ġfine - tun ed Ġon Ġdownstream Ġlanguage Ġunderstanding Ġtasks Ġsuch Ġas Ġsentiment Ġclassification ĠB IB REF 6 , Ġnatural Ġlanguage Ġinference ĠB IB REF 7 Ġand Ġreading Ġcomprehension ĠB IB REF 8 , ĠB IB REF 9 , Ġhave Ġachieved Ġstate - of - the - art Ġperformance . ĠHowever , Ġthe Ġlarge Ġnumber Ġof Ġparameters Ġin Ġthese Ġmodels , Ġoften Ġabove Ġhundreds Ġof Ġmillions , Ġmakes Ġit Ġimpossible Ġto Ġhost Ġthem Ġon Ġresource - con str ained Ġtasks Ġsuch Ġas Ġdoing Ġreal - time Ġinference Ġon Ġmobile Ġand Ġedge Ġdevices . </s> Besides Ġutilizing Ġmodel Ġquant ization Ġtechniques ĠB IB REF 10 , ĠB IB REF 11 Ġwhich Ġaim Ġto Ġreduce Ġthe Ġfloating - point Ġaccuracy Ġof Ġthe Ġparameters , Ġsignificant Ġrecent Ġresearch Ġhas Ġfocused Ġon Ġknowledge Ġdist illation ĠB IB REF 12 , ĠB IB REF 13 Ġtechniques . ĠHere , Ġthe Ġgoal Ġis Ġto Ġtrain Ġa Ġsmall - foot print Ġstudent Ġmodel Ġby Ġborrowing Ġknowledge , Ġsuch Ġas Ġthrough Ġa Ġsoft Ġpredicted Ġlabel Ġdistribution , Ġfrom Ġa Ġlarger Ġpre - trained Ġteacher Ġmodel . </s> However , Ġa Ġsignificant Ġbottleneck Ġthat Ġhas Ġbeen Ġoverlooked Ġby Ġprevious Ġefforts Ġis Ġthe Ġinput Ġvocabulary Ġsize Ġand Ġits Ġcorresponding Ġword Ġembed ding Ġmatrix , Ġoften Ġaccounting Ġfor Ġa Ġsignificant Ġproportion Ġof Ġall Ġmodel Ġparameters . ĠFor Ġinstance , Ġthe Ġembed ding Ġtable Ġof Ġthe ĠB ERT B ASE Ġmodel , Ġcomprising Ġover Ġ30 K ĠWord P iece Ġtokens ĠB IB REF 14 , Ġaccounts Ġfor Ġover Ġ$ 21 \ % $ Ġof Ġthe Ġmodel Ġsize . ĠWhile Ġthere Ġhas Ġbeen Ġexisting Ġwork Ġon Ġreducing ĠN LP Ġmodel Ġvocabulary Ġsizes ĠB IB REF 15 , Ġdist illation Ġtechniques Ġcannot Ġutilize Ġthese , Ġsince Ġthey Ġrequire Ġthe Ġstudent Ġand Ġteacher Ġmodels Ġto Ġshare Ġthe Ġsame Ġvocabulary Ġand Ġoutput Ġspace . ĠThis Ġprofoundly Ġlimits Ġtheir Ġpotential Ġto Ġfurther Ġreduce Ġmodel Ġsizes . </s> We Ġpresent Ġtwo Ġnovel Ġideas Ġto Ġimprove Ġthe Ġeffectiveness Ġof Ġknowledge Ġdist illation , Ġin Ġparticular Ġfor ĠB ERT , Ġwith Ġthe Ġfocus Ġon Ġbringing Ġdown Ġmodel Ġsizes Ġto Ġas Ġmuch Ġas Ġa Ġfew Ġmega - bytes . ĠOur Ġmodel Ġis Ġamong Ġthe Ġfirst Ġto Ġpropose Ġto Ġuse Ġa Ġsignificantly Ġsmaller Ġvocabulary Ġfor Ġthe Ġstudent Ġmodel Ġlearned Ġduring Ġdist illation . ĠIn Ġaddition , Ġinstead Ġof Ġdist illing Ġsolely Ġon Ġthe Ġteacher Ġmodel 's Ġfinal - layer Ġoutputs , Ġour Ġmodel Ġlever ages Ġlayer - wise Ġteacher Ġmodel Ġparameters Ġto Ġdirectly Ġoptimize Ġthe Ġparameters Ġof Ġthe Ġcorresponding Ġlayers Ġin Ġthe Ġstudent Ġmodel . ĠSpecifically , Ġour Ġcontributions Ġare : </s> [ left margin = * ] </s> Dual ĠTraining : ĠOur Ġteacher Ġand Ġstudent Ġmodels Ġhave Ġdifferent Ġvoc ab ular ies Ġand Ġincompatible Ġtoken izations Ġfor Ġthe Ġsame Ġsequence . ĠTo Ġaddress Ġthis Ġduring Ġdist illation , Ġwe Ġfeed Ġthe Ġteacher Ġmodel Ġa Ġmix Ġof Ġteacher Ġvocabulary - token ized Ġand Ġstudent Ġvocabulary - token ized Ġwords Ġwithin Ġa Ġsingle Ġsequence . ĠCou pled Ġwith Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask , Ġthis Ġencourages Ġan Ġimplicit Ġalignment Ġof Ġthe Ġteacher Ġand Ġstudent ĠWord P iece Ġembed d ings , Ġsince Ġthe Ġstudent Ġvocabulary Ġembed ding Ġmay Ġbe Ġused Ġas Ġcontext Ġto Ġpredict Ġa Ġword Ġtoken ized Ġby Ġthe Ġteacher Ġvocabulary Ġand Ġvice Ġversa . </s> Sh ared ĠVariable ĠProject ions : ĠTo Ġminimize Ġthe Ġloss Ġof Ġinformation Ġfrom Ġreducing Ġthe Ġhidden Ġstate Ġdimension , Ġwe Ġintroduce Ġa Ġseparate Ġloss Ġto Ġalign Ġthe Ġteacher Ġand Ġstudent Ġmodels ' Ġtrain able Ġvariables . ĠThis Ġallows Ġfor Ġmore Ġdirect Ġlayer - wise Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent Ġmodel . </s> Using Ġthe Ġcombination Ġof Ġdual Ġtraining Ġand Ġshared Ġvariable Ġprojections , Ġwe Ġtrain Ġa Ġ12 - layer Ġhighly - comp ressed Ġstudent ĠB ERT Ġmodel , Ġachieving Ġa Ġmaximum Ġcompression Ġratio Ġof Ġ$\ sim Ġ$ 61 . 94 x Ġ( with Ġ48 Ġdimension Ġsize ) Ġcompared Ġto Ġthe Ġteacher ĠB ERT B ASE Ġmodel . ĠWe Ġconduct Ġexperiments Ġfor Ġmeasuring Ġboth Ġgeneralized Ġlanguage Ġmodeling Ġperspective Ġand Ġfor Ġdownstream Ġtasks , Ġdemonstrating Ġcompetitive Ġperformance Ġwith Ġhigh Ġcompression Ġratios Ġfor Ġboth Ġfamilies Ġof Ġtasks . </s> Related ĠWork </s> Research Ġin Ġneural Ġnetwork Ġmodel Ġcompression Ġhas Ġbeen Ġcon com itant Ġwith Ġthe Ġrise Ġin Ġpopularity Ġof Ġneural Ġnetworks Ġthemselves , Ġsince Ġthese Ġmodels Ġhave Ġoften Ġbeen Ġmemory - intensive Ġfor Ġthe Ġhardware Ġof Ġtheir Ġtime . ĠWork Ġin Ġmodel Ġcompression Ġfor ĠN LP Ġapplications Ġfalls Ġbroadly Ġinto Ġfour Ġcategories : Ġmatrix Ġapproximation , Ġparameter Ġpr uning / sharing , Ġweight Ġquant ization Ġand Ġknowledge Ġdist illation . </s> A Ġfamily Ġof Ġapproaches ĠB IB REF 16 , ĠB IB REF 17 Ġseeks Ġto Ġcompress Ġthe Ġmatrix Ġparameters Ġof Ġthe Ġmodels Ġby Ġlow - rank Ġapproximation Ġi . e . Ġthe Ġfull - rank Ġmatrix Ġparameter Ġis Ġapprox imated Ġusing Ġmultiple Ġlow - rank Ġmat rices , Ġthereby Ġreducing Ġthe Ġeffective Ġnumber Ġof Ġmodel Ġparameters . ĠAnother Ġline Ġof Ġwork Ġexplores Ġparameter Ġpr uning Ġand Ġsharing - based Ġmethods ĠB IB REF 18 , ĠB IB REF 19 , ĠB IB REF 20 , ĠB IB REF 21 , Ġwhich Ġexplore Ġthe Ġredundancy Ġin Ġmodel Ġparameters Ġand Ġtry Ġto Ġremove Ġredundant Ġweights Ġas Ġwell Ġas Ġneurons , Ġfor Ġa Ġvariety Ġof Ġneural Ġnetwork Ġarchitectures . </s> Model Ġweight Ġquant ization Ġtechniques ĠB IB REF 22 , ĠB IB REF 23 , ĠB IB REF 24 , ĠB IB REF 25 Ġfocus Ġon Ġmapping Ġmodel Ġweights Ġto Ġlower - pre cision Ġintegers Ġand Ġfloating - point Ġnumbers . ĠThese Ġcan Ġbe Ġespecially Ġeffective Ġwith Ġhardware Ġsupporting Ġefficient Ġlow - pre cision Ġcalculations . ĠMore Ġrecently , ĠB IB REF 26 Ġapply Ġquant ization Ġto ĠB ERT - based Ġtransformer Ġmodels . </s> Know ledge Ġdist illation ĠB IB REF 12 , ĠB IB REF 13 Ġdiffers Ġfrom Ġthe Ġother Ġdiscussed Ġapproaches : Ġthe Ġsmaller Ġstudent Ġmodel Ġmay Ġbe Ġparam et ri zed Ġdifferently Ġfrom Ġthe Ġbigger Ġteacher Ġmodel , Ġaff ording Ġmore Ġmodeling Ġfreedom . ĠTeaching Ġa Ġstudent Ġmodel Ġto Ġmatch Ġthe Ġsoft Ġoutput Ġlabel Ġdistributions Ġfrom Ġa Ġlarger Ġmodel Ġalongside Ġthe Ġhard Ġground - truth Ġdistribution Ġworks Ġwell Ġfor Ġmany Ġtasks , Ġsuch Ġas Ġmachine Ġtranslation ĠB IB REF 27 Ġand Ġlanguage Ġmodeling ĠB IB REF 28 . </s> Not Ġlimited Ġto Ġthe Ġteacher Ġmodel Ġoutputs , Ġsome Ġapproaches Ġperform Ġknowledge Ġdist illation Ġvia Ġattention Ġtransfer ĠB IB REF 29 , Ġor Ġvia Ġfeature Ġmaps Ġor Ġintermediate Ġmodel Ġoutputs ĠB IB REF 30 , ĠB IB REF 31 , ĠB IB REF 32 . ĠMore Ġrelevant Ġto Ġcurrent Ġwork , ĠB IB REF 33 Ġand ĠB IB REF 34 Ġemploy Ġvariants Ġof Ġthese Ġtechniques Ġto ĠB ERT Ġmodel Ġcompression Ġby Ġreducing Ġthe Ġnumber Ġof Ġtransformer Ġlayers . ĠHowever , Ġas Ġexplained Ġbefore , Ġthese Ġapproaches Ġare Ġnot Ġimmediately Ġapplicable Ġto Ġour Ġsetting Ġdue Ġto Ġincompatible Ġteacher Ġand Ġstudent Ġmodel Ġvoc ab ular ies , Ġand Ġdo Ġnot Ġfocus Ġsufficiently Ġon Ġthe Ġembed ding Ġmatrix Ġsize ĠB IB REF 35 . </s> Method ology </s> Our Ġknowledge Ġdist illation Ġapproach Ġis Ġcentered Ġaround Ġreducing Ġthe Ġnumber Ġof ĠWord P iece Ġtokens Ġin Ġthe Ġmodel Ġvocabulary . ĠIn Ġthis Ġsection , Ġwe Ġfirst Ġdiscuss Ġthe Ġrationale Ġbehind Ġthis Ġreduction Ġand Ġthe Ġchallenges Ġit Ġintroduces , Ġfollowed Ġby Ġour Ġtechniques , Ġnamely Ġdual Ġtraining Ġand Ġshared Ġprojection . </s> Method ology Ġ: :: ĠOpt imal ĠSub word ĠEmb edd ings Ġvia ĠKnowledge ĠDist illation </s> We Ġfollow Ġthe Ġgeneral Ġknowledge Ġdist illation Ġparadigm Ġof Ġtraining Ġa Ġsmall Ġstudent Ġmodel Ġfrom Ġa Ġlarge Ġteacher Ġmodel . ĠOur Ġteacher Ġmodel Ġis Ġa Ġ12 - layer Ġunc ased ĠB ERT B ASE , Ġtrained Ġwith Ġ305 22 ĠWord P iece Ġtokens Ġand Ġ768 - dimensional Ġembed d ings Ġand Ġhidden Ġstates . ĠWe Ġdenote Ġthe Ġteacher Ġmodel Ġparameters Ġby Ġ$\ the ta Ġ_ { t } $. ĠOur Ġstudent Ġmodel Ġconsists Ġof Ġan Ġequal Ġnumber Ġof Ġtransformer Ġlayers Ġwith Ġparameters Ġden oted Ġby Ġ$\ the ta Ġ_ { s } $, Ġbut Ġwith Ġa Ġsmaller Ġvocabulary Ġas Ġwell Ġas Ġembed ding / hidden Ġdimensions , Ġillustrated Ġin ĠFigure ĠFIG REF 4 . ĠUsing Ġthe Ġsame ĠWord P iece Ġalgorithm Ġand Ġtraining Ġcorpus Ġas ĠB ERT , Ġwe Ġobtain Ġa Ġvocabulary Ġof Ġ49 28 ĠWord Pie ces , Ġwhich Ġwe Ġuse Ġfor Ġthe Ġstudent Ġmodel . </s> Word P iece Ġtokens ĠB IB REF 14 Ġare Ġsub - word Ġunits Ġobtained Ġby Ġapplying Ġa Ġgreedy Ġsegment ation Ġalgorithm Ġto Ġthe Ġtraining Ġcorpus : Ġa Ġdesired Ġnumber Ġ( say , Ġ$ D $ ) Ġof ĠWord Pie ces Ġare Ġchosen Ġsuch Ġthat Ġthe Ġsegment ed Ġcorpus Ġis Ġminimal Ġin Ġthe Ġnumber Ġof ĠWord Pie ces Ġused . ĠA Ġcurs ory Ġlook Ġat Ġboth Ġvoc ab ular ies Ġreveals Ġthat Ġ$ 93 . 9 \ % $ Ġof Ġthe ĠWord Pie ces Ġin Ġthe Ġstudent Ġvocabulary Ġalso Ġexist Ġin Ġthe Ġteacher Ġvocabulary , Ġsuggesting Ġroom Ġfor Ġa Ġreduction Ġin Ġthe ĠWord P iece Ġvocabulary Ġsize Ġfrom Ġ30 K Ġtokens . </s> Since Ġwe Ġseek Ġto Ġtrain Ġa Ġgeneral - purpose Ġstudent Ġlanguage Ġmodel , Ġwe Ġelect Ġto Ġreuse Ġthe Ġteacher Ġmodel 's Ġoriginal Ġtraining Ġobjective Ġto Ġoptimize Ġthe Ġstudent Ġmodel , Ġi . e ., Ġmasked Ġlanguage Ġmodeling Ġand Ġnext Ġsentence Ġprediction , Ġbefore Ġany Ġfine - tun ing . ĠIn Ġthe Ġformer Ġtask , Ġwords Ġin Ġcontext Ġare Ġrandomly Ġmasked , Ġand Ġthe Ġlanguage Ġmodel Ġneeds Ġto Ġpredict Ġthose Ġwords Ġgiven Ġthe Ġmasked Ġcontext . ĠIn Ġthe Ġlatter Ġtask , Ġgiven Ġa Ġpair Ġof Ġsentences , Ġthe Ġlanguage Ġmodel Ġpredicts Ġwhether Ġthe Ġpair Ġis Ġconsistent . </s> However , Ġsince Ġthe Ġstudent Ġvocabulary Ġis Ġnot Ġa Ġcomplete Ġsubset Ġof Ġthe Ġteacher Ġvocabulary , Ġthe Ġtwo Ġvoc ab ular ies Ġmay Ġtoken ize Ġthe Ġsame Ġwords Ġdifferently . ĠAs Ġa Ġresult , Ġthe Ġoutputs Ġof Ġthe Ġteacher Ġand Ġstudent Ġmodel Ġfor Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask Ġmay Ġnot Ġalign . ĠEven Ġwith Ġthe Ġhigh Ġoverlap Ġbetween Ġthe Ġtwo Ġvoc ab ular ies , Ġthe Ġneed Ġto Ġtrain Ġthe Ġstudent Ġembed ding Ġfrom Ġscratch , Ġand Ġthe Ġchange Ġin Ġembed ding Ġdimension Ġpre cludes Ġexisting Ġknowledge Ġdist illation Ġtechniques , Ġwhich Ġrely Ġon Ġthe Ġalignment Ġof Ġboth Ġmodels ' Ġoutput Ġspaces . ĠAs Ġa Ġresult , Ġwe Ġexplore Ġtwo Ġalternative Ġapproaches Ġthat Ġenable Ġimplicit Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent Ġmodel , Ġwhich Ġwe Ġdescribe Ġbelow . </s> Method ology Ġ: :: ĠDual ĠTraining </s> During Ġdist illation , Ġfor Ġa Ġgiven Ġtraining Ġsequence Ġinput Ġto Ġthe Ġteacher Ġmodel , Ġwe Ġpropose Ġto Ġmix Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies Ġby Ġrandomly Ġselecting Ġ( with Ġa Ġprobability Ġ$ p _{ DT } $, Ġa Ġhyper param eter ) Ġtokens Ġfrom Ġthe Ġsequence Ġto Ġsegment Ġusing Ġthe Ġstudent Ġvocabulary , Ġwith Ġthe Ġother Ġtokens Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary . ĠAs Ġillustrated Ġin ĠFigure ĠFIG REF 4 , Ġgiven Ġthe Ġinput Ġcontext Ġ[ Ġ` I ', Ġ` like ', Ġ` machine ', Ġ` learning ' ], Ġthe Ġwords Ġ` I ' Ġand Ġ` machine ' Ġare Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary Ġ( in Ġgreen ), Ġwhile Ġ` like ' Ġand Ġ` learning ' Ġare Ġsegment ed Ġusing Ġthe Ġstudent Ġvocabulary Ġ( in Ġblue ). ĠSimilar Ġto Ġcross - ling ual Ġtraining Ġin ĠB IB REF 36 , Ġthis Ġencourages Ġalignment Ġof Ġthe Ġrepresentations Ġfor Ġthe Ġsame Ġword Ġas Ġper Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies . ĠThis Ġis Ġeffected Ġthrough Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask : Ġthe Ġmodel Ġnow Ġneeds Ġto Ġlearn Ġto Ġpredict Ġwords Ġfrom Ġthe Ġstudent Ġvocabulary Ġusing Ġcontext Ġwords Ġsegment ed Ġusing Ġthe Ġteacher Ġvocabulary , Ġand Ġvice Ġversa . </s> The Ġexpectation Ġis Ġthat Ġthe Ġstudent Ġembed d ings Ġcan Ġbe Ġlearned Ġeffectively Ġthis Ġway Ġfrom Ġthe Ġteacher Ġembed d ings Ġas Ġwell Ġas Ġmodel Ġparameters Ġ$\ the ta Ġ_ { t } $. ĠNote Ġthat Ġwe Ġperform Ġdual Ġtraining Ġonly Ġfor Ġthe Ġteacher Ġmodel Ġinputs : Ġthe Ġstudent Ġmodel Ġreceives Ġwords Ġsegment ed Ġexclusively Ġusing Ġthe Ġstudent Ġvocabulary . ĠAlso , Ġduring Ġmasked Ġlanguage Ġmodeling , Ġthe Ġmodel Ġuses Ġdifferent Ġsoft max Ġlayers Ġfor Ġthe Ġteacher Ġand Ġthe Ġstudent Ġvoc ab ular ies Ġdepending Ġon Ġwhich Ġone Ġwas Ġused Ġto Ġsegment Ġthe Ġword Ġin Ġquestion . </s> Method ology Ġ: :: ĠShared ĠProject ions </s> Re lying Ġsolely Ġon Ġteacher Ġmodel Ġoutputs Ġto Ġtrain Ġthe Ġstudent Ġmodel Ġmay Ġnot Ġgeneral ize Ġwell ĠB IB REF 34 . ĠTherefore , Ġsome Ġapproaches Ġutilize Ġand Ġtry Ġto Ġalign Ġthe Ġstudent Ġmodel 's Ġintermediate Ġpredictions Ġto Ġthose Ġof Ġthe Ġteacher ĠB IB REF 30 . ĠIn Ġour Ġsetting , Ġhowever , Ġsince Ġthe Ġstudent Ġand Ġteacher Ġmodel Ġoutput Ġspaces Ġare Ġnot Ġidentical , Ġintermediate Ġmodel Ġoutputs Ġmay Ġprove Ġhard Ġto Ġalign . ĠInstead , Ġwe Ġseek Ġto Ġdirectly Ġminimize Ġthe Ġloss Ġof Ġinformation Ġfrom Ġthe Ġteacher Ġmodel Ġparameters Ġ$\ the ta Ġ_ { t } $ Ġto Ġthe Ġstudent Ġparameters Ġ$\ the ta Ġ_ { s } $ Ġwith Ġsmaller Ġdimensions . ĠWe Ġachieve Ġthis Ġby Ġprojecting Ġthe Ġmodel Ġparameters Ġinto Ġthe Ġsame Ġspace , Ġto Ġencourage Ġalignment . </s> More Ġspecifically , Ġas Ġin ĠFigure ĠFIG REF 4 , Ġwe Ġproject Ġeach Ġtrain able Ġvariable Ġin Ġ$\ the ta Ġ_ { t } $ Ġto Ġthe Ġsame Ġshape Ġas Ġthe Ġcorresponding Ġvariable Ġin Ġ$\ the ta Ġ_ { s } $. ĠFor Ġexample , Ġfor Ġall Ġthe Ġtrain able Ġvariables Ġ$\ the ta Ġ_ { t } $ Ġwith Ġshape Ġ$ 768 \ times Ġ768 $, Ġwe Ġlearn Ġtwo Ġprojection Ġmat rices Ġ$\ math bf Ġ{ U }\ in Ġ\ math bb Ġ{ R } ^{ d \ times Ġ768 } $ Ġand Ġ$\ math bf Ġ{ V }\ in Ġ\ math bb Ġ{ R } ^{ 768 \ times Ġd } $ Ġto Ġproject Ġthem Ġinto Ġthe Ġcorresponding Ġspace Ġof Ġthe Ġstudent Ġmodel Ġvariable Ġ$\ the ta Ġ_ { t } ^ \ prime Ġ$ , Ġwhere Ġ$ d $ Ġis Ġthe Ġstudent Ġmodel 's Ġhidden Ġdimension . Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġare Ġcommon Ġto Ġall ĠB ERT Ġmodel Ġparameters Ġof Ġthat Ġdimension ality ; Ġin Ġaddition , Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġare Ġnot Ġneeded Ġfor Ġfine - tun ing Ġor Ġinference Ġafter Ġdist illation . ĠIn Ġorder Ġto Ġalign Ġthe Ġstudent Ġvariable Ġand Ġthe Ġteacher Ġvariable 's Ġprojection , Ġwe Ġintroduce Ġa Ġseparate Ġmean Ġsquare Ġerror Ġloss Ġdefined Ġin ĠEqu ation ĠDIS PLAY _ FORM 7 , Ġwhere Ġ$\ down arrow Ġ$ Ġstands Ġfor Ġdown Ġprojection Ġ( since Ġthe Ġprojection Ġis Ġto Ġa Ġlower Ġdimension ). </s> The Ġabove Ġloss Ġfunction Ġalign s Ġthe Ġtrain able Ġvariables Ġin Ġthe Ġstudent Ġspace . ĠAlternatively , Ġwe Ġcan Ġproject Ġtrain able Ġvariables Ġin Ġ$\ the ta Ġ_ { s } $ Ġto Ġthe Ġsame Ġshape Ġas Ġin Ġ$\ the ta Ġ_ { t } $. ĠThis Ġway , Ġthe Ġloss Ġfunction Ġin ĠEqu ation ĠDIS PLAY _ FORM 8 , Ġ($ \ up arrow Ġ$ Ġdenotes Ġup Ġprojection ) Ġcan Ġcompare Ġthe Ġtrain able Ġvariables Ġin Ġthe Ġteacher Ġspace . </s> Method ology Ġ: :: ĠOptim ization ĠObjective </s> Our Ġfinal Ġloss Ġfunction Ġincludes , Ġin Ġaddition Ġto Ġan Ġoptional Ġprojection Ġloss , Ġmasked Ġlanguage Ġmodeling Ġcross - ent ropy Ġlosses Ġfor Ġthe Ġstudent Ġas Ġwell Ġas Ġthe Ġteacher Ġmodels , Ġsince Ġthe Ġteacher Ġmodel Ġis Ġtrained Ġwith Ġdual - voc abulary Ġinputs Ġand Ġis Ġnot Ġstatic . Ġ$ P ( y _ i = c | \ the ta Ġ_ { s }) $ Ġand Ġ$ P ( y _ i = c | \ the ta Ġ_ { t }) $ Ġdenote Ġthe Ġstudent Ġand Ġteacher Ġmodel Ġprediction Ġprobabilities Ġfor Ġclass Ġc Ġrespectively , Ġand Ġ$\ math bb Ġ{ 1 } $ Ġdenotes Ġan Ġindicator Ġfunction . ĠEqu ations ĠDIS PLAY _ FORM 10 Ġand Ġbelow Ġdefine Ġthe Ġfinal Ġloss Ġ$ L _{ final } $, Ġwhere Ġ$\ ep sil on Ġ$ Ġis Ġa Ġhyper param eter . </s> Exper iments </s> To Ġevaluate Ġour Ġknowledge Ġdist illation Ġapproach , Ġwe Ġdesign Ġtwo Ġclasses Ġof Ġexperiments . ĠFirst , Ġwe Ġevaluate Ġthe Ġdistilled Ġstudent Ġlanguage Ġmodels Ġusing Ġthe Ġmasked Ġword Ġprediction Ġtask Ġon Ġan Ġunseen Ġevaluation Ġcorpus , Ġfor Ġan Ġexplicit Ġevaluation Ġof Ġthe Ġlanguage Ġmodel . ĠSecond , Ġwe Ġfine - t une Ġthe Ġlanguage Ġmodel Ġby Ġadding Ġa Ġtask - specific Ġaff ine Ġlayer Ġon Ġtop Ġof Ġthe Ġstudent Ġlanguage Ġmodel Ġoutputs , Ġon Ġa Ġsuite Ġof Ġdownstream Ġsentence Ġand Ġsentence Ġpair Ġclassification Ġtasks . ĠThis Ġis Ġmeant Ġto Ġbe Ġan Ġimplicit Ġevaluation Ġof Ġthe Ġquality Ġof Ġthe Ġrepresentations Ġlearned Ġby Ġthe Ġstudent Ġlanguage Ġmodel . ĠWe Ġdescribe Ġthese Ġexperiments , Ġalong Ġwith Ġdetails Ġon Ġtraining , Ġimplementation Ġand Ġour Ġbas elines Ġbelow . </s> Exper iments Ġ: :: ĠLanguage ĠModel ĠTraining </s> During Ġthe Ġdist illation Ġof Ġthe Ġteacher ĠB ERT Ġmodel Ġto Ġtrain Ġthe Ġstudent ĠB ERT Ġlanguage Ġmodel , Ġwe Ġutilize Ġthe Ġsame Ġcorpus Ġas Ġwas Ġused Ġto Ġtrain Ġthe Ġteacher Ġi . e . ĠBooks Corp us ĠB IB REF 37 Ġand ĠEnglish ĠWikipedia , Ġwith Ġwhites paces Ġused Ġtoken ize Ġthe Ġtext Ġinto Ġwords . ĠWe Ġonly Ġuse Ġthe Ġmasked Ġlanguage Ġmodeling Ġtask Ġto Ġcalculate Ġthe Ġoverall Ġdist illation Ġloss Ġfrom ĠSection ĠSEC REF 6 , Ġsince Ġthe Ġnext Ġsentence Ġprediction Ġloss Ġhurt Ġperformance Ġslightly . ĠDual Ġtraining Ġis Ġenabled Ġfor Ġteacher Ġmodel Ġinputs , Ġwith Ġ$ p _{ DT } $, Ġthe Ġprobability Ġof Ġsegment ing Ġa Ġteacher Ġmodel Ġinput Ġword Ġusing Ġthe Ġstudent Ġvocabulary , Ġset Ġto Ġ0 . 5 . ĠFor Ġexperiments Ġincluding Ġshared Ġprojection , Ġthe Ġprojection Ġmat rices Ġ$\ math bf Ġ{ U } $ Ġand Ġ$\ math bf Ġ{ V } $ Ġutilized ĠXavier Ġinitialization ĠB IB REF 38 . ĠThe Ġloss Ġweight Ġcoefficient Ġ$\ ep sil on Ġ$ Ġis Ġset Ġto Ġ1 Ġafter Ġtuning . </s> It Ġis Ġworth Ġnoting Ġthat Ġin Ġcontrast Ġto Ġa Ġnumber Ġof Ġexisting Ġapproaches , Ġwe Ġdirectly Ġdist ill Ġthe Ġteacher ĠB ERT Ġlanguage Ġmodel , Ġnot Ġyet Ġfine - tun ed Ġon Ġa Ġdownstream Ġtask , Ġto Ġobtain Ġa Ġstudent Ġlanguage Ġmodel Ġthat Ġis Ġtask - agn ostic . ĠFor Ġdownstream Ġtasks , Ġwe Ġfine - t une Ġthis Ġdistilled Ġstudent Ġlanguage Ġmodel . </s> Dist illation Ġis Ġcarried Ġout Ġon ĠCloud ĠT PU s Ġin Ġa Ġ4 x 4 Ġpod Ġconfiguration Ġ( 32 ĠT PU Ġcores Ġoverall ). ĠWe Ġoptimized Ġthe Ġloss Ġusing ĠL AM B ĠB IB REF 39 Ġfor Ġ250 K Ġsteps , Ġwith Ġa Ġlearning Ġrate Ġof Ġ0 . 00 125 Ġand Ġbatch Ġsize Ġof Ġ4096 . ĠDepending Ġon Ġthe Ġstudent Ġmodel Ġdimension , Ġtraining Ġtook Ġbetween Ġ2 - 4 Ġdays . </s> Exper iments Ġ: :: ĠModels Ġand ĠBas elines </s> We Ġevaluate Ġthree Ġvariants Ġof Ġour Ġdistilled Ġstudent Ġmodels : Ġwith Ġonly Ġdual Ġtraining Ġof Ġthe Ġteacher Ġand Ġstudent Ġvoc ab ular ies Ġ( Dual Train ) Ġand Ġwith Ġdual Ġtraining Ġalong Ġwith Ġdown - project ion Ġ( Dual Train Ġ+ ĠShared Pro j Down ) Ġor Ġup - project ion Ġ( Dual Train Ġ+ ĠShared Pro j Up ) Ġof Ġthe Ġteacher Ġmodel Ġparameters . ĠFor Ġeach Ġof Ġthese Ġconfigurations , Ġwe Ġtrain Ġstudent Ġmodels Ġwith Ġembed ding Ġand Ġhidden Ġdimensions Ġ48 , Ġ96 Ġand Ġ192 , Ġfor Ġ9 Ġtotal Ġvariants , Ġeach Ġusing Ġa Ġcompact Ġ5 K - Word P iece Ġvocabulary . ĠTable ĠT AB REF 14 Ġpresents Ġsome Ġstatistics Ġon Ġthese Ġmodels ' Ġsizes : Ġour Ġsmallest Ġmodel Ġcontains Ġtwo Ġorders Ġof Ġmagnitude Ġfewer Ġparameters , Ġand Ġrequires Ġonly Ġ1 % Ġfloating - point Ġoperations Ġwhen Ġcompared Ġto Ġthe ĠB ERT B ASE Ġmodel . </s> For Ġthe Ġlanguage Ġmodeling Ġevaluation , Ġwe Ġalso Ġevaluate Ġa Ġbaseline Ġwithout Ġknowledge Ġdist illation Ġ( ter med ĠNo K D ), Ġwith Ġa Ġmodel Ġparameter ized Ġident ically Ġto Ġthe Ġdistilled Ġstudent Ġmodels Ġbut Ġtrained Ġdirectly Ġon Ġthe Ġteacher Ġmodel Ġobjective Ġfrom Ġscratch . ĠFor Ġdownstream Ġtasks , Ġwe Ġcompare Ġwith ĠNo K D Ġas Ġwell Ġas ĠPatient ĠKnowledge ĠDist illation Ġ( PK D ) Ġfrom ĠB IB REF 34 , Ġwho Ġdist ill Ġthe Ġ12 - layer ĠB ERT B ASE Ġmodel Ġinto Ġ3 Ġand Ġ6 - layer ĠB ERT Ġmodels Ġby Ġusing Ġthe Ġteacher Ġmodel 's Ġhidden Ġstates . </s> Exper iments Ġ: :: ĠEvaluation ĠT asks Ġand ĠDat as ets </s> For Ġexplicit Ġevaluation Ġof Ġthe Ġgeneralized Ġlanguage Ġperspective Ġof Ġthe Ġdistilled Ġstudent Ġlanguage Ġmodels , Ġwe Ġuse Ġthe ĠReddit Ġdataset ĠB IB REF 40 Ġto Ġmeasure Ġword Ġmask Ġprediction Ġaccuracy Ġof Ġthe Ġstudent Ġmodels , Ġsince Ġthe Ġlanguage Ġused Ġon ĠReddit Ġis Ġdifferent Ġfrom Ġthat Ġin Ġthe Ġtraining Ġcorpor a . ĠThe Ġdataset Ġis Ġpre process ed Ġsimilarly Ġto Ġthe Ġtraining Ġcorpor a , Ġexcept Ġwe Ġdo Ġnot Ġneed Ġto Ġtoken ize Ġit Ġusing Ġthe Ġteacher Ġvocabulary , Ġsince Ġwe Ġonly Ġrun Ġand Ġevaluate Ġthe Ġstudent Ġmodels . </s> For Ġimplicit Ġevaluation Ġon Ġdownstream Ġlanguage Ġunderstanding Ġtasks , Ġwe Ġfine - t une Ġand Ġevaluate Ġthe Ġdistilled Ġstudent Ġmodels Ġon Ġthree Ġtasks Ġfrom Ġthe ĠGL UE Ġbenchmark ĠB IB REF 41 : </s> [ left margin = *, top se p = 0 pt ] </s> Stan ford ĠSent iment ĠTree bank Ġ( S ST - 2 ) ĠB IB REF 6 , Ġa Ġtwo - way Ġsentence Ġsentiment Ġclassification Ġtask Ġwith Ġ67 K Ġtraining Ġinstances , </s> Microsoft ĠResearch ĠPar aph rase ĠCorpus Ġ( MR PC ) ĠB IB REF 42 , Ġa Ġtwo - way Ġsentence Ġpair Ġclassification Ġtask Ġto Ġidentify Ġparaph r ases , Ġwith Ġ3 . 7 K Ġtraining Ġinstances , Ġand </s> Multi - Gen re ĠNatural ĠLanguage ĠIn ference Ġ( MN LI ) ĠB IB REF 7 , Ġa Ġthree - way Ġsentence Ġpair Ġclassification Ġtask Ġwith Ġ39 3 K Ġtraining Ġinstances , Ġto Ġidentify Ġpremise - hyp ot hesis Ġrelations . ĠThere Ġare Ġseparate Ġdevelopment Ġand Ġtest Ġsets Ġfor Ġgenre - matched Ġand Ġgenre - m ism atched Ġpremise - hyp ot hesis Ġpairs ; Ġwe Ġtune Ġour Ġmodels Ġsolely Ġon Ġthe Ġgenre - matched Ġdevelopment Ġset . </s> For Ġall Ġdownstream Ġtask Ġevaluations , Ġwe Ġfine - t une Ġfor Ġ10 Ġepoch s Ġusing ĠL AM B Ġwith Ġa Ġlearning Ġrate Ġof Ġ0 . 0002 Ġand Ġbatch Ġsize Ġof Ġ32 . ĠSince Ġour Ġlanguage Ġmodels Ġare Ġtrained Ġwith Ġa Ġmaximum Ġsequence Ġlength Ġof Ġ128 Ġtokens , Ġwe Ġdo Ġnot Ġevaluate Ġon Ġreading Ġcomprehension Ġdatasets Ġsuch Ġas ĠS Qu AD ĠB IB REF 8 Ġor ĠR ACE ĠB IB REF 9 , Ġwhich Ġrequire Ġmodels Ġsupporting Ġlonger Ġsequences . </s> Results </s> Table ĠT AB REF 20 Ġcontains Ġmasked Ġword Ġprediction Ġaccuracy Ġfigures Ġfor Ġthe Ġdifferent Ġmodels Ġand Ġthe ĠNo K D Ġbaseline . ĠWe Ġobserve Ġthat Ġdual Ġtraining Ġsignificantly Ġimproves Ġover Ġthe Ġbaseline Ġfor Ġall Ġmodel Ġdimensions , Ġand Ġthat Ġboth Ġshared Ġprojection Ġlosses Ġadded Ġto Ġdual Ġtraining Ġfurther Ġimprove Ġthe Ġword Ġprediction Ġaccuracy . ĠIt Ġis Ġinteresting Ġto Ġnote Ġthat Ġfor Ġall Ġmodel Ġdimensions , ĠShared Pro j Up Ġprojecting Ġinto Ġthe Ġteacher Ġspace Ġoutper forms ĠShared Pro j Down , Ġsignificantly Ġso Ġfor Ġdimension Ġ48 . ĠEx pected ly , Ġthere Ġis Ġa Ġnoticeable Ġperformance Ġdrop Ġgoing Ġfrom Ġ192 Ġto Ġ96 Ġto Ġ48 - dimensional Ġhidden Ġstate Ġmodels . ĠNote Ġthat Ġbecause Ġof Ġthe Ġdiffering Ġteacher Ġand Ġstudent Ġmodel Ġvoc ab ular ies , Ġmasked Ġword Ġprediction Ġaccuracy Ġfor Ġthe Ġteacher ĠB ERT B ASE Ġmodel Ġis Ġnot Ġdirectly Ġcomparable Ġwith Ġthe Ġstudent Ġmodels . </s> Table ĠT AB REF 21 Ġshows Ġresults Ġon Ġthe Ġdownstream Ġlanguage Ġunderstanding Ġtasks , Ġas Ġwell Ġas Ġmodel Ġsizes , Ġfor Ġour Ġapproaches , Ġthe ĠB ERT B ASE Ġteacher Ġmodel , Ġand Ġthe ĠPK D Ġand ĠNo K D Ġbas elines . ĠWe Ġnote Ġthat Ġmodels Ġtrained Ġwith Ġour Ġproposed Ġapproaches Ġperform Ġstrongly Ġand Ġconsistently Ġimprove Ġupon Ġthe Ġident ically Ġparam et ri zed ĠNo K D Ġbas elines , Ġindicating Ġthat Ġthe Ġdual Ġtraining Ġand Ġshared Ġprojection Ġtechniques Ġare Ġeffective , Ġwithout Ġinc urring Ġsignificant Ġlosses Ġagainst Ġthe ĠB ERT B ASE Ġteacher Ġmodel . ĠComp aring Ġwith Ġthe ĠPK D Ġbaseline , Ġour Ġ192 - dimensional Ġmodels , Ġachieving Ġa Ġhigher Ġcompression Ġrate Ġthan Ġeither Ġof Ġthe ĠPK D Ġmodels , Ġperform Ġbetter Ġthan Ġthe Ġ3 - layer ĠPK D Ġbaseline Ġand Ġare Ġcompetitive Ġwith Ġthe Ġlarger Ġ6 - layer Ġbaseline Ġon Ġtask Ġaccuracy Ġwhile Ġbeing Ġnearly Ġ5 Ġtimes Ġas Ġsmall . </s> Another Ġobservation Ġwe Ġmake Ġis Ġthat Ġthe Ġperformance Ġdrop Ġfrom Ġ192 - dimensional Ġto Ġ96 - dimensional Ġmodels Ġis Ġminimal Ġ( less Ġthan Ġ2 % Ġfor Ġmost Ġtasks ). ĠFor Ġthe ĠMR PC Ġtask , Ġin Ġfact , Ġthe Ġ96 - dimensional Ġmodel Ġtrained Ġwith Ġdual Ġtraining Ġachieves Ġan Ġaccuracy Ġof Ġ80 . 5 %, Ġwhich Ġis Ġhigher Ġthan Ġeven Ġthe ĠPK D Ġ6 - layer Ġbaseline Ġwith Ġnearly Ġ12 Ġtimes Ġas Ġmany Ġparameters . ĠFinally , Ġour Ġhighly - comp ressed Ġ48 - dimensional Ġmodels Ġalso Ġperform Ġrespect ably : Ġthe Ġbest Ġ48 - dimensional Ġmodels Ġare Ġin Ġa Ġsimilar Ġperformance Ġbracket Ġas Ġthe Ġ3 - layer ĠPK D Ġmodel , Ġa Ġmodel Ġ25 Ġtimes Ġlarger Ġby Ġmemory Ġfootprint . </s> Discussion </s> Sh ared Ġprojections Ġand Ġmodel Ġperformance : ĠWe Ġsee Ġthat Ġfor Ġdownstream Ġtask Ġperformance , Ġdual Ġtraining Ġstill Ġconsistently Ġimproves Ġupon Ġthe Ġdirect Ġfine - tun ing Ġapproach Ġfor Ġvirtually Ġall Ġexperiments . ĠThe Ġeffect Ġof Ġshared Ġvariable Ġprojection , Ġhowever , Ġis Ġless Ġpronounced , Ġwith Ġconsistent Ġimprovements Ġvisible Ġonly Ġfor ĠMR PC Ġand Ġfor Ġthe Ġ48 - dimensional Ġmodels Ġi . e . Ġthe Ġsmallest Ġdataset Ġand Ġmodels Ġrespectively Ġin Ġour Ġexperiments . ĠThis Ġalign s Ġwith Ġour Ġintuition Ġfor Ġvariable Ġprojection Ġas Ġa Ġmore Ġdirect Ġway Ġto Ġprovide Ġa Ġtraining Ġsignal Ġfrom Ġthe Ġteacher Ġmodel Ġintern als , Ġwhich Ġcan Ġassume Ġmore Ġimportance Ġfor Ġa Ġlow - data Ġor Ġsmall - model Ġscenario . ĠHowever , Ġfor Ġlarger Ġmodels Ġand Ġmore Ġdata , Ġthe Ġlinear Ġprojection Ġof Ġparameters Ġmay Ġbe Ġreducing Ġthe Ġdegrees Ġof Ġfreedom Ġavailable Ġto Ġthe Ġmodel , Ġsince Ġlinear Ġprojection Ġis Ġa Ġfairly Ġsimple Ġfunction Ġto Ġalign Ġthe Ġteacher Ġand Ġstudent Ġparameter Ġspaces . </s> A Ġrelated Ġcomparison Ġof Ġinterest Ġis Ġbetween Ġup - project ion Ġand Ġdown - project ion Ġof Ġthe Ġmodel Ġvariables : Ġwe Ġnote Ġup - project ion Ġdoes Ġvisibly Ġbetter Ġon Ġthe Ġlanguage Ġmodeling Ġtask Ġand Ġslightly Ġbetter Ġon Ġthe Ġdownstream Ġtasks . ĠThe Ġparameters Ġof Ġa Ġwell - trained Ġteacher Ġmodel Ġrepresent Ġa Ġhigh - quality Ġlocal Ġminimum Ġin Ġthe Ġteacher Ġspace , Ġwhich Ġmay Ġbe Ġeasier Ġto Ġsearch Ġfor Ġduring Ġup - project ion . </s> V oc abulary Ġsize Ġtrade offs : ĠIssues Ġwith Ġinput Ġvocabulary Ġsize Ġare Ġpeculiar Ġto Ġproblems Ġin Ġnatural Ġlanguage Ġprocessing : Ġthey Ġdo Ġnot Ġalways Ġapply Ġto Ġother Ġareas Ġsuch Ġas Ġcomputer Ġvision , Ġwhere Ġa Ġsmall Ġfixed Ġnumber Ġof Ġsymbols Ġcan Ġencode Ġmost Ġinputs . ĠThere Ġhas Ġbeen Ġsome Ġwork Ġon Ġreducing Ġinput Ġvocabulary Ġsizes Ġfor ĠN LP , Ġbut Ġtypically Ġnot Ġtargeting Ġmodel Ġcompression . ĠOne Ġconcern Ġwith Ġreducing Ġthe Ġvoc ab ular ies Ġof ĠN LP Ġmodels Ġis Ġit Ġpushes Ġthe Ġaverage Ġtoken ized Ġsequence Ġlengths Ġup , Ġmaking Ġmodel Ġtraining Ġharder . ĠIn Ġthis Ġwork , Ġhowever , Ġwe Ġconsider Ġclassification Ġtasks Ġon Ġshorter Ġtexts , Ġwhich Ġare Ġnot Ġas Ġaffected Ġby Ġinput Ġsequence Ġlengths Ġas , Ġsay , Ġtasks Ġsuch Ġas Ġmachine Ġtranslation Ġare . ĠFurthermore , Ġmany Ġreal - world Ġapplications Ġrev olve Ġaround Ġshort Ġtext Ġinputs , Ġwhich Ġis Ġwhy Ġa Ġbetter Ġtrade - off Ġbetween Ġvocabulary Ġsize Ġand Ġsequence Ġlengths Ġmay Ġbe Ġworthwhile Ġfor Ġsuch Ġapplications . </s> Order Ġof Ġdist illation Ġand Ġfine - tun ing : ĠMost Ġof Ġthe Ġexisting Ġwork Ġon Ġdist illing Ġlanguage Ġmodels Ġsuch Ġas ĠB ERT Ġand Ġreporting Ġresults Ġon Ġdownstream Ġtasks , Ġincluding Ġsome Ġof Ġthe Ġbas elines Ġin Ġthis Ġwork , Ġfirst Ġfine - t une Ġa Ġteacher Ġmodel Ġon Ġthe Ġdownstream Ġtasks , Ġand Ġthen Ġdist ill Ġthis Ġmodel . ĠOur Ġgoal Ġin Ġthis Ġwork , Ġhowever , Ġis Ġto Ġexplore Ġthe Ġlimits Ġto Ġwhich ĠB ERT 's Ġlanguage Ġmodeling Ġcapacity Ġitself , Ġand Ġhow Ġmuch Ġof Ġit Ġis Ġdriven Ġby Ġits Ġlarge ĠWord P iece Ġvocabulary . ĠWe Ġleave Ġexperiments Ġon Ġdist illing Ġfine - tun ed Ġteacher Ġmodels , Ġpotentially Ġyielding Ġbetter Ġresults Ġon Ġdownstream Ġtasks , Ġto Ġfuture Ġwork . </s> Conclusion </s> We Ġproposed Ġtwo Ġnovel Ġideas Ġto Ġimprove Ġthe Ġeffectiveness Ġof Ġknowledge Ġdist illation Ġfor ĠB ERT , Ġfocusing Ġon Ġusing Ġa Ġsignificantly Ġsmaller Ġvocabulary , Ġas Ġwell Ġas Ġsmaller Ġembed ding Ġand Ġhidden Ġdimensions Ġfor Ġthe Ġstudent ĠB ERT Ġlanguage Ġmodels . ĠOur Ġdual Ġtraining Ġmechanism Ġencourages Ġimplicit Ġalignment Ġof Ġthe Ġteacher Ġand Ġstudent ĠWord P iece Ġembed d ings , Ġand Ġshared Ġvariable Ġprojection Ġallows Ġfor Ġthe Ġfaster Ġand Ġdirect Ġlayer - wise Ġtransfer Ġof Ġknowledge Ġto Ġthe Ġstudent ĠB ERT Ġmodel . ĠComb ining Ġthe Ġtwo Ġtechniques , Ġwe Ġtrained Ġa Ġseries Ġof Ġhighly - comp ressed Ġ12 - layer Ġstudent ĠB ERT Ġmodels . ĠExper iments Ġon Ġthese Ġmodels , Ġto Ġevaluate Ġboth Ġgeneralized Ġlanguage Ġperspective Ġand Ġfour Ġstandardized Ġdownstream Ġtasks , Ġdemonstrate Ġthe Ġeffectiveness Ġof Ġour Ġproposed Ġmethods Ġon Ġboth Ġmodel Ġaccuracy Ġand Ġcompression Ġefficiency . </s> One Ġfuture Ġdirection Ġof Ġinterest Ġis Ġto Ġcombine Ġour Ġapproach Ġwith Ġexisting Ġwork Ġto Ġreduce Ġthe Ġnumber Ġof Ġlayers Ġin Ġthe Ġstudent Ġmodels Ġand Ġexplore Ġother Ġapproaches Ġsuch Ġas Ġlow - rank Ġmatrix Ġfactor ization Ġto Ġtransfer Ġmodel Ġparameters Ġfrom Ġthe Ġteacher Ġspace Ġto Ġthe Ġstudent Ġspace . ĠIn Ġaddition , Ġtaking Ġinto Ġaccount Ġthe Ġfrequency Ġdistribution Ġof Ġthe ĠWord P iece Ġtokens Ġwhile Ġtraining Ġembed d ings Ġmay Ġhelp Ġoptimize Ġthe Ġmodel Ġsize Ġfurther .