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# (参考訳) オブジェクト構造に関する言語から概念ライブラリを識別する [全文訳有]

Identifying concept libraries from language about object structure ( http://arxiv.org/abs/2205.05666v1 )

ライセンス: CC BY 4.0
Catherine Wong, William P. McCarthy, Gabriel Grand, Yoni Friedman, Joshua B. Tenenbaum, Jacob Andreas, Robert D. Hawkins, Judith E. Fan(参考訳) 私たちの視覚世界に対する理解は、オブジェクトを意味のある部分、属性、関係に解析する能力を含む、オブジェクトの命名を超えています。 本研究では,自然言語記述を多種多様な2Kプロシージャ生成オブジェクトの集合に活用して,人々が使用する部分と,これらを他よりも好むべき原則を特定する。 我々は,各ライブラリで表現されたプログラムが,人間の言語とどのように一致しているかを評価するために,機械翻訳のツールを用いて,異なる部分概念を含むプログラムライブラリの空間を探索する際の問題を定式化する。 自然言語を大規模に構成されたプログラム表現と組み合わせることで、各オブジェクトの簡潔な記述を許容するレキシコンと、レキシコン自体のサイズを最小化する部分概念を統治する基本的な情報理論上のトレードオフが発見される。

Our understanding of the visual world goes beyond naming objects, encompassing our ability to parse objects into meaningful parts, attributes, and relations. In this work, we leverage natural language descriptions for a diverse set of 2K procedurally generated objects to identify the parts people use and the principles leading these parts to be favored over others. We formalize our problem as search over a space of program libraries that contain different part concepts, using tools from machine translation to evaluate how well programs expressed in each library align to human language. By combining naturalistic language at scale with structured program representations, we discover a fundamental information-theoreti c tradeoff governing the part concepts people name: people favor a lexicon that allows concise descriptions of each object, while also minimizing the size of the lexicon itself.
公開日: Wed, 11 May 2022 17:49:25 GMT

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英語(論文から抽出)日本語訳スコア
Identifyingconceptli brariesfromlanguagea boutobjectstructureC atherineWong? コンセプタリブリアの言語的対象から同定する : キャサリン・ウォン 0.08
,WilliamP.McCarthy? ウィリアム・マッカーシー? 0.67
2,GabrielGrand? 2ガブリエルグランド? 0.40
1,YoniFriedman1,Josh uaB.Tenenbaum1,Jacob Andreas1,RobertD.Haw kins3andJudithE.Fan2 1MIT,2UniversityofCa liforniaSanDiego,3Pr incetonNeuroscienceI nstitute? 1,YoniFriedman1,Josh uaB.Tenenbaum1,Jacob Andreas1,RobertD.Haw kins3andJudithE.Fan2 1MIT,2UniversityofCa liforniaSanDiego,3Pr incetonNeuroscienceI nstitute? 0.16
denotesequalcontribu tion,correspondencet ocatwong@mit.eduAbst ractOurunderstanding ofthevisualworldgoes beyondnamingobjects, encompassingourabili tytoparseobjectsinto meaningfulparts,attr ibutes,andrelations. Inthiswork,weleverag enaturallanguagedesc riptionsforadiverses etof2Kprocedurallyge neratedobjectstoiden tifythepartspeopleus eandtheprincipleslea dingthesepartstobefa voredoverothers.Wefo rmalizeourproblemass earchoveraspaceofpro gramlibrariesthatcon taindifferentpartcon cepts,usingtoolsfrom machinetranslationto evaluatehowwellprogr amsexpressedineachli braryaligntohumanlan guage.Bycombiningnat uralisticlanguageats calewithstructuredpr ogramrepresentations ,wediscoverafundamen talinformation-theor etictradeoffgovernin gthepartconceptspeop lename:peoplefavoral exiconthatallowsconc isedescriptionsofeac hobject,whilealsomin imizingthesizeofthel exiconitself.Keyword s:abstraction;compositionality;parts;percep-tion;programsTheworldisfilledwithagreatvariet yofobjects,yetpeople havelittledifficultymakingsenseofth em.Pre-sentedwithano velobject,peoplecanr eadilyidentifyitspar ts(Schyns&Murphy,1994),guessit sfunction(Tversky&am p;Hemenway,1984),andre fertoitunambigu-ousl y(Hawkinsetal.,2020) . denotesequalcontribu tion,correspondencet ocatwong@mit.eduAbst ractOurunderstanding ofthevisualworldgoes beyondnamingobjects, encompassingourabili tytoparseobjectsinto meaningfulparts,attr ibutes,andrelations. Inthiswork,weleverag enaturallanguagedesc riptionsforadiverses etof2Kprocedurallyge neratedobjectstoiden tifythepartspeopleus eandtheprincipleslea dingthesepartstobefa voredoverothers.Wefo rmalizeourproblemass earchoveraspaceofpro gramlibrariesthatcon taindifferentpartcon cepts,usingtoolsfrom machinetranslationto evaluatehowwellprogr amsexpressedineachli braryaligntohumanlan guage.Bycombiningnat uralisticlanguageats calewithstructuredpr ogramrepresentations ,wediscoverafundamen talinformation-theor etictradeoffgovernin gthepartconceptspeop lename:peoplefavoral exiconthatallowsconc isedescriptionsofeac hobject,whilealsomin imizingthesizeofthel exiconitself.Keyword s:abstraction;compositionality;parts;percep-tion;programsTheworldisfilledwithagreatvariet yofobjects,yetpeople havelittledifficultymakingsenseofth em.Pre-sentedwithano velobject,peoplecanr eadilyidentifyitspar ts(Schyns&Murphy,1994),guessit sfunction(Tversky&am p;Hemenway,1984),andre fertoitunambigu-ousl y(Hawkinsetal.,2020) . 0.06
Theseabilitiesreston thecapacitytorobustl yconnectfeaturesofth eexternalworldtoaric hlibraryofmentalconc eptsdescribingnotjus twholeobjects,butthe irpartsandhowtheyare arranged(Miller&Johnson-Laird,1976;Landau&Jackendoff,1993;Rosch&Mervis,1975;Mukherjeeetal.,2019) . theseabilitiesreston thecapacitytorobustl yconnectfeaturesofth eexternalworldtoaric hlibraryofmentalconc eptsdescribingnotjus twholeobjects, buttheirpartsandhowt heyareranged (Miller&Johnson-Laird, 1976;Landau&Jackendoff,1993;Rosch&Mervis,1975;Mukherjeeetal, 2019)。 0.07
Forexample,considert hebottom-mostgadgeti nFig.1A:eventhoughth isobjectdoesnotcorre spondtoafamiliarcate gory,wemightsaythati tcontainsarowofbutto nsordials,andthatiti stoppedbyanantennaor aknob.Butjustaswedon othaveapre-existingc on-ceptforeveryobjec tweencounter,wedonot haveaconceptcorrespo ndingtoeverypart:inF ig.1A,forex-ample,mo stpeopledonothaveaco nceptcorrespondingto arowofexactlyfivedia ls.Indeed,acomplexob jectcanbedecomposedi nahugenumberofdiffer entways,butpeopleare likelytofavoronlyati nysubsetofthem.Whatc haracterizesthesetof partconceptsthatpeop ledouse? Forexample,considert hebottom-mostgadgeti nFig.1A:eventhoughth isobjectdoesnotcorre spondtoafamiliarcate gory,wemightsaythati tcontainsarowofbutto nsordials,andthatiti stoppedbyanantennaor aknob.Butjustaswedon othaveapre-existingc on-ceptforeveryobjec tweencounter,wedonot haveaconceptcorrespo ndingtoeverypart:inF ig.1A,forex-ample,mo stpeopledonothaveaco nceptcorrespondingto arowofexactlyfivedia ls.Indeed,acomplexob jectcanbedecomposedi nahugenumberofdiffer entways,butpeopleare likelytofavoronlyati nysubsetofthem.Whatc haracterizesthesetof partconceptsthatpeop ledouse? 0.06
Whythese,andnotother s? Identifyingwhichpart speopleusetoparsevis ualob-jectshasbeenac oregoalforclassicthe oriesofpercep-tualor ganization(Palmer,19 77;Marr&Nishihara,1978;Hoffman&Richards,1984;Biederman,1987)andco n-tinuestoposechalle ngesformodernvisionm odels(Moetal.,2019;Bearetal.,2020). なぜ、他の人は? Palmer, 1977;Marr&Nishihara, 1978;Hoffman&Richards, 1984;Biederman, 1987) andcon-tinuestoposec hallengesfor Modernvisionmodels (Moetal., 2019;Bearetal., 2020)。 0.39
Buthowcanwetellwheth eranyoftheseproposal sactuallyexplainvisu alob-jectunderstandi ng? しかし、プロポサクティカルな見地から見れば、どうだろう? 0.10
Empiricaltestsofthes etheorieshavegeneral lyrelieduponsimpledi scriminationtasksrat herthanricherbehavio ralreadouts(Tversky, 1989;Markman&Wachtel,1988),limiti ngtheirabilitytoeval uatecorre-spondences betweenacandidateobj ectrepresentationand thefullsetofpartsand relationsthatpeoplec anidentify.Naturalla nguageoffersapowerfu lwindowintoourconcep tualrepresentations, givenabundantevidenc ethatourvocabularies havebeenshapedtoefficientlycommu-nicatea bouttheconceptswefindrelevant(Regiereta l.,2015;Kirbyetal.,2015;Zaslavskyetal.,2018;Sun&Firestone,2021). Empiricaltestsofthes etheorieshavegeneral lyrelieduponsimpledi scriminationtasksrat herthanricherbehavio ralreadouts(Tversky, 1989;Markman&Wachtel,1988),limiti ngtheirabilitytoeval uatecorre-spondences betweenacandidateobj ectrepresentationand thefullsetofpartsand relationsthatpeoplec anidentify.Naturalla nguageoffersapowerfu lwindowintoourconcep tualrepresentations, givenabundantevidenc ethatourvocabularies havebeenshapedtoefficientlycommu-nicatea bouttheconceptswefindrelevant(Regiereta l.,2015;Kirbyetal.,2015;Zaslavskyetal.,2018;Sun&Firestone,2021). 0.05
Inthiswork,ourgoalis toleveragenaturalist iclanguageproduction toidentifytheconcep- tuallibrariesofparts andrelationsusedforv isualob-jectundersta nding,usinglibraries ofsymbolicprogramcom ponentstomodelhowthe seconceptsarementall yrepresented(Fig.1B) . inthiswork,ourgoalis toleveragenaturalist iclanguageproduction toidifytheconcep-tua llibrariesofpartsand relationsusedforvisu alob-jectunderstandi ng,usinglibrariesofs ymbolicprogramcompon entstomodelhowthesec onceptsarementallyre presented(図1b) 0.04
Inthisframework,each libraryinstantiatesa differenthypothesisa bouttheunderlyinginv entoryofpartconcepts thatpeopleareusingto decom-posevisualobje cts.InPartI,wedescri beourstrategyforcrea tingadi-versecollect ionofnovelobjectsgen eratedusinggraph-ics programs(Fig.1A),and forelicitingopen-end eddescriptionsofthes eobjects.Analyzingth esedescrip-tionsreve alshallmarksofthesec onceptlibraries:peop leproducelongerdescr iptionstodescribemor ecomplexobjects,andi nvokedifferentpartco nceptstodescribeobje ctsfromdifferentcate gories.InPartII,were finethispicturewithafo rmallibraryidentificationmodelthatmeasu resthecorrespondence betweenlanguageandca ndidateprogramlibrar iescontainingpartcon ceptsofvaryingcomple xity,buildingonrecen tworkinprogramlibrar ydiscovery(Ellisetal .,2020;Tianetal.,2020;Wangetal.,2021;Wongetal.,2021). Inthisframework,each libraryinstantiatesa differenthypothesisa bouttheunderlyinginv entoryofpartconcepts thatpeopleareusingto decom-posevisualobje cts.InPartI,wedescri beourstrategyforcrea tingadi-versecollect ionofnovelobjectsgen eratedusinggraph-ics programs(Fig.1A),and forelicitingopen-end eddescriptionsofthes eobjects.Analyzingth esedescrip-tionsreve alshallmarksofthesec onceptlibraries:peop leproducelongerdescr iptionstodescribemor ecomplexobjects,andi nvokedifferentpartco nceptstodescribeobje ctsfromdifferentcate gories.InPartII,were finethispicturewithafo rmallibraryidentificationmodelthatmeasu resthecorrespondence betweenlanguageandca ndidateprogramlibrar iescontainingpartcon ceptsofvaryingcomple xity,buildingonrecen tworkinprogramlibrar ydiscovery(Ellisetal .,2020;Tianetal.,2020;Wangetal.,2021;Wongetal.,2021). 0.04
Thismodelrevealsadee perinformation-theor eticprinciplegoverni ngthepartconceptspeo pleinvokeinlanguage: theyreflectafundamentaltrade -offbetweenthecomple xityofacon-ceptlibra ryandthecomplexityof objectsrepresentedus ingthatlibrary.arXiv :2205.05666v1 [cs.CL] 11 May 2022 Thismodelrevealsadee perinformation-theor eticprinciplegoverni ngthepartcons Peopleinvokein Language:theyreflect afundamentaltrade-of fbetweenthecomplexit yofacon-ceptlibrary andthecomplexityofob jectsrepresentedusin g thatlibrary.arXiv:22 05.05666v1 [cs.CL] 11 May 2022 0.08
英語(論文から抽出)日本語訳スコア
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SGDMATHKC@OXQ@LHCQNNEBNMBDOSKHAQ@QXK@MFT@FDroof( )door()window()vert( )horiz()right()0-9Fi gure1:(A)Exampleobje ctsfromtheDrawingsan dTowersdomains.Eachd omaincontains4subdom ainsof250novelobject s.Eachdomainandsubdo mainwasdesignedtoinc ludehighvariationove rthetypeandnumberofb aseprimitives(i.e.,s hapes,blocks). FDroof()door()window ()vert()horiz()right ()0-9Figure1:(A)Exam pleobjectsfromtheDra wingsandTowers Domains.Each domaincontains4sub domainsof250novelobj ects.Each domainandsubdomainwa sdesignedtoinclude toincludehighvariati onoverthetypeandnumb erofbaseprimitives(つまり、shapes,blocks)。 0.21
(B)Thisworkaimstoinf erthelatentconceptli brarythatpeopleareus ingtodecomposecomple xobjectsintoparts,wh ereobjectsarereprese ntedbyexecutablegrap hicsprograms.PartI:E licitinglanguageabou tobjectstructureOurc entralaimistoidentif ythelibraryofpartcon ceptsthatpeopleinvok etodecomposeobjects. Towardsthisend,wenee dedasufficientlylargeandvarie dcollectionofobjects ,andanaturalistictas kforelicitingdetaile ddescriptionsoftheir structure.MethodsPar ticipantsWerecruited 465participantsfromP ro-lifictocompletethetask.P articipantsprovidedi nformedconsentandwer epaidapproximately$1 5perhour.StimuliToen surethatwehadasufficientlylargeanddiver secollectionofobject s,wedevelopedahierar chi-calprocedurefors ynthesizingcomplexco nfigurationsofshapes.Ta kinginspirationfromr ecentworkemployingli nedrawingsandblockto werstoinvestigatehow peoplelearnandrepres entthecompositionals tructureofobjects(Ti anetal.,2020;McCarthyetal.,2021;Wangetal.,2021),wede finedtwostimulusdomain s,distinguishedbythe setofbaseshapeprimit ivesusedtogenerateth em(Fig.1A). (B)Thisworkaimstoinf erthelatentconceptli brarythatpeopleareus ingtodecomposecomple xobjectsintoparts,wh ereobjectsarereprese ntedbyexecutablegrap hicsprograms.PartI:E licitinglanguageabou tobjectstructureOurc entralaimistoidentif ythelibraryofpartcon ceptsthatpeopleinvok etodecomposeobjects. Towardsthisend,wenee dedasufficientlylargeandvarie dcollectionofobjects ,andanaturalistictas kforelicitingdetaile ddescriptionsoftheir structure.MethodsPar ticipantsWerecruited 465participantsfromP ro-lifictocompletethetask.P articipantsprovidedi nformedconsentandwer epaidapproximately$1 5perhour.StimuliToen surethatwehadasufficientlylargeanddiver secollectionofobject s,wedevelopedahierar chi-calprocedurefors ynthesizingcomplexco nfigurationsofshapes.Ta kinginspirationfromr ecentworkemployingli nedrawingsandblockto werstoinvestigatehow peoplelearnandrepres entthecompositionals tructureofobjects(Ti anetal.,2020;McCarthyetal.,2021;Wangetal.,2021),wede finedtwostimulusdomain s,distinguishedbythe setofbaseshapeprimit ivesusedtogenerateth em(Fig.1A). 0.03
Drawingsarecomposedo fsimplegeometriccurv es(i.e.,line,circle) andareevocativeoffam iliarobjectcategorie s;Towersarecomposedofr ectangularblocks(i.e .,horizontalandverti caldominoes)andareev ocativeofsimplearchi tecturalmodels.Toinv estigatethedegreetow hichpeopleinvokedcat egory-specificpartconceptstodescr ibetheseobjects,rath erthanthesamesetof“atomic”baseprimitivesinallc ases,wefurtherdefinedfoursubdomainsnes tedwithineachdomain. WithinDrawings,these wereinformallydesign atedasnuts&bolts,vehicles,gadge ts,andfurni-ture;andwithinTowers,asbr idges,cities,houses, andcastles(Fig.1A). Drawingsarecomposedo fsimplegeometriccurv es(i.e.,line,circle) andareevocativeoffam iliarobjectcategorie s;Towersarecomposedofr ectangularblocks(i.e .,horizontalandverti caldominoes)andareev ocativeofsimplearchi tecturalmodels.Toinv estigatethedegreetow hichpeopleinvokedcat egory-specificpartconceptstodescr ibetheseobjects,rath erthanthesamesetof“atomic”baseprimitivesinallc ases,wefurtherdefinedfoursubdomainsnes tedwithineachdomain. WithinDrawings,these wereinformallydesign atedasnuts&bolts,vehicles,gadge ts,andfurni-ture;andwithinTowers,asbr idges,cities,houses, andcastles(Fig.1A). 0.15
Foreachsubdomain,wep rocedurallygenerated 250uniqueexamples,hi erarchicallycomposin gthebaseprimitivesin toincreasinglycomple x,recursivelydefinedparts.Adresser,fo rexample,iscomposedo fdrawers,whichareint urncomposedofapanela ndknobs,themselvesde finedbycombiningcircle sandlines.Insum,this procedureyieldedavar iedcollectionof2000o bjectstimuli:1000Dra wingsand1000Towers,e achaccompaniedbyagra phicsprogramthatcanb eusedtoregenerateiti ntermsofthebaseprimi tives.TaskprocedureE achparticipantwasins tructedtopro-videste p-by-stepinstruction sforhowto“draw”or“build”10different“drawings”or“models”sampledfromasin-gles ubdomain.Atthestarto feachsession,partici pantswerefirstfamiliarizedwitht hegeneralcharacteris ticsofthesubdomainby viewing25examples(no neofwhichthenappeare dduringthemainexperi ment,andnoneofwhichw ereaccompaniedbyanyl inguisticlabelsforth esubdomain). Foreachsubdomain,wep rocedurallygenerated 250uniqueexamples,hi erarchicallycomposin gthebaseprimitivesin toincreasinglycomple x,recursivelydefinedparts.Adresser,fo rexample,iscomposedo fdrawers,whichareint urncomposedofapanela ndknobs,themselvesde finedbycombiningcircle sandlines.Insum,this procedureyieldedavar iedcollectionof2000o bjectstimuli:1000Dra wingsand1000Towers,e achaccompaniedbyagra phicsprogramthatcanb eusedtoregenerateiti ntermsofthebaseprimi tives.TaskprocedureE achparticipantwasins tructedtopro-videste p-by-stepinstruction sforhowto“draw”or“build”10different“drawings”or“models”sampledfromasin-gles ubdomain.Atthestarto feachsession,partici pantswerefirstfamiliarizedwitht hegeneralcharacteris ticsofthesubdomainby viewing25examples(no neofwhichthenappeare dduringthemainexperi ment,andnoneofwhichw ereaccompaniedbyanyl inguisticlabelsforth esubdomain). 0.08
Throughoutthesession ,theywerealsoshownth e7upcomingobjectsthe ywouldbeaskedtodescr ibe,toprovideconcurr entinformationabouth owobjectsvariedwithi nthesubdomain.Becaus ewewereprimarilyfocu sedoninterrogatingwh ichpartdescriptorspe opleinvoke,wedesigne dthetext-entryinterf acetoen-courageparti cipantstodescribeeac hstepbycomposingawha t-phraseandawhere-ph rase,whichwereentere dintoseparatetextbox es.Participantscould includeasmanyinstruc tionstepsastheydeeme dnecessaryandtherewa snotrialtimelimit. Theywere alsoshownthe7upcomin gobjectstheywouldbea skedtodescribe,topro videconcurrentinform ationabouthowobjects variedwithinthesub domain.bywedesignedt hetext-entryinterfac etoen-couragepartici pantstodescribestepb ycomposingawhat-phra seandawhere-phrase,w hichwereenteredintos eparatetextboxes。 0.05
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bridgecityhousecastl enuts−boltswheelsdialsfurn iture−202−2−10123−3−2−1012−202−2−1012−2−1012−101234−3−2−101−2−10123−2−10123−1012−2−10123−2−1012−2−10123−2−1012−2−1012normalized program description length (base library)normalized linguistic description lengthMTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDR(1153 8) blue(9574) block(7659) red(2833) brick(2513) of(1711) horizontal(1330) vertical(1261) rectangle(1031) and(1016) on(2897) rectangle(2562) small(2067) circle(1480) line(1382) square(1140) of(581) vertical(566) large(553) horizontal(541) hexagon(1.96) hexagon(1.58) octagon(1.14) size(1.01) item(0.96) percent(0.56) border(0.51) page(0.46) cm(0.34) square(0.16) circle(1.95) wheel(1.40) tire(1.26) button(1.26) stand(1.15) window(1.09) star(1.05) rim(1.05) standing(1.05) drawing(1.01) stamp(1.47) inch(1.38) dial(1.36) line(1.16) image(1.13) frame(0.99) distance(0.99) segment(0.95) ring(0.95) position(0.90) radius(1.69) drawer(1.65) leg(1.47) approx(1.44) circumference(1.31) knob(1.29) ball(1.29) table(1.24) handle(0.97) vertical(0.88) rectangular(1.76) height(1.71) column(1.48) leg(1.30) bar(1.25) position(1.24) pillar(1.23) pair(1.18) width(1.18) tile(1.12) size(1.64) beam(1.43) horizontal(1.37) landscape(1.23) replica(1.12) time(1.10) orange(1.08) drawing(1.02) upside(0.99) hrs(0.92) vertical(2.01) window(1.80) figure(1.54) box(1.43) door(1.37) gap(1.10) center(1.04) rectangle(0.91) story(0.89) imagine(0.88) piece(1.13) tower(1.09) length(1.01) design(0.94) rectangularly(0.92) way(0.90) format(0.87) sequence(0.85) platform(0.83) image(0.75) formationMTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDRAB(11 538) blue(9574) block(7659) red(2833) brick(2513) of(1711) horizontal(1330) vertical(1261) rectangle(1031) and(1016) on(2897) rectangle(2562) small(2067) circle(1480) line(1382) square(1140) of(581) vertical(566) large(553) horizontal(541) hexagon%3"8*/(4508&34 BNTMSR 1.* 1.* BNTMSR Figure2:(A)Relations hipbetweenlengthofba se-libraryprogramsan dlengthoflinguisticd escriptions. bridgecityhousecastl enuts−boltswheelsdialsfurn iture−202−2−10123−3−2−1012−202−2−1012−2−1012−101234−3−2−101−2−10123−2−10123−1012−2−10123−2−1012−2−10123−2−1012−2−1012normalized program description length (base library)normalized linguistic description lengthMTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDR(1153 8) blue(9574) block(7659) red(2833) brick(2513) of(1711) horizontal(1330) vertical(1261) rectangle(1031) and(1016) on(2897) rectangle(2562) small(2067) circle(1480) line(1382) square(1140) of(581) vertical(566) large(553) horizontal(541) hexagon(1.96) hexagon(1.58) octagon(1.14) size(1.01) item(0.96) percent(0.56) border(0.51) page(0.46) cm(0.34) square(0.16) circle(1.95) wheel(1.40) tire(1.26) button(1.26) stand(1.15) window(1.09) star(1.05) rim(1.05) standing(1.05) drawing(1.01) stamp(1.47) inch(1.38) dial(1.36) line(1.16) image(1.13) frame(0.99) distance(0.99) segment(0.95) ring(0.95) position(0.90) radius(1.69) drawer(1.65) leg(1.47) approx(1.44) circumference(1.31) knob(1.29) ball(1.29) table(1.24) handle(0.97) vertical(0.88) rectangular(1.76) height(1.71) column(1.48) leg(1.30) bar(1.25) position(1.24) pillar(1.23) pair(1.18) width(1.18) tile(1.12) size(1.64) beam(1.43) horizontal(1.37) landscape(1.23) replica(1.12) time(1.10) orange(1.08) drawing(1.02) upside(0.99) hrs(0.92) vertical(2.01) window(1.80) figure(1.54) box(1.43) door(1.37) gap(1.10) center(1.04) rectangle(0.91) story(0.89) imagine(0.88) piece(1.13) tower(1.09) length(1.01) design(0.94) rectangularly(0.92) way(0.90) format(0.87) sequence(0.85) platform(0.83) image(0.75) formationMTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDRAB(11 538) blue(9574) block(7659) red(2833) brick(2513) of(1711) horizontal(1330) vertical(1261) rectangle(1031) and(1016) on(2897) rectangle(2562) small(2067) circle(1480) line(1382) square(1140) of(581) vertical(566) large(553) horizontal(541) hexagon%3"8*/(4508&34 BNTMSR 1.* 1.* BNTMSR Figure2:(A)Relations hipbetweenlengthofba se-libraryprogramsan dlengthoflinguisticd escriptions. 0.39
(B)Left:Top-10wordst hatappearedmostfrequ entlyindescriptionsf oreachdomain.Right:T op-10wordswithhighes tpointwisemutualinfo rmation(PMI)withinea chsubdomain.Language preprocessingToinves tigatethecontentofth einstructionsgenerat edbyparticipants,weu sedthespaCyNLPlibrar ytoextractandlemmati zewords,in-cludingpa rt-of-speech(POS)tag gingtoremovedeter-mi nersandpunctuation.W ealsoreplacedcommont ypos(“sqaure,”“cirlce,”etc.)andspellingvari ationswiththeircanon icalspellingsinUSEng lish.ResultsPeopleus emorewordsformorecom plexobjectsThesimple stwaythatobjectstruc turemaybeexposedinla nguageisthroughdescr iptioncomplexity.Wec onsiderthreepossibil ities.First,insofara sparticipantsdecom-p oseallobjectsintothe samenumberofparts,re gardlessofhowcomplex thesepartsare,thelen gthoftheirde-scripti onswouldbepredictedt oremainconstantovera widerangeofobjects.S econd,ifparticipants tendtodecomposeobjec tsintoasetofcommonly recurringparts,andme ntioneachpart,thelen gthoftheirdescriptio nswouldbepredictedto positivelycorrelatew ithobjectcomplexity: themoreparts,thelong erthedescription.Ath irdpossibilityisthat thereisasystematicbu tnon-linearrelations hipbetweenobjectcomp lexityandlinguisticd e-scriptionlength(Su n&Firestone,2021),cons istentwithacompromis ebetweenthefirsttwostrategies.Weo perationalizeobjectc omplexityhereasthele ngthofthe(base)graph icsprogramthatgenera tedit.Wemea-surethel engthoflinguisticdes criptionsasthenumber ofwordsprovidedinthe whatphrases(ignoring fornowspatiallanguag einthewherephrases). (B)Left:Top-10wordst hatappearedmostfrequ entlyindescriptionsf oreachdomain.Right:T op-10wordswithhighes tpointwisemutualinfo rmation(PMI)withinea chsubdomain.Language preprocessingToinves tigatethecontentofth einstructionsgenerat edbyparticipants,weu sedthespaCyNLPlibrar ytoextractandlemmati zewords,in-cludingpa rt-of-speech(POS)tag gingtoremovedeter-mi nersandpunctuation.W ealsoreplacedcommont ypos(“sqaure,”“cirlce,”etc.)andspellingvari ationswiththeircanon icalspellingsinUSEng lish.ResultsPeopleus emorewordsformorecom plexobjectsThesimple stwaythatobjectstruc turemaybeexposedinla nguageisthroughdescr iptioncomplexity.Wec onsiderthreepossibil ities.First,insofara sparticipantsdecom-p oseallobjectsintothe samenumberofparts,re gardlessofhowcomplex thesepartsare,thelen gthoftheirde-scripti onswouldbepredictedt oremainconstantovera widerangeofobjects.S econd,ifparticipants tendtodecomposeobjec tsintoasetofcommonly recurringparts,andme ntioneachpart,thelen gthoftheirdescriptio nswouldbepredictedto positivelycorrelatew ithobjectcomplexity: themoreparts,thelong erthedescription.Ath irdpossibilityisthat thereisasystematicbu tnon-linearrelations hipbetweenobjectcomp lexityandlinguisticd e-scriptionlength(Su n&Firestone,2021),cons istentwithacompromis ebetweenthefirsttwostrategies.Weo perationalizeobjectc omplexityhereasthele ngthofthe(base)graph icsprogramthatgenera tedit.Wemea-surethel engthoflinguisticdes criptionsasthenumber ofwordsprovidedinthe whatphrases(ignoring fornowspatiallanguag einthewherephrases). 0.05
Toteaseaparttheabove hypotheses,wefitamixed-effectsmodel topre-dictlinguistic descriptionlengthfro mgraphicsprogramleng th,includingrandomin terceptsforparticipa ntsandrandomeffectso fprogramlengthatthep articipantlevel.Weob servedasignificantmaineffectofprog ramlength(t(318)=14.8,p<0.001acrossallsubdom ains),provid-ingstro ngevidenceagainstthe firstview.Wealsofoundt hatamodelincludingan additionalquadratice ffectofprogramlength ,allowingforanon-lin earrelationship,sign ificantlyimprovedthefit(χ2(3)=38.6),althoughthestr engthofthisrelations hipvariedacrosssubdo mains(Fig.2A). Toteaseaparttheabove hypotheses,wefitamixed-effectsmodel topre-dictlinguistic descriptionlengthfro mgraphicsprogramleng th,includingrandomin terceptsforparticipa ntsandrandomeffectso fprogramlengthatthep articipantlevel.Weob servedasignificantmaineffectofprog ramlength(t(318)=14.8,p<0.001acrossallsubdom ains),provid-ingstro ngevidenceagainstthe firstview.Wealsofoundt hatamodelincludingan additionalquadratice ffectofprogramlength ,allowingforanon-lin earrelationship,sign ificantlyimprovedthefit(χ2(3)=38.6),althoughthestr engthofthisrelations hipvariedacrosssubdo mains(Fig.2A). 0.08
Thesefindingssuggestthatpeo plegenerallyusemorew ordstodescribemoreco mplexobjects,butthes trengthandnatureofth isrelationshipcanvar ywidelyacrossobjectc ategories.Peopleused ifferentpartsfordiff erentsubdomainsIfdes criptionlengthscales withobjectcomplexity (ex-pressedinthebase library),anaturalpos sibilityisthatspeake rsaresimplyproviding descriptionsatthelev elofthoselow-levelpr imitives.Forexample, theymaybegivingblock -by-blockinstruction sfortowersandline-by -lineinstructionsfor thedrawings.Inthisca se,wewouldnotexpectd ifferencesinthedistr ibutionofwordsusedac rosssubdomains(e g “bridges”and“houses”wouldbothbedescribed intermsofthesamereda ndblueblocks). Thesefindingssuggestthatpeo plegenerallyusemorew ordstodescribemoreco mplexobjects,butthes trengthandnatureofth isrelationshipcanvar ywidelyacrossobjectc ategories.Peopleused ifferentpartsfordiff erentsubdomainsIfdes criptionlengthscales withobjectcomplexity (ex-pressedinthebase library),anaturalpos sibilityisthatspeake rsaresimplyproviding descriptionsatthelev elofthoselow-levelpr imitives.Forexample, theymaybegivingblock -by-blockinstruction sfortowersandline-by -lineinstructionsfor thedrawings.Inthisca se,wewouldnotexpectd ifferencesinthedistr ibutionofwordsusedac rosssubdomains(e g “bridges”and“houses”wouldbothbedescribed intermsofthesamereda ndblueblocks). 0.04
Alternatively,ifspea kersgeneratedescript ionsathigherlevelsof conceptualabstractio n—forexample,intermsof “pillars”or“windows”—wewouldexpecttheirla nguagetoreflectthevaryingpartstr uctureofthesubdomain s.Toassessthesecompe tinghypotheses,wecom putedthepointwisemut ualinformation(PMI)f oreachuniquewordwint helanguagedatawithre specttothefoursubdom ainsd(Fig.2B):PMI(w) =logp(w,d)p(w)p(d)(1) Intuitively,PMIishig hforwordsthatoccurmo refre-quentlyinapart icularsubdomain(nume rator)thanwould あるいは、ifspeakers generatedescriptions athigherlevelsofconc eptualabstraction—forexample, intermsof “pillars”or“windows”—wewouldexpecttheir Languagetoreflectthe variouspartstructure ofthesub domains.Toassestheth eetinghypotheses,wec omputedthepointwisem utualinformation(PMI )foreachuniquewordwi nthelanguagedatawith respecttothefoursub domainsd(Fig.2B):PMI (w)=logp(w,d)p(w)p(d)(1) Intuitivelyly,PMIish ighforwordsthatococm ore-quentlylyinapart icular sub domains. 0.18
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beexpectedgiventheov erallprevalenceofthe wordacrosssubdomains andtheamountoflangua gedataineachsubdomai n(denominator). beexpectedgiventheov erallprevalence ofthewordacrosssub domainsandtheamounto flangdataineachsub domain(デノミネーター)。 0.19
Thisanalysisrevealed highlyspecializedvoc abulariesusedforpart icularsub-domains,bu tnotothers(e g ,drawerandknobinthef urnituresubdomain),s uggestingthatpartici pantsdidinvokesubdom ain-specificpartconceptstosomee xtent.Tobetterevalua tewhetherthesehighly diagnosticwordsreflectedmoresystematicd ifferencesinwordus-a geacrosssubdomains,w ecomputedtheJensen-S hannondistance(JSD)b etweenthewordfrequen cydistributionsineac hsetofsubdomains,agg regatingacrossalltri alsinthatsubdomain.T hismetriciszerowhent wodistribu-tionareid enticalandlargewhent wodistributionsarefa rapart.Wecomparedthe themeanofallpairwise JSDstoanulldistribut iongeneratedbyrandom lypermutingthesubdom aingroupofeachtrial. Wefoundthatthedistan cebetweensubdomainsw assignificantlygreaterthanex- pectedunderthenull(D rawings:d=0.439,p<0.001;Towers:d=0.328,p<0.001). Thisanalysisrevealed highlyspecializedvoc abulariesusedforpart icularsub-domains,bu tnotothers(e g ,drawerandknobinthef urnituresubdomain),s uggestingthatpartici pantsdidinvokesubdom ain-specificpartconceptstosomee xtent.Tobetterevalua tewhetherthesehighly diagnosticwordsreflectedmoresystematicd ifferencesinwordus-a geacrosssubdomains,w ecomputedtheJensen-S hannondistance(JSD)b etweenthewordfrequen cydistributionsineac hsetofsubdomains,agg regatingacrossalltri alsinthatsubdomain.T hismetriciszerowhent wodistribu-tionareid enticalandlargewhent wodistributionsarefa rapart.Wecomparedthe themeanofallpairwise JSDstoanulldistribut iongeneratedbyrandom lypermutingthesubdom aingroupofeachtrial. Wefoundthatthedistan cebetweensubdomainsw assignificantlygreaterthanex- pectedunderthenull(D rawings:d=0.439,p<0.001;Towers:d=0.328,p<0.001). 0.06
Takentogether,thesea nalysesindicatethatp eoplemaychoosedistin ctlabelstodescribevi suallysimilarpartsde pendingontherestofth escene(e g acirclemaybeaknobino nedomainandawheelina notherdomain),evenwh ensimplegraphicsprim itiveswouldhavebeens ufficient.PartII:Identif yingconceptsfromlang uageTheresultssofars uggestthatpeopleinvo kesubdomain-specificpartconceptswhendes cribingtheobjectsino urstimulusset,suchas knobsanddrawers,orwi ndowsanddoors.Whatac countsforobservedpre ferencesforthislexic on—howmanyandwhichpartc onceptsdopeoplehaven amesfor? Takentogether,thesea nalysesindicatethatp eoplemaychoosedistin ctlabelstodescribevi suallysimilarpartsde pendingontherestofth escene(e g acirclemaybeaknobino nedomainandawheelina notherdomain),evenwh ensimplegraphicsprim itiveswouldhavebeens ufficient.PartII:Identif yingconceptsfromlang uageTheresultssofars uggestthatpeopleinvo kesubdomain-specificpartconceptswhendes cribingtheobjectsino urstimulusset,suchas knobsanddrawers,orwi ndowsanddoors.Whatac countsforobservedpre ferencesforthislexic on—howmanyandwhichpartc onceptsdopeoplehaven amesfor? 0.04
Inthissection,weform alizethislibraryiden tificationproblembymodel ingthecorrespondence betweenpeo-ple’svocabulariesandaspa ceofcandidateconcept li-braries,eachconta iningpartconceptsatv aryinglevelsofcomple xity.Wedescribeaproc edureforconstructing can-didatelibrariesb asedonthehierarchica lstructureofeachsubd omain.Wethenintroduc ealibrary-to-vocabul aryalignmentmodeltha tmeasureshowwellprog ramswrit-tenineachli brarypredictpeople’sobjectdescriptions( Wongetal.,2021). 本条において,Weformalizethislibr aryidentificationpro blembymodelingthecor correspondingencebet weenpeo-ple’svocabulariesandaspa ceofcandateconceptli -braries,each containingpartconcep tsat various Levelsofcomplexity.W edescribeaproceduref orconstructingcan-di datelibraries basedonthehierarchic alstructureofeachsub domain.Wethenintrodu cealibrary-to-vocabu laryalignmentmodelme asureshowwell programsswrit-tenine achlibrarypredict People'sobjectdescriptions( Wongetal,2021) 0.06
Priorworksuggeststha tpeopleuselanguageth atef-ficientlycompressescon ceptsintowords(Regie retal.,2015;Kirbyetal.,2015;Zaslavskyetal.,2018;Sun&Firestone,2021). Priorworksuggeststha t peopleuse languagesthatef-fici entlycompressesconce ptsinwords (Regieretal.,2015;Kirbyetal.,2015;Zaslavskyetal.,2018;Sun&Firestone,2021) 0.23
Ourmodelallowsustode riveaninformation-th eoreticaccountoflexi calchoiceinourobject descriptions,whichfo rmallylinkslanguaget oeffi-cientcommunicationo fanobject’sunderlyingconceptua lrepresentation–wefindthatpeoplefavorale xiconthattradesoffbe tweenconcisedescript ionsofobjectsonav-er age,andthesizeoftheo verallconceptlibrari es.LbaseL1L2L3B@MCHC @SDBNMBDOSKHAQ@QHDROQNFQ@LO@QS ROQNFQ@LO@QSRblue_bl ock()red_block()...w indow()...row(6)...f loor(window, door, window)...house(h=2, w=3)roof(6)rotate(line (s=1), th=pi/6, r=1)...circle(scale=0.5)rotate(circle(s=0.1), th=pi/8, r=0.7)...hexagon(s=1)circle(s=0.5)rotate(circle(s=0.1), th=pi/8, r=0.7)...hexagon(s=1)circle(s=0.5)med_ring( circle(s=0.1), n=8)hex_circ_med_ring( n=8)KHAQ@QXRHYDOQNFQ@LKDMFSGFigure3:Graphi cslibrariesweredefinedbyprogressivelyad dingsubroutinesathig herlevelsofabstracti on,result-inginmoree fficientexpressionofany particularprogramatt heexpenseofalargerli brary.MethodsModelin gaspaceofcandidateco nceptlibrariesBydesi gn,theobjectsinourst imulussetarehighlyst ruc-tured,havingbeen generatedthroughtheh ierarchicalcombinati onofincreasinglycomp lexparts.However,the correspondinggraphic sprogramsthatrecreat ethemwerewrittenusin gaconceptlibrarycont ainingonlythebasepri mitives(Lbase):block sandlines.Asaconsequ ence,theseprogramsar emaximallyverbose:th eymustcom-posemanyin dividualblockstorepr esentadoor,letalonea nentirehouse;andmanyindividuallin estorepresentapolygo nlikeahexagon,letalo neacomplexwheel.Tore presentmorecomplexsh apes,wedefinehigher-ordergraphi cslibrariesthataugme nttheinitialsetofbas eprimitiveswithprogr amsubroutines(Fig.3) thatencap-sulatepart structure(e g ,asubroutineforgener atinganentireroof).1 Weconstructedtheseli brariesbyabstract-in goutthenested,parame tricfunctionsusedtog enerateeachsubdomain .Inourexperiments,we evaluatethreelibrari es(L1,L2,andL3),each containingsubroutine sthatbuildrecursivel yonthoseatthepreviou sleveltoyieldincreas inglycomplexvisualpa rts.Forinstance,L1co ntainssubroutinestha tabstractdirectlyove rthebaselibrary(e g ,fromlinestopolygons );andL2con-tainssubrou tinesthatabstractadd itionallyoverthosein L1(e g ,polygonstoringsofpo lygons). Ourmodelallowsustode riveaninformation-th eoreticaccountoflexi calchoiceinourobject descriptions,whichfo rmallylinkslanguaget oeffi-cientcommunicationo fanobject’sunderlyingconceptua lrepresentation–wefindthatpeoplefavorale xiconthattradesoffbe tweenconcisedescript ionsofobjectsonav-er age,andthesizeoftheo verallconceptlibrari es.LbaseL1L2L3B@MCHC @SDBNMBDOSKHAQ@QHDROQNFQ@LO@QS ROQNFQ@LO@QSRblue_bl ock()red_block()...w indow()...row(6)...f loor(window, door, window)...house(h=2, w=3)roof(6)rotate(line (s=1), th=pi/6, r=1)...circle(scale=0.5)rotate(circle(s=0.1), th=pi/8, r=0.7)...hexagon(s=1)circle(s=0.5)rotate(circle(s=0.1), th=pi/8, r=0.7)...hexagon(s=1)circle(s=0.5)med_ring( circle(s=0.1), n=8)hex_circ_med_ring( n=8)KHAQ@QXRHYDOQNFQ@LKDMFSGFigure3:Graphi cslibrariesweredefinedbyprogressivelyad dingsubroutinesathig herlevelsofabstracti on,result-inginmoree fficientexpressionofany particularprogramatt heexpenseofalargerli brary.MethodsModelin gaspaceofcandidateco nceptlibrariesBydesi gn,theobjectsinourst imulussetarehighlyst ruc-tured,havingbeen generatedthroughtheh ierarchicalcombinati onofincreasinglycomp lexparts.However,the correspondinggraphic sprogramsthatrecreat ethemwerewrittenusin gaconceptlibrarycont ainingonlythebasepri mitives(Lbase):block sandlines.Asaconsequ ence,theseprogramsar emaximallyverbose:th eymustcom-posemanyin dividualblockstorepr esentadoor,letalonea nentirehouse;andmanyindividuallin estorepresentapolygo nlikeahexagon,letalo neacomplexwheel.Tore presentmorecomplexsh apes,wedefinehigher-ordergraphi cslibrariesthataugme nttheinitialsetofbas eprimitiveswithprogr amsubroutines(Fig.3) thatencap-sulatepart structure(e g ,asubroutineforgener atinganentireroof).1 Weconstructedtheseli brariesbyabstract-in goutthenested,parame tricfunctionsusedtog enerateeachsubdomain .Inourexperiments,we evaluatethreelibrari es(L1,L2,andL3),each containingsubroutine sthatbuildrecursivel yonthoseatthepreviou sleveltoyieldincreas inglycomplexvisualpa rts.Forinstance,L1co ntainssubroutinestha tabstractdirectlyove rthebaselibrary(e g ,fromlinestopolygons );andL2con-tainssubrou tinesthatabstractadd itionallyoverthosein L1(e g ,polygonstoringsofpo lygons).
訳抜け防止モード: Ourmodelallowsustode riveaninformation - Theoreticaccountofle xicalchoiceinourobje ctdescriptions, whichformallylinksla ngtoeffi-cientcommun icationofanobject’sunderlyingconceptua lrepresentation – wefindthatpeoplefavo ralexiconthattradesb etweenconcisedescrip tionsofobjectsonav - erage, andthesizeoftheovera llconceptlibraries . LbaseL1L2L3B@MCHC@SD \BNMBDOS\KHAQ@QHDROQ NFQ@LOSROQNQQQQ@LOSR blue_block()red_bloc k() window...() floor(6, house, house, house, house, house, house, house, 2, house, house) w=3roof(6)rotate(line( s=1 ), th = pi/6, r=1) ... circle(scale=0.5)rotate(circle(s=0.1 ), th = pi/8, r=0.7) ... hexagon(s=0.5)circle(s=0.1)rotate(circle(s=0.1), th = pi/8, r=0.7) ... hexagon(s=0.5)med_ring( circle(s=0.1), n=8)hex_circ_med_ring( n=8)KHAQ@QX\RHYDOQNFQ@ L\KDMFSGFigure3 : Graphicslibrarieswer edefinedbyprogressiv elyaddingsubroutines athigherlevelsofabst raction, result - inginmoreefficientex pressionofanyicular programsatenseofthee xpenseofargerallibra ry Methods Modelsacancaningspac esconceptordinationB resigns, the highjectorlevelsofab straction. havingbeen generatedthroughtheh ierarchicalcombinati onofineasinglycomple xparts. しかし、conceptlibrary containsonlythebasep rimitives(Lbase):blo cksandlines . Asaconsequence, these programsaremaximally verbose : theymustcom - posemanyindividualbl ockstorepresentadoor , letaloneanentirehous e;andmanyindividuallin estorepresentapolygo nlikeahexagon, letaloneacomplexwhee l . Torepresentmorecompl exshapes, wedefinehigher - ordergraphicslibrari esthataugmenttheinit ialsetofbaseprimitiv eswith programssubroutines( Fig.3)thatencap - sulatepartstructure( e g, asubroutineforgenera tinganentireroof).1W econstructedtheselib rariesbyabstract - ingoutthenested, parametricfunctionsu sedtogenerateeach sub domain . Inourexperiments, weevaluate Threelibraries(L1,L2 ,andL3),each containingsubroutine sthatbuildrecursivel yonthoseatpreviousle veltoyieldincreasing lycomplexvisualparts . Forinstance, L1containssubroutine sthatabstractlyovert hebaselibrary(e g, fromlinestopolygons) ;andL2con - tainssubroutinesthat abstractitionallyove rthoseinL1(e g, polygonstoringsofpol ygons )
0.13
Agiven1Ourapproachto definingthesehigher-orde rlibrariesisanalogou stotheautomatedprogr amlibrarylearningmet hodsin(Ellisetal.,20 20;Tianetal.,2020;McCarthyetal.,2021;Wangetal.,2021;Wongetal.,2021),whic hdiscoversubroutines fromadatasetcontaini ngprogramsthatoftenc orrespondqualitative lytodomain-relevantc oncepts. Agiven1Ourapproachto definingthesehigher- orderlibrariesisanal ogoustotheautomated programslibrarylearn ingmethodsin (Ellisetal.,2020;Tianetal.,2020;McCarthyetal.,2021;Wangetal.,2021;Wongetal.,2021) whichdiscoversubrout inesfromadataset containing programss Thatoftencorqualitat ivelyto domain-relevantconce pts。 0.12
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programπLbasewritteninthebas elibrarycantherefore beexpressedequivalen tly—andmoreconcisely—asπLiinoneofthehigher-o rderlibraries.Itiswo rthnotingthathigher- orderlibrariesarethu sdefinedcumulatively:L1co ntainsthenewsubrouti nesplustheinitialset ofprimitivesinLbase;andL2containsevenhig her-ordersubroutines plusalloftheconcepts inL1.Modelingalignme ntbetweenlibrariesan dvocab-ulariesForeac hsubdomain,thesetofl ibraries{Lbase,L1,L2,L3}specifiesahypothesisspaceof alterna-tiverepresen tationsatdifferingle velsofabstraction.We cannowask:whichofthe selibrariesbestcorre spondstothelexiconpe opleuseforeachsubdom ain? programπLbasewritteninthebas elibrarycantherefore beexpressedequivalen tly—andmoreconcisely—asπLiinoneofthehigher-o rderlibraries.Itiswo rthnotingthathigher- orderlibrariesarethu sdefinedcumulatively:L1co ntainsthenewsubrouti nesplustheinitialset ofprimitivesinLbase;andL2containsevenhig her-ordersubroutines plusalloftheconcepts inL1.Modelingalignme ntbetweenlibrariesan dvocab-ulariesForeac hsubdomain,thesetofl ibraries{Lbase,L1,L2,L3}specifiesahypothesisspaceof alterna-tiverepresen tationsatdifferingle velsofabstraction.We cannowask:whichofthe selibrariesbestcorre spondstothelexiconpe opleuseforeachsubdom ain? 0.05
Weformalizethisnotio noflexicalcorrespond encewithalibrary-to- vocabularyalignmentm etricthatreflectshowcloselythecon ceptsinagivenlibrary co-occurwithwordsacr osseachsubdomain.Thi smetricisbasedalangu age-guidedlibrarylea rningmodelfromthepro gramsynthesislitera- ture(Wongetal.,2021) . Weformalizethisnotio noflexicalcor correspondingence withalibrary-to-voca bularyalignmentmetri cthatreflectshowclos elytheconceptsinagiv enlibraryco-occurwit hwordsacrosseachsub domain. Thismetricisbaseda Language-guidedlibra ry learningmodel fromthe programming synthesislitera-ture (Wongetal.,2021) 0.04
Inbrief,weleverageas tandardmachinetransl ationmodel,IBMModel1 (Brownetal.,1993),wh ichcanbefittopairedprogramsand instructionstoestima tetoken-tokentransla tionprobabilitiesP(w |ρ)foreachwordw∈Winthelinguisticvoca bularyandprogramcomp onentρ∈Linthelibrary.Foreac hsubdo-main,weevalua teeachlibraryLiusing across-validationsch eme(withbatchesofn=5heldoutstimuli). Inbrief,weleverageas tandardmachine translationmodel,IBM Model1 (Brownetal., 1993) whichcanbefittopaire d programssandinstruct ionstoestimatetoken- token translationprobabili tiesP(w|ρ)foreachwordw・Winthelinguisticvoca bulary・ programcomponentρ・Linthelibrary.Foreac hsubdo-main,weevalua teeachlibraryLiusing across-validationsch eme(withbatchesofn=5heldoutstimuli) 0.17
Wefitthemodeltoallbutthe held-outstimuliandev aluatethemeanper-wor dlog-likelihoodforea chheldoutinstruc-tio ngivenitsprograminli braryLi.Thismetricva riesmonotonicallyasa functionofnegativepe rplexity(Wuetal.,201 6)andnormalizesforin structionlengths.Asi nPartI,weconsideronl ythewhatphrasesforea chstimulus.ResultsLi brariesproducediffer enttrade-offbetweenc onciseobjectrepresen tationandoveralllibr arysizeSup-posingtha tanyoftheselibraries capturesthepartcon-c eptsthatpeopleusewhe ndescribingtheseobje cts,whatwouldleadpar ticipantstofavoroneo veranother? Wefitthemodeltoallbutthe held-outstimuliandev aluatethemeanper-wor dlog-likelihoodforea chheldoutinstruc-tio ngivenitsprograminli braryLi.Thismetricva riesmonotonicallyasa functionofnegativepe rplexity(Wuetal.,201 6)andnormalizesforin structionlengths.Asi nPartI,weconsideronl ythewhatphrasesforea chstimulus.ResultsLi brariesproducediffer enttrade-offbetweenc onciseobjectrepresen tationandoveralllibr arysizeSup-posingtha tanyoftheselibraries capturesthepartcon-c eptsthatpeopleusewhe ndescribingtheseobje cts,whatwouldleadpar ticipantstofavoroneo veranother? 0.03
Ourhypothesisisthatt hischoicereflectsatrade-offbetwee nthevalueofcompressi ngthelengthofprogram s|πLi|thatrepresentindivid ualobjectsandthevalu eofreducingthetotaln umberofconcepts|Li|storedinthelibrary(F ig.3)2.Higher-orderl ibrariescontainconce ptsthatcom-pressprog ramstoagreaterdegree ,aseachprogramcanbew rittenbyinvokingasma llernumberofmoreabst ractsubroutines.Howe ver,eachhigher-order libraryisalsolargert hanthelastbecauseita ddsnewconceptsthatmu stberepresentedalong withallofthelower-le velones.2Thistrade-o ffbetweenprogramdesc riptionlength|πLi|andlibrarysize|Li|isdescribedingreater detailin(Ellisetal., 2020)andanalogoustot heformulationin(Kirb yetal.,2015). Ourhypothesisisthatt hischoicereflectsatrade-offbetwee nthevalueofcompressi ngthelengthofprogram s|πLi|thatrepresentindivid ualobjectsandthevalu eofreducingthetotaln umberofconcepts|Li|storedinthelibrary(F ig.3)2.Higher-orderl ibrariescontainconce ptsthatcom-pressprog ramstoagreaterdegree ,aseachprogramcanbew rittenbyinvokingasma llernumberofmoreabst ractsubroutines.Howe ver,eachhigher-order libraryisalsolargert hanthelastbecauseita ddsnewconceptsthatmu stberepresentedalong withallofthelower-le velones.2Thistrade-o ffbetweenprogramdesc riptionlength|πLi|andlibrarysize|Li|isdescribedingreater detailin(Ellisetal., 2020)andanalogoustot heformulationin(Kirb yetal.,2015). 0.04
Whilelibrarysizeincr easesmonotonicallywi thab-stractionlevel, everysubdomainhasano n-monotoniccombinedr epresentationalcostC Li=|Li|+1N∑π|πLi|,whereNisthenumberof programsinthesubdoma in.Aone-wayANOVAconfirmsthat,ineverysubdo main,thiscombinedcos tmeasuresystematical lyvariesbetweenli-br aries(ps(cid:28)0.00 1),validatingourassu mptionthattheselibra riescapturedifferent waysofnegotiatingthe trade-offbetweenobje ctcompressionandlibr arysize.Further,asFi g.4reveals,CLi(dashe dline)typicallyfollo wsaU-shapedcurve.Att heextremes,CLbaseish ighbecauseprogramsin Lbaseareverbose,wher easCL3ishighduetothe largesizeofL3.Inalls ubdomains,CL1andCL2t endtobeoptimalbecaus etheseintermediateli brariescontainasetof usefulpart-basedabst ractionsthatcapturer ecurringstructureacr ossmanyobjects.Peopl efavorvocabulariesth atjointlyminimizeob- jectrepresentationan dlibrarysizeWecannow con-sidertheresultso fourlibrary-to-vocab ularyalignmentmodel: whichlibrariesbestpr edictthewordspeopleu seacrosseachsubdomai n? Whilelibrarysizeincr easesmonotonicallywi thab-stractionlevel, everysubdomainhasano n-monotoniccombinedr epresentationalcostC Li=|Li|+1N∑π|πLi|,whereNisthenumberof programsinthesubdoma in.Aone-wayANOVAconfirmsthat,ineverysubdo main,thiscombinedcos tmeasuresystematical lyvariesbetweenli-br aries(ps(cid:28)0.00 1),validatingourassu mptionthattheselibra riescapturedifferent waysofnegotiatingthe trade-offbetweenobje ctcompressionandlibr arysize.Further,asFi g.4reveals,CLi(dashe dline)typicallyfollo wsaU-shapedcurve.Att heextremes,CLbaseish ighbecauseprogramsin Lbaseareverbose,wher easCL3ishighduetothe largesizeofL3.Inalls ubdomains,CL1andCL2t endtobeoptimalbecaus etheseintermediateli brariescontainasetof usefulpart-basedabst ractionsthatcapturer ecurringstructureacr ossmanyobjects.Peopl efavorvocabulariesth atjointlyminimizeob- jectrepresentationan dlibrarysizeWecannow con-sidertheresultso fourlibrary-to-vocab ularyalignmentmodel: whichlibrariesbestpr edictthewordspeopleu seacrosseachsubdomai n? 0.05
Tovalidatethatthisal ignmentmetricisablet odiscriminatebetween librariesatall,wefirstconductedaone-way ANOVAonthealignments coresandfoundlargean dreliabledifferences betweenlibrariesinev erysubdomain(ps<0.001;Fig.4). tovalidatethatthisal ignmentmetricisablet odiscriminate betweenlibrariesatal l,wefirstconductedao ne-wayanovaonthealig nmentscoresandfounda ndreliabledifference s betweenlibrariesinev erysubdomain(ps<0.001;fig.4) 0.07
Whenwevisualizedthes ealignmentscores(Fig .4,solidlines),weobs ervedthatforthemajor ityofthesubdomains,t hemeanlog-likelihood sfollowsanin-vertedU -shapedcurve.Moreove r,wegenerallyfindthattheconceptlibr ariesthatbestpredict languagetendtobethos econtainingpartsofin termediatecomplexity —forexample,partconce pts(e g ,individualwindowsor wheels)thatliebetwee nthelowest(e g ,lines)andhighest(e g ,hexagonwithaninnerr ingofcircularholes)l evelsofabstractionin eachdomain.Finally,w eobservedastrikingco rrespondencebe-tween thelibrariesthatopti mizecombinedrepresen ta-tionalcost(CLi)an dthosethatscorehighl yontheirabil-itytopr edictlanguage.Thispa ttern,whichheldformo st(thoughnotall)subd omains,suggeststhatp eoplegener-allyprefe rdecomposingobjectsi ntonameablepartsthat canbereusedformanyob jectsacrossthefullsu bdomain.DiscussionTh elanguageweusetodesc ribetheworldrevealst heconceptswithwhichw erepresentit.Inthisp aper,welooktonatural languagetoinvestigat ehowpeopleparsecompl exobjectsintomeaning fulparts—forexample,howpeople decomposeawholetrain intoitstraincarsandw heels,orahouseintoit swindows,walls,andro of.Weeliciteddescrip tionsforalargedatase tofobjectsgeneratedf romgraphicsprograms, andpresentacomputati onalapproachforlinki ngtheirgenerative Whenwevisualizedthes ealignmentscores(Fig .4,solidlines),weobs ervedthatforthemajor ityofthesubdomains,t hemeanlog-likelihood sfollowsanin-vertedU -shapedcurve.Moreove r,wegenerallyfindthattheconceptlibr ariesthatbestpredict languagetendtobethos econtainingpartsofin termediatecomplexity —forexample,partconce pts(e g ,individualwindowsor wheels)thatliebetwee nthelowest(e g ,lines)andhighest(e g ,hexagonwithaninnerr ingofcircularholes)l evelsofabstractionin eachdomain.Finally,w eobservedastrikingco rrespondencebe-tween thelibrariesthatopti mizecombinedrepresen ta-tionalcost(CLi)an dthosethatscorehighl yontheirabil-itytopr edictlanguage.Thispa ttern,whichheldformo st(thoughnotall)subd omains,suggeststhatp eoplegener-allyprefe rdecomposingobjectsi ntonameablepartsthat canbereusedformanyob jectsacrossthefullsu bdomain.DiscussionTh elanguageweusetodesc ribetheworldrevealst heconceptswithwhichw erepresentit.Inthisp aper,welooktonatural languagetoinvestigat ehowpeopleparsecompl exobjectsintomeaning fulparts—forexample,howpeople decomposeawholetrain intoitstraincarsandw heels,orahouseintoit swindows,walls,andro of.Weeliciteddescrip tionsforalargedatase tofobjectsgeneratedf romgraphicsprograms, andpresentacomputati onalapproachforlinki ngtheirgenerative 0.07
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-HAQ@QXRHYD OQNFQ@LKDMFSG C@RGDC -HAQ@QXSNUNB@ATK@QX@KHFMLDMS RNKHC BaseL1L2L31401601802 00220240260-4.5-4.0- 3.5-3.0-2.5-2.0BaseL 1L2L3501001502002503 00-5.0-4.5-4.0-3.5-3 .0-2.5-2.0-1.5BaseL1 L2L350100150200250-5 .0-4.5-4.0-3.5-3.0-2 .5BaseL1L2L312515017 5200225250275-4.0-3. 5-3.0-2.5BaseL1L2L31 00120140160180200-4. 0-3.8-3.6-3.4-3.2-3. 0-2.8BaseL1L2L360801 00120140160180-3.3-3 .2-3.1-3.0-2.9-2.8-2 .7BaseL1L2L375100125 150175200225-3.8-3.6 -3.4-3.2-3.0-2.8Base L1L2L380100120140160 180-3.0-2.8-2.6-2.4- 2.2MTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDR#@RD- --#@RD---#@RD---#@RD---#@RD---#@RD---#@RD---#@RD---Figure4:Relationship betweenconceptlibrar ies{Lbase,L1,L2,andL3}(x-axis);combinedlibrarysizea ndaverageprogramleng thinthatlibrary(dash ed);andlibrary-to-vocabu laryalignment(solid) . -HAQ@QXRHYD OQNFQ@LKDMFSG C@RGDC -HAQ@QXSNUNB@ATK@QX@KHFMLDMS RNKHC BaseL1L2L31401601802 00220240260-4.5-4.0- 3.5-3.0-2.5-2.0BaseL 1L2L3501001502002503 00-5.0-4.5-4.0-3.5-3 .0-2.5-2.0-1.5BaseL1 L2L350100150200250-5 .0-4.5-4.0-3.5-3.0-2 .5BaseL1L2L312515017 5200225250275-4.0-3. 5-3.0-2.5BaseL1L2L31 00120140160180200-4. 0-3.8-3.6-3.4-3.2-3. 0-2.8BaseL1L2L360801 00120140160180-3.3-3 .2-3.1-3.0-2.9-2.8-2 .7BaseL1L2L375100125 150175200225-3.8-3.6 -3.4-3.2-3.0-2.8Base L1L2L380100120140160 180-3.0-2.8-2.6-2.4- 2.2MTSRANKSRF@CFDSRUDGHBKDR ETQMHSTQDB@RSKDRGNTR DRAQHCFDRBHSHDR#@RD- --#@RD---#@RD---#@RD---#@RD---#@RD---#@RD---#@RD---Figure4:Relationship betweenconceptlibrar ies{Lbase,L1,L2,andL3}(x-axis);combinedlibrarysizea ndaverageprogramleng thinthatlibrary(dash ed);andlibrary-to-vocabu laryalignment(solid) . 0.10
andhierarchicalstruc turewithhumandescrip tions.Wefindthatthelengthofpeo ple’sdescriptionsvariesw iththelengthofanobje ct’sgenerativeprogram,e stablish-ingabasicco rrespondencebetweenl anguageandapro-gramr epresentationsofobje ctstructure.Byconstr uctinghigher-orderco nceptlibrarieswhichr e-representeachobjec tusingmoreabstractpr ogramcomponents,wefindevidencethatpeople ’slanguagereflectsanunderlyingrep- resentationaltrade-o ff–peopleprefercompactl ibrariesofpartconcep tsthatefficientlycapturestruct uralmotifsappearingi nmanyobjects.Anintri guingimplicationofth esefindingsisthatthereexi stsa“basiclevel”forpartnaming,byanal ogytothewellknownbas iclevelforobjectcate gories,andthatcanbee xplainedbysimilarinf ormation-theoreticpr inciples(Roschetal., 1976). andhierarchicalstruc turewithhumandescrip tions.Wefindthatthelengthofpeo ple’sdescriptionsvariesw iththelengthofanobje ct’sgenerativeprogram,e stablish-ingabasicco rrespondencebetweenl anguageandapro-gramr epresentationsofobje ctstructure.Byconstr uctinghigher-orderco nceptlibrarieswhichr e-representeachobjec tusingmoreabstractpr ogramcomponents,wefindevidencethatpeople ’slanguagereflectsanunderlyingrep- resentationaltrade-o ff–peopleprefercompactl ibrariesofpartconcep tsthatefficientlycapturestruct uralmotifsappearingi nmanyobjects.Anintri guingimplicationofth esefindingsisthatthereexi stsa“basiclevel”forpartnaming,byanal ogytothewellknownbas iclevelforobjectcate gories,andthatcanbee xplainedbysimilarinf ormation-theoreticpr inciples(Roschetal., 1976). 0.06
Whiletheselinguistic abstractionlayersena blegreatercompressio n,theymayalsointrodu cedownstreamchal-len gesforcommunication: termswithmoreabstrac tmeaningsmaybelessin terpretableand/ortoo lossyinsomecases(e g ,pedagogicalcontexts wherelearnersmaynotb efamiliarwithcertain concepts). Theseselinguisticabs tractionlayersenable Greatercompression,t heymay also alsointroducedownstr eamchal-lengesforcom munication:termswith moreabstract meaningsmaybelessint erpretableand/ortool ossyinsomecases (e g ,pedagogicalcontexts wherelearnersmaynotb efamiliarwithcertain concepts)。 0.08
Tobetterunderstandho wpeoplecommunicatein thesescenarios,itmay beusefultoconductexp erimentsmanipulating whatknowledgeisshare dbetweencommunicator stoin-vestigatethero leofaudiencedesignan dadaptationininterac tivesettings(Clark&a mp;Murphy,1982;Krauss&Fussell,1991;McCarthyetal.,2021). Tobetterunderstandho w Peoplecommunicateint hesescenarios,itmayb eusefultoconductexpe riments Manipulatingwhatknow ledgeissharedbetween communicatorstoin-ve stigatetheroleofaudi encedesignandadaptat ionininteractivesett ings (Clark&Murphy,1982;Krauss&Fussell, 1991;McCarthyetal.,2021)。 0.07
Inothersettings,thel evelofdetailcontaine dinthedescriptionswe collectedmaynotbenec essarytoachievecerta incommunicativegoals ,suchasobjectidentification.Apromisingdir ectionistocompareour descriptionstothosep roducedinreferencega meswherecoarserdisti nc-tionsbetweenwhole objectsaresufficient,withtheaimofun derstandinghowtaskgo alsandcontextshapeth erelevanceofdifferen tlevelsofabstraction (Degenetal.,2020;Bisketal.,2020). Inothersettings,thel evelofdetailcontaine dinthedescriptionswe collectedmaynotbenec essarytoachievecerta incommunicativegoals ,suchasobjectidentif ication.Apromisingdi rectionistocompareou rdescriptionstothose producedinreferenceg ameswherecoarserdist inc-tionsbetweenwhol eobjectsaresufficien t,withtheaimofunders tandinghowtaskgoalsa ndcontextshapetherel evanceofdifferentlev elsofabstraction (Degenetal, 2020; Bisketal, 2020) 0.03
Itisnaturaltoexpects ubstantialvariationa crossde-scriptionsin howwelltheysupportob jectunderstandingino thers.Tobetterunders tandwhysomedescripti onsaremoreinformativ ethanothers,futurewo rkshouldalsomeasureh owwellthedescription swecollectedinthecur rentstudysupportthea bilityofotherpartici pantstoaccuratelyrec onstructthetargetobj ects.Ourapproachandfindingsbuildonarecent andgrow-ingliteratur eusingprograms(Lakee tal.,2015;Goodmanetal.,2014)an dlibrariesoffunction alcomponents(Tianeta l.,2020;McCarthyetal.,2021;Wongetal.,2021)tomod elhowpeoplerepresent andcommunicateaboutt heworld.Ourworkgener alizespreviousinsigh tsintothestatistical learningmechanismsth atenabletherapidlear ningofvisualregulari ties(Fiser&Aslin,2001;Orb´anetal.,2008;Austerweil&Griffiths,2013)byproposing amoreexpressiveprogr am-likerepresentatio nthatcanaccommodates tructureatmultiplele velsofabstraction.Mo rebroadly,ourworkpro posesandvalidatesage n-eralstrategyforlev eragingcomplexbehavi oralreadouts(e g ,naturallanguagedesc riptions)todrawricha ndmeaningfulinferenc esaboutthecontentand structureofmentalrep resentations.Suchapp roacheshavetremen-do uspromisenotonlytoad vancecognitivetheory ,butmaycontributetot hedesignofartificialsystemsthatlearn morehuman-likeabstra ctions. Itisnaturaltoexpects ubstantialvariationa crossde-scriptionsin howwelltheysupportob jectunderstandingino thers.Tobetterunders tandwhysomedescripti onsaremoreinformativ ethanothers,futurewo rkshouldalsomeasureh owwellthedescription swecollectedinthecur rentstudysupportthea bilityofotherpartici pantstoaccuratelyrec onstructthetargetobj ects.Ourapproachandfindingsbuildonarecent andgrow-ingliteratur eusingprograms(Lakee tal.,2015;Goodmanetal.,2014)an dlibrariesoffunction alcomponents(Tianeta l.,2020;McCarthyetal.,2021;Wongetal.,2021)tomod elhowpeoplerepresent andcommunicateaboutt heworld.Ourworkgener alizespreviousinsigh tsintothestatistical learningmechanismsth atenabletherapidlear ningofvisualregulari ties(Fiser&Aslin,2001;Orb´anetal.,2008;Austerweil&Griffiths,2013)byproposing amoreexpressiveprogr am-likerepresentatio nthatcanaccommodates tructureatmultiplele velsofabstraction.Mo rebroadly,ourworkpro posesandvalidatesage n-eralstrategyforlev eragingcomplexbehavi oralreadouts(e g ,naturallanguagedesc riptions)todrawricha ndmeaningfulinferenc esaboutthecontentand structureofmentalrep resentations.Suchapp roacheshavetremen-do uspromisenotonlytoad vancecognitivetheory ,butmaycontributetot hedesignofartificialsystemsthatlearn morehuman-likeabstra ctions. 0.04
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AcknowledgmentsRDHis supportedbyNSFgrant# 1911835andaPrince-to nC.V. AcknowledgmentsRDHis SupportedbyNSFgrant# 1911835anda Prince-tonC.V 0.24
StarrFellowship.JEFi ssupportedbyNSFCA-RE ER#2047191,anONRScie nceofAutonomyaward,a ndaStanfordHoffman-Y eegrant.GGissupporte dbyanMITPresidential FellowshipandanNSFGr aduateResearchFellow ship.CW,JBT,andJDAar esupportedbytheMITQu estforIntelligence,a ndCWandJBThaveadditi onalsupportfromAFOSR Grant#FA9550-19-1-02 69,theMIT-IBMWatsonA ILab,ONRScienceofAIa ndDARPAMachineCommon Sense.Allcodeandmate rialsavailableat:htt ps://github.com/cogt oolslab/lax-cogsci22 ReferencesAusterweil ,J.L.,&Griffiths,T.L.(2013). StarrFellowship.JEFi s SupportedbyNSFCA-REE R#2047191,anONRScien ceofAutonomyaward,an daStanfordHoffman-Ye egrant.GGis SupportedbyanMITPres identialFellowshipan danNSFGraduateResear chFellowship.CW,JBT, andJDAare supportededMITQuestf orIntelligence,andCW andJBThaveadditional SupportfromAFOSRGran t#FA9550-19-1-0269,t heMIT-IBMWatsonAILab ,ONRScienceofAIandDA RPAMachineCommonSens e.AllcodeandSappatat :https://thub.comto/ coto/cocococos.cos.c os.cos.cos.cos.cos.c os.L.L.(2013) 0.12
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Supplemental:Identif yingconceptlibraries fromlanguageaboutobj ectstructureS1.PartI SupplementalDetailsT hissectioncontainsad ditionaldetailsonthe stimulusgenerationpr ocedureinPartIofthem ainpaper.Stimulusgen erationAsdiscussedin themainpaper,thedata setcomprisestwodisti nctstimulusdomains(d rawingsandtowers). supplemental:identif yingconceptlibraries fromlanguageaboutobj ectstructures1.parti supplementaldetails thissectioncontainsa dditionaldetailsonth estimulusgenerationp rocedureinpartiofthe mainpaper.stimulusge nerationasdiscussedi nthemainpaper,thedat asetcomprisestwodist inctstimulusdomains( drawingsandtowers) 0.04
Eachdomainisdefinedformallyoveranini tiallibraryofbasepro gramprimitivesLbase, andahierarchicalgene rativemodeltoprocedu rallyconstructgraphi csprogramsforrenderi ngobjectstimuliwithi ngfournestedsubdomai nswithvaryinghigher- orderpartstructure.T hissectionprovidesad ditionaldetailsonthe sedo-mains.Thefullge nerativemodelsforbot hdomains,alongwithth egeneratedstimuli,ar ereleasedattherepos- itory.Drawingsstimul usgeneration.Initial primitivesLbase.Thei nitialprogramprimiti vesforthedrawingdoma inconsistofaCAD-like setofsimplebaseshape primitivesandmatrixo perationsfortransfor m-ingandcombiningthe seshapesintoafinaldrawing:•line:aunit-lengthhor izontallineshape. Eachdomainisdefinedformallyoveranini tiallibraryofbasepro gramprimitivesLbase, andahierarchicalgene rativemodeltoprocedu rallyconstructgraphi csprogramsforrenderi ngobjectstimuliwithi ngfournestedsubdomai nswithvaryinghigher- orderpartstructure.T hissectionprovidesad ditionaldetailsonthe sedo-mains.Thefullge nerativemodelsforbot hdomains,alongwithth egeneratedstimuli,ar ereleasedattherepos- itory.Drawingsstimul usgeneration.Initial primitivesLbase.Thei nitialprogramprimiti vesforthedrawingdoma inconsistofaCAD-like setofsimplebaseshape primitivesandmatrixo perationsfortransfor m-ingandcombiningthe seshapesintoafinaldrawing:•line:aunit-lengthhor izontallineshape. 0.03
•circle:aunit-radiusc ircleshape. circle:aunit-radiusc ircleshape。 0.32
•square:aunitlengthsq uareshape. ^ square:aunitlength squareshape 0.34
•scaledrect(w,h):arec tangleparameterizedb ywidthandheight. •scaledrect(w,h):arec tangleparameterized bywidthandheight。 0.45
•graphicsmatrix(scale ,theta,x,y):pro-duce satransformationmatr ixparameterizedbysca le,rotationangle,and xandytranslationangl e. •graphicsmatrix(scale ,theta,x,y):pro-duce satransformationmatr ixparameterizedbysca le,rotationangle,and xandytranslationangl e。 0.24
•applytransform(shape ,matrix):appliesatra ns-formationmatrixto ashape. •applytransform(shape ,matrix):appliesatra ns-formationmatrixto ashape 0.47
•repeat(shape,n,matri x):Appliesthesametra nsformationsuccessiv elyntimestoagivensha peandreturnsallofthe nshapes. •repeat(shape,n,matri x):appliesthesametra nsformationsuccessiv elyntimestoagivensha peandreturnsallofthe nshapes 0.09
•connect(shape,shape) :Connectstwoshapesin toasinglecomplexshap e. •connect(shape,shape) :Connectstwoshapesin toasinglecomplexshap e。 0.22
•Mathematicaloperatio ns(eg.plus,minus,sin )overfloatingconstants.Draw ingsgenerativemodel. Drawingsstimuliarede -finedoverthebaseprimit ivesasprogramswhichc om-binesubdomain-spe cificpartsaccordingtovar iedpro-gramtemplates ,parameterizedbythen umberandsizeofeachpa rt.Wegeneratestimuli bysamplingrandomized parameterizationsove rthesetemplatestopro ducethe250stimulisam pledforeachsubdomain .Thesesubdomainarede scribedbelowusingsem antictermsfortheirhi erar-chialpartstruct ure,butthesetermssim plycorrespondtotempl atedgraphicsprograms parameterizedrecursi velybysizeandnumbero fsubparts.Wedefinethefollowingfourdr awingssubdomains,des cribedwithahigh-leve loverviewoftheirunde rlyingpartstructure: •nutsandbolts:combine spartsforanoutershap e(eg.ahexagonalnut)o fvaryingsize,andinne rper-forationofvaryi ngsize(eg.acircularh ole),and1ormoreringp erforationsofvarying size(eg.aringofcircu larholes.)•vehicles:combinespar tsfornwheels,vehicle basesofvaryingsizesa ndtemplatedtypes,and varyingnum-bersofpar ameterizedantennaorw indows. •Mathematicaloperatio ns(eg.plus,minus,sin )overfloatingconstants.Draw ingsgenerativemodel. Drawingsstimuliarede -finedoverthebaseprimit ivesasprogramswhichc om-binesubdomain-spe cificpartsaccordingtovar iedpro-gramtemplates ,parameterizedbythen umberandsizeofeachpa rt.Wegeneratestimuli bysamplingrandomized parameterizationsove rthesetemplatestopro ducethe250stimulisam pledforeachsubdomain .Thesesubdomainarede scribedbelowusingsem antictermsfortheirhi erar-chialpartstruct ure,butthesetermssim plycorrespondtotempl atedgraphicsprograms parameterizedrecursi velybysizeandnumbero fsubparts.Wedefinethefollowingfourdr awingssubdomains,des cribedwithahigh-leve loverviewoftheirunde rlyingpartstructure: •nutsandbolts:combine spartsforanoutershap e(eg.ahexagonalnut)o fvaryingsize,andinne rper-forationofvaryi ngsize(eg.acircularh ole),and1ormoreringp erforationsofvarying size(eg.aringofcircu larholes.)•vehicles:combinespar tsfornwheels,vehicle basesofvaryingsizesa ndtemplatedtypes,and varyingnum-bersofpar ameterizedantennaorw indows. 0.07
•gadgets:combinespart sforndialsorbuttons, tem-platedgadgetbase sofvaryingsizes,andv aryingnum-bersofante nna. •gadgets:combinespart sforndialsorbuttons, tem-platedgadgetbase sofvariants, and variousnum-bersofant enna 0.21
•furniture:combinespa rtsfornknobs,drawers ,tem-platedfurniture basesofvaryingsizesa ndfurniturefeet.Towe rsstimulusgeneration .InitialprimitivesLb ase.Theinitialprogra mprimitivesforthestr ucturesdomainbuildon thetowersplanningdom ainfrom(Ellisetal.,2 020),whichconsistsof simpleprimitivesforp ickingandplacingcolo redblocks:•verticalred:aunit-le ngthverticalredblock . •furniture:combinespa rtsfornknobs,drawers ,tem-platedfurniture basesofvariantsizesa ndfurniturefeet.Towe rsstimulusgeneration .InitialprimitivesLb ase.Theinitialprocpr imitivesforthestruct ures domainbuildonthetowe rsplanning domainfrom (Ellisetal.,2020), whichconsistofsimple primitivesforpicking andplacingcolorblock s:•verticalred:aunit-le ngthverticalredblock s. 0.09
•horizontalblue:aunit -lengthverticalblueb lock. •ホリゾンタルブルー:aunit-lengthvertica lblueblock。 0.55
•left(n,canvas,block) :movesasimulatedcurs orleftnstepsonacanva sandplacesablock. •left(n,canvas,block) :movesasimulatedcurs orleftnstepsonacanva sandplacesablock 0.16
•right(n,canvas,block ):movesasimulatedcur -sorrightnstepsonaca nvasandplacesablock. Structuresgenerative model.Structuresstim uliarede-finedoverthebaseprimit ivesusinggroupsoflow -levelarXiv:2205.056 66v1 [cs.CL] 11 May 2022 •right(n,canvas,block ):movesasimulatedcur -sorrightnstepsonaca nvasandplacesablock. structuresgenerative model.structuresstim uliarede-finedoverpr imitivesusinggroupso flow-levelarxiv:2205 .05666v1 [cs.cl] 11 may 2022 0.16
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partabstractions:til es,arches,andhouse-p artscon-tainedfixedarrangementsofblo cks;rows(width)andpillar s(height)wereparamet erizedfunctions.Dif- ferentsubsetsofthese werehierarchicallyco mbinedindifferentway stocreateeachsubdoma in.Eachsubdomainwasp arameterizedbynumeri calparameters(e g numberofarches),aswe llasbyparttypeparame ters(e g walltile). partabstractions:til es,arches,andhouse-p artscon-tainedfixeda rrangementsofblocks;rows(width)andpillar s(height)wereparamet erizedfunctions.Dif- ferentsubsetsofthese werehierarchicallyco mbinedindifferentway stcreateeachsub domain.Eachsub domainwasparameteriz edbynumericalparamet ers(e g numberofarches),aswe llasbyparttypeparame ters(e g walltile)。 0.14
Bridgescontainedupto 2externalarches,andu pto5internalarchesof adifferenttype.Eachl ow-levelarchabstract ioncontainedtworedpi llars,whichcouldallb eextendeduptoamaximu mheight.Eachbridgeco uldsupportamid-level viaductabstrac-tionc onsistingofmultipler ows.Wealsodefinedasuspension(suspe nsion-type)functiont hatplacedredblocksdi rectlyabovethepillar s,ofauniformheight,o rthatdecreasedorincr easedinheighttowards thecenterofthebridge .Citiescontainedtwos kyscrapersplacedaran domdistanceapart.Eac hskyscraperwasdefinedbyawalltile,which wasstacked(height)ve rticallyandop-tional lymirrored,andtopped witharoworpyramidroo f.Houseswereeachtopp edwithapyramidroof,d e-finedbythewidthoftheho use.Thewidthofthehou sewasdeterminedbythe widthofthefirstfloor,whichcouldc ontainedanypermutati onofwindow,bricks,do or.Uptotwoadditional floorscontainedpermuta tionsofwindow,bricks .Castlesweredefinedbyacentralmirrore dwalloftiles,andtwoflankingstacksoftiles, eachpa-rameterizedby aheight(withstackhei ght<wallheight),andthewa lladditionallyparame terizedbywidth.Thewa llandstacksweretoppe dwiththesametypeofro of,providingtherewas space.Eachroofcouldb eapyramidordome-simi lartoapyramidwithana ddi-tionalshorterrow beneath.Weexhaustive lyenumerateditemsfro meachsubdo-main(with asmallrangeforeachpa rameter),rejectingan ytowerthatextendedbe yonda20x20grid.S2.Pa rtIISupplementalDeta ilsThissectiondescri besadditionaltechnic aldetailsforthelibra ryidentificationmodelusedinPar tIIofthemainpaper.Co deforboththedefinedhypothesisspacesa ndalignmentmodelisal soreleasedattheprovi dedreposi-tory.Definingcandidateprogram librariesAllstimulus fromeachsubdomainare generatedfromtheshar edsetofbaseprogrampr imitivesL0describedi nS1.However,asdescri bedinthemainpaper,ou rgoalistodefinecandidateprogramli brariesLithataugment theini-tialbaseprimi tiveswithadditionalp rogramsubroutineswhi chencapsulatehigher- levelpartstructuresp ecifictoagivensubdomain(s uchasthewheelcompone ntssharedacrosstheve hiclesstimuli,orthee xternalarchcompo-nen tssharedacrossthebri dgestimuli.Inparticu lar,weaimtoconstruct cumulativelydefinedlibrariessuchthat eachLicontainsalloft heprogramconceptsinl ibraryLi−1,alongwithnewprogra msubroutinesatahighe rlevelofcomplexity.W hilewecoulddefineanenormoussetofpos siblecandidatelibrar iescontainingallposs ibleprogramsub-routi nesacrossourstimulus subdomains,weconside rarestrictedsetofrep resentativelibraries constructedfromthena turalhierarchicalstr uctureusedtogenerate theun-derlyingstimul i,andwhicharedesigne dtospanthemax-imalra ngeofcandidatepartco nceptsonoursubdomain s(fromthecommonbasep rimitivesinL0toextre melycomplexsubroutin esthatcorrespondtoen tirecategoricalclass esofstimulioneachsub domain.)Inparticular ,weconstructagivenli braryLitocon-tainnew primitivescorrespond ingroughlytothe’nexthighestouterloop ofparametricvariatio n’overthepartcomponent sinLi−1.Onthenutsandboltsd omain,forinstance,L0 containstheoriginalu nitlineandunitcircle shapeprimitives,L1co ntainsadditionalpoly gonsdefinedbyparameterizingr otationovertheunitli nes,L2containsadditi onalringsofshapes(in cludingringsofpolygo ns)definedbyparameterizingr otationoverallofthes hapesinL1,andL3conta inscategoricalstimul usconcepts(likeaoute rshapewitharingofsha peperforationsparame terizedbytheparticul arshapeandsizeofitsc omponents.Thisproced ureisdesignedtomaxim izediscriminabil-ity ofthecandidatelibrar ieswhilestillcorresp ondingtotheunderlyin grecursiveprogramstr uctureofeachsub-doma ininaprincipledway.H owever,infutureworkw ehopetolooktoautomat edprogramlibrarycons truc-tionproceduresw hichcanbeusedtogener ateamuchlargerspaceo fcandidatelibraries, likethosein(Elliseta l.,2020;Wang,Polikarpova,&am p;Fan,2021;Wong,Ellis,Tenenbaum ,&Andreas,2021). Bridgescontainedupto 2externalarches,andu pto5internalarchesof adifferenttype.Eachl ow-levelarchabstract ioncontainedtworedpi llars,whichcouldallb eextendeduptoamaximu mheight.Eachbridgeco uldsupportamid-level viaductabstrac-tionc onsistingofmultipler ows.Wealsodefinedasuspension(suspe nsion-type)functiont hatplacedredblocksdi rectlyabovethepillar s,ofauniformheight,o rthatdecreasedorincr easedinheighttowards thecenterofthebridge .Citiescontainedtwos kyscrapersplacedaran domdistanceapart.Eac hskyscraperwasdefinedbyawalltile,which wasstacked(height)ve rticallyandop-tional lymirrored,andtopped witharoworpyramidroo f.Houseswereeachtopp edwithapyramidroof,d e-finedbythewidthoftheho use.Thewidthofthehou sewasdeterminedbythe widthofthefirstfloor,whichcouldc ontainedanypermutati onofwindow,bricks,do or.Uptotwoadditional floorscontainedpermuta tionsofwindow,bricks .Castlesweredefinedbyacentralmirrore dwalloftiles,andtwoflankingstacksoftiles, eachpa-rameterizedby aheight(withstackhei ght<wallheight),andthewa lladditionallyparame terizedbywidth.Thewa llandstacksweretoppe dwiththesametypeofro of,providingtherewas space.Eachroofcouldb eapyramidordome-simi lartoapyramidwithana ddi-tionalshorterrow beneath.Weexhaustive lyenumerateditemsfro meachsubdo-main(with asmallrangeforeachpa rameter),rejectingan ytowerthatextendedbe yonda20x20grid.S2.Pa rtIISupplementalDeta ilsThissectiondescri besadditionaltechnic aldetailsforthelibra ryidentificationmodelusedinPar tIIofthemainpaper.Co deforboththedefinedhypothesisspacesa ndalignmentmodelisal soreleasedattheprovi dedreposi-tory.Definingcandidateprogram librariesAllstimulus fromeachsubdomainare generatedfromtheshar edsetofbaseprogrampr imitivesL0describedi nS1.However,asdescri bedinthemainpaper,ou rgoalistodefinecandidateprogramli brariesLithataugment theini-tialbaseprimi tiveswithadditionalp rogramsubroutineswhi chencapsulatehigher- levelpartstructuresp ecifictoagivensubdomain(s uchasthewheelcompone ntssharedacrosstheve hiclesstimuli,orthee xternalarchcompo-nen tssharedacrossthebri dgestimuli.Inparticu lar,weaimtoconstruct cumulativelydefinedlibrariessuchthat eachLicontainsalloft heprogramconceptsinl ibraryLi−1,alongwithnewprogra msubroutinesatahighe rlevelofcomplexity.W hilewecoulddefineanenormoussetofpos siblecandidatelibrar iescontainingallposs ibleprogramsub-routi nesacrossourstimulus subdomains,weconside rarestrictedsetofrep resentativelibraries constructedfromthena turalhierarchicalstr uctureusedtogenerate theun-derlyingstimul i,andwhicharedesigne dtospanthemax-imalra ngeofcandidatepartco nceptsonoursubdomain s(fromthecommonbasep rimitivesinL0toextre melycomplexsubroutin esthatcorrespondtoen tirecategoricalclass esofstimulioneachsub domain.)Inparticular ,weconstructagivenli braryLitocon-tainnew primitivescorrespond ingroughlytothe’nexthighestouterloop ofparametricvariatio n’overthepartcomponent sinLi−1.Onthenutsandboltsd omain,forinstance,L0 containstheoriginalu nitlineandunitcircle shapeprimitives,L1co ntainsadditionalpoly gonsdefinedbyparameterizingr otationovertheunitli nes,L2containsadditi onalringsofshapes(in cludingringsofpolygo ns)definedbyparameterizingr otationoverallofthes hapesinL1,andL3conta inscategoricalstimul usconcepts(likeaoute rshapewitharingofsha peperforationsparame terizedbytheparticul arshapeandsizeofitsc omponents.Thisproced ureisdesignedtomaxim izediscriminabil-ity ofthecandidatelibrar ieswhilestillcorresp ondingtotheunderlyin grecursiveprogramstr uctureofeachsub-doma ininaprincipledway.H owever,infutureworkw ehopetolooktoautomat edprogramlibrarycons truc-tionproceduresw hichcanbeusedtogener ateamuchlargerspaceo fcandidatelibraries, likethosein(Elliseta l.,2020;Wang,Polikarpova,&am p;Fan,2021;Wong,Ellis,Tenenbaum ,&Andreas,2021). 0.04
Library-to-vocabular yalignmentmodelThisp rovidesfurtherimplem entationaldetailsont hemodelusedtoproduce thelibrary-to-vocabu laryalign-mentmetric showninFigure4ofthem ainpaper.Thismetricm easuresthemeantokenl og-likelihood(whichc orrelatesnegativelyw ithperplexity)foreac hsub-domainwithrespe cttothesetofdescript ionsforeachobjectsti mulus,programsthatge neratethatobjectstim u-lus,andagivenlibra ryinwhichthoseprogra mscanberepresented.M orespecifically,eachlibraryLii scomprisedofρi0,ρi1.. Library-to-vocabular yalignmentmodel Thisprovidesfurtheri mplementationaldetai lsonthemodelusedtopr oducethelibrary-to-v ocabularyalign-mentm etricshowninFigure4o fthemainpaper. Thismetric measuressthemeantoke nlog-likelihood (whichcorrelates negativelywithperple xity)foreachsub-doma inwithrespecttothese tofdescriptionsforea chobjectstimulus, programss thatgenerate thatobjectstimu-lus, andagivenlibraryinwh ichthose programsscanberepres ented。 0.07
.∈Li.Thegraphicsprogra msforeachobjectstimu lusareinitiallyrepre sentedasaprogramπbase,but Thegraphics programssforeachobje ctstimulusareinallyr epresentedasa programπbase, but 0.05
英語(論文から抽出)日本語訳スコア
theycanberewrittenau tomaticallywithrespe cttoanygivenlibraryL iintoasemanticallyeq uivalentprogramπithatmaximallycompre ssestheoriginalprogr amtousetheencapsulat edsubroutinesinthene wlibrary.Wecalltheto kenizationofaprogram πiitsleft-ordertreetr aver-sal(omittingvar iables),suchthatthet okenizationofaprogra misanorderedsequence ofprogramcomponents[ρπ...]. Theycanbere writtenallywithrespe cttoanygivenlibraryL iintoasemanticallyeq uivalent programsπithatmaximallycompre ssesthe original programtousetheencap sulatedsubroutinesin thenewlibrary.Wecall thetokenizationofa programsπiitsleft-ordertreetr aver-sal(omittingvar iables),suchthetoken izationofa programisanorderedse quenceof programscomponents[ρπ...] 0.06
Thegoalofourmetricis toestimatetheaverage align-mentprobabilit iesbetweenprogramcom ponentsinto-kenizedp rogramsforeachobject stimulus(writteninag ivenlibrary)andthewo rdsinthetokenizedwha tdescrip-tionsfortha tobjectstimulus.Weus etheIBMModel1transla tionmodel(Brown,Dell aPietra,DellaPietra, &Mercer,1993),whichta kesasinputacorpusofp aired(programtoken,d escriptiontoken)sequ encesforallob-jectst imuliinagivensubdoma in,andestimatescorpu s-widetype-typetrans lationprobabilitiesP (w|ρ)foreachwordtypewacr ossalldescriptions,a ndeachprogramtypeρacrossallprogramswri ttenunderagivenlibra ry.Thismodelalsojoin tlyestimatesalignmen tsbetweentheindividu alprogramandwordtoke nsina(description,pr ogram)pair–itfindstheMAPalignmentsα(w,ρ)suchthatΠαP(w|ρ)ismaximizedforallal ignedwordsandprogram components.Wereporta cross-validatedalign mentmetricovereachsu bdomainusingbatcheso fn=5heldout-stimuli:wer an-domlyorderall(des cription,program)pai rs,fittheIBMmodeltoestima teP(w|ρ)basedonallbutthehel doutstimuli,andthenr eportourmetricwithre specttotheMAPalignme ntsontheheldout(desc ription,program)pair s.Morespecifically,weneachofthese heldout(de-scription ,program)pairs,theme antokenlog-likelihoo dcorrespondstothemea nlogP(w|ρ)wherethemeanistaken overtheMAPalignments α(w,ρ). Thegoalofourmetricis toestimatetheaverage align-mentprobabilit iesbetweenprogramcom ponentsinto-kenizedp rogramsforeachobject stimulus(writteninag ivenlibrary)andthewo rdsinthetokenizedwha tdescrip-tionsfortha tobjectstimulus.Weus etheIBMModel1transla tionmodel(Brown,Dell aPietra,DellaPietra, &Mercer,1993),whichta kesasinputacorpusofp aired(programtoken,d escriptiontoken)sequ encesforallob-jectst imuliinagivensubdoma in,andestimatescorpu s-widetype-typetrans lationprobabilitiesP (w|ρ)foreachwordtypewacr ossalldescriptions,a ndeachprogramtypeρacrossallprogramswri ttenunderagivenlibra ry.Thismodelalsojoin tlyestimatesalignmen tsbetweentheindividu alprogramandwordtoke nsina(description,pr ogram)pair–itfindstheMAPalignmentsα(w,ρ)suchthatΠαP(w|ρ)ismaximizedforallal ignedwordsandprogram components.Wereporta cross-validatedalign mentmetricovereachsu bdomainusingbatcheso fn=5heldout-stimuli:wer an-domlyorderall(des cription,program)pai rs,fittheIBMmodeltoestima teP(w|ρ)basedonallbutthehel doutstimuli,andthenr eportourmetricwithre specttotheMAPalignme ntsontheheldout(desc ription,program)pair s.Morespecifically,weneachofthese heldout(de-scription ,program)pairs,theme antokenlog-likelihoo dcorrespondstothemea nlogP(w|ρ)wherethemeanistaken overtheMAPalignments α(w,ρ). 0.12
ReferencesBrown,P.F. ,DellaPietra,S.A.,De llaPietra,V.J.,&Mercer,R.L.(1993). 参照:Brown,P.F.,DellaPie tra,S.A.,DellaPietra ,V.J.,&Mercer,R.L. (1993)。 0.71
Themathematicsofstat isticalmachinetransl ation:Parameterestim ation.Computa-tional Linguistics,19(2),26 3–311.Ellis,K. Themathematicsofstat isticalmachinetransl ation:Parameterestat ion.Computa-tionalLi nguistics,19(2),263–311.Ellis,K 0.15
,Wong,C. ,Nye,M. とWong,C。 そうです。 0.46
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Dreamcoder:Growingge neralizable,interpre tableknowledgewithwa ke-sleepbayesianprog ramlearning.arXivpre printarXiv:2006.0838 1.Wang,H. Dreamcoder:Growing generalizable,interp retableknowledgewith wake-sleepbayesian programminglearning. arXivpreprintarXiv:2 006.08381.Wang,H. 0.19
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Learningpart-basedab stractionsforvisualo bjectconcepts.InProc eedingsoftheAnnualMe etingoftheCognitiveS cienceSociety.Wong,C . 学習部に基づくvisualobjectconcepts .inproceedingsofthea nnualmeetingofthecog nitivesciencesociety .wong,c. 0.05
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(2021). Leveraginglanguageto learnprogramabstrac- tionsandsearchheuris tics.InInternational ConferenceonMachineL earning(pp.11193–11204). (2021). InInternationalConfe renceonMachineLearni ng (pp.11193–11204) 0.26
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