The Neural Basis ofThought and LanguageWeek 14Administrivia•Final exam review session Monday–7-9pm in 310 Soda•Final in class next Thursday, May 8th•Be there on time!•Format:–closed books, closed notes–short answers, no blue books•Final paper due on bSpace on Monday, May 11Questions1. How does the analyzer use the constructions to parse a sentence?2. How can we learn new ECG constructions?3. What are ways to re-organize and consolidate the current grammar?4. What metric is used to determine when to form a new construction?“you”youschema Addresseesubcase of HumanFORM (sound)MEANING (stuff)Analyzing “You Throw The Ball”“throw”throwschema Throwroles:throwerthrowee“ball”ballschema Ballsubcase of Object“block”blockschema Blocksubcase of Objectt1 before t2t2 before t3Thrower-Throw-Objectt2.thrower ↔ t1t2.throwee t3↔“the”AddresseeThrowthrowerthroweeBallDo not forget the SemSpec!Analyzing in ECGcreate a recognizer for each construction in the grammarfor each level j (in ascending order)repeatfor each recognizer r in jfor each position p of utteranceinitiate r starting at puntil we don't find anything newRecognizer for the Transitive-Cn• an example of a level-1 construction is Red-Ball-Cn• each recognizer looks for its constituents in order (the ordering constraints on the constituents can be a partial ordering)agt v objI get cuplevel 0level 2level 1Questions1. How does the analyzer use the constructions to parse a sentence?2. How can we learn new ECG constructions?3. What are ways to re-organize and consolidate the current grammar?4. What metric is used to determine when to form a new construction?Constructions(Utterance, Situation)1. Learner passes input (Utterance + Situation) and current grammar to Analyzer.AnalyzeSemantic Specification,Constructional Analysis2. Analyzer produces SemSpec and Constructional Analysis.3. Learner updates grammar:Hypothesizea. Hypothesize new map.Reorganizeb. Reorganize grammar(merge or compose).c. Reinforce(based on usage).Learning-Analysis Cycle (Chang, 2004)AcquisitionReorganizeHypothesizeProductionUtterance(Comm. Intent, Situation)GenerateConstructions(Utterance, Situation)AnalysisComprehensionAnalyzePartialUsage-based Language LearningBasic Learning Idea• The learner’s current grammar produces a certain analysis for an input sentence•The context contains richer information (e.g. bindings) that are unaccounted for in the analysis• Find a way to account for these meaning relations (by looking for corresponding form relations)SemSpecr1r2r1r2r3r1r2Contextr1r2r1r2r3r1r2“you”“throw”“ball”youthrowball“block”blockschema Addresseesubcase of HumanFORM (sound)MEANING (stuff)lexical constructionsInitial Single-Word Stageschema Throwroles:throwerthroweeschema Ballsubcase of Objectschema Blocksubcase of Object“you”youschema Addresseesubcase of HumanFORM MEANINGNew Data: “You Throw The Ball”“throw”throwschema Throwroles:throwerthrowee“ball”ballschema Ballsubcase of Object“block”blockschema Blocksubcase of Object“the”AddresseeThrowthrowerthroweeBallSelfSITUATIONAddresseeThrowthrowerthroweeBallbeforerole-fillerthrow-ballRelational Mapping ScenariosAfBfAmBmABform-relationrole-fillerthrow ball throw.throwee ball↔AfBfAmBmABform-relationrole-fillerXrole-fillerput ball down put.mover ball↔down.tr ball↔AfBfAmBmABform-relationrole-fillerYrole-fillerNomi ball possession.possessor Nomi↔possession.possessed ball↔Questions1. How does the analyzer use the constructions to parse a sentence?2. How can we learn new ECG constructions?3. What are ways to re-organize and consolidate the current grammar?4. What metric is used to determine when to form a new construction?Merging Similar Constructionsthrow before blockThrow.throwee = Blockthrow before ballThrow.throwee = Ballthrow before-s ingThrow.aspect = ongoingthrow-ing the ballthrow the blockthrow before ObjectfTHROW.throwee = ObjectmTHROW-OBJECTResulting Constructionconstruction THROW-OBJECTconstructional constituentst : THROWo : OBJECTformtf before ofmeaning tm.throwee o↔mComposing Co-occurring Constructionsball before offMotion mm.mover = Ballm.path = Offball offthrow before ballThrow.throwee = Ballthrow the ballthrow before ball ball before offTHROW.throwee = BallMotion mm.mover = Ballm.path = OffTHROW-BALL-OFFResulting Constructionconstruction THROW-BALL-OFFconstructional constituentst : THROWb : BALLo : OFFformtf before bfbf before ofmeaning evokes MOTION as m tm.throwee b↔m m.mover b↔m m.path o↔mQuestions1. How does the analyzer use the constructions to parse a sentence?2. How can we learn new ECG constructions?3. What are ways to re-organize and consolidate the current grammar?4. What metric is used to determine when to form a new construction?Size Of Grammar•Size of the grammar G is the sum of the size of each construction:• Size of each construction c is:where •nc = number of constituents in c,•mc = number of constraints in c,• length(e) = slot chain length of element reference e∑∈=GccG )size()size(∑∈++=ceccemnc )length()size(Example: The Throw-Ball Cxnconstruction THROW-BALLconstructional constituentst : THROWb : BALLformtf before bfmeaning tm.throwee b↔msize(THROW-BALL) = 2 + 2 + (2 + 3) = 9∑∈=ceccemnc )length(++)size(Complexity of Data Given Grammar•Complexity of the data D given grammar G is the sum of the analysis score of each input token d:•Analysis score of each input token d is:where • c is a construction used in the analysis of d•weightc relative frequency of ≈ c,•|typer| = number of ontology items of type r used,•heightd = height of the derivation graph,•semfitd = semantic fit provide by the analyzer∑∈=DddGD )score()|(complexitydddc crrcsemfitheighttypeweightd ++⋅+=∑ ∑∈ ∈η)score(Minimum Description Length•Choose grammar G to minimize cost(G|D):– cost(G|D) = α • size(G) + β • complexity(D|G)– Approximates Bayesian learning; cost(G|D) 1/posterior probability 1/P(G|D)≈ ≈•Size of grammar = size(G) 1/prior 1/P(G)≈ ≈– favor fewer/smaller constructions/roles; isomorphic mappings•Complexity of data given grammar 1/likelihood ≈ 1/P(D|G)≈– favor simpler analyses(fewer, more likely constructions)– based on derivation length + score of derivationFinal Remark• The goal here is to build a cognitive plausible model of language learning• A very different game that one