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Ch 5. Language Change: A Preliminary Model 5.1 ~ 5.2 The Computational Nature of Language Learning and Evolution P. Niyogi 2006 Summarized by Kwonill,

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Presentation on theme: "Ch 5. Language Change: A Preliminary Model 5.1 ~ 5.2 The Computational Nature of Language Learning and Evolution P. Niyogi 2006 Summarized by Kwonill,"— Presentation transcript:

1 Ch 5. Language Change: A Preliminary Model 5.1 ~ 5.2 The Computational Nature of Language Learning and Evolution P. Niyogi 2006 Summarized by Kwonill, Kim Biointelligence Laboratory, Seoul National University http://bi.snu.ac.kr/ 2009.07.30

2 Contents 5.0 Language Acquisition vs. Language Change  Slightly imperfect individual learning  Language change in the population level  Learning vs. Evolutionary dynamics 5.1 An Acquisition-Based Model of Language Change  Qualitative explanation 5.2 A Preliminary Model  5.2.1 Learning by Individuals  5.2.2 Population Dynamics  5.2.3 Some Examples  Memoryless Learners  Batch Error-Based Learner  Cue-Based Learner 5.3 Implications and Further Directions 2(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

3 Language Acquisition vs. Language Change Language Acquisition  The mechanism by which language is transmitted from parrent to child Perfect acquisition = Perfect transmission  Perfectly same language = No change! However, a number of language-change cases are reported.  Imperfect learning! 3(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

4 Is it Possible Language Change by Slightly imperfect learning ? It is possible  Slightly imperfect individual learning  Language change in the population level  Lightfoot (1991)  Someone’s new parameter setting  New grammar  Different output  Linguistic environmental change  New parameter setting in younger people  New grammar …  Let’s show formally  Relations between Learning & Evolutionary dynamics  A model of language change emerges as a logical consequence of language acquisition 4(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

5 An Acquisition-Based Model of Language Change (1/3) We want …  Grammatical theory + Learning algorithm  Model of language change  Individual level problem  Population level problem Learning problem (Individual level)  PLD(Primary Linguistic Data)  “How children acquire the target language from their PLD?” Linguistic composition change problem (Population level)  Changeable Case 1: PLD for children is altered  By foreign speakers, disfluencies, …  Changeable Case 2: Finite sentences from grammar 5(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

6 An Acquisition-Based Model of Language Change (2/3) Finite sentences from the adults’ grammar  Slightly different grammar of children  Over successive generations, the linguistic composition evolves as a dynamical system Microscopic & macroscopic view Different learning models  Different evolutionary results 6(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

7 An Acquisition-Based Model of Language Change (3/3) Assumptions  Grammar hypothesis space  The space of possible grammars that humans might acquire  Usually simplified to particular parameters  Language acquisition device  The learning algorithm the child uses to develop grammatical hypotheses on the basis of data  Primary linguistic data (PLD)  The distribution of sentences that a child is exposed to and that affect its linguistic development 7(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

8 A Primary Model Σ: a finite alphabet Σ*: all possible series of character Language: L i ⊂ Σ* In general, L 1 ∩ L 2 ≠ g i means the grammar of the language L i 8(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

9 A Primary Model Consider ONLY TWO languages, L 1 & L 2 Monolingual case: just ONE language for ONE user Population: TWO generations State variable  α t : proportion of users of L 1 at the t th generation  1- α t : `` `` L 2 `` Sentence : s ∈ Σ* P 1 : Probability distribution of sentences of L 1  P 1 (s) : Probability to produce a sentence s by a user of L 1 9(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

10 Learning by Individuals : learning algorithm 10(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

11 Population Dynamics Finite sentences for learning  “Mature” after K examples Begin  All uses L 1  All example are s ~ P 1 11(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

12 Summary Phase Space  Linear Stability Analysis  Nullclines  Poincare-Bendixson Theorem  Hopf Bifurcation Population Dynamics in the Wilson-Cowan Model 12(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

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