Chapter 5 Language Change: A Preliminary Model (2/2) The Computational Nature of Language Learning and Evolution P. Niyogi, 2004. Summary by Byoung-Hee Kim Biointelligence Lab School of Computer Sci. & Eng. Seoul National University

(C) 2009 SNU CSE Biointelligence Lab Contents 5.1 An Acquisition-Based Model of Language Change 5.2 A Preliminary Model Learning by individuals Population dynamics Some examples Memoreless learners batch error-based learner cue-based learner 5.3 Implications and Further Directions An example from Yiddish Discussion – major insights Future directions – relaxing simplifying assumptions (C) 2009 SNU CSE Biointelligence Lab

Setting for Population Dynamics Choices: K (maturation time), A (learning algorithm) (C) 2009 SNU CSE Biointelligence Lab

Batch Error-Based Learner Batch learner waits until the entire data set of K examples has been received Simply chooses the language that is more consistent L1 L2 K example sentences = n1 + n2 + n3 L1∩L2 n1 n2 n3 Choose L1 if n1 ≥ n3, Choose L2 if n1 < n3 (C) 2009 SNU CSE Biointelligence Lab

Analysis on the Map of BE Learners (C) 2009 SNU CSE Biointelligence Lab

Analysis on the Map of BE Learners (C) 2009 SNU CSE Biointelligence Lab

Cue-Based Learner Cue-based learner Examines the data set for cues to a linguistic parameter setting Choose the language with more cues if p : the probability with which an L1 user produces a cue (C) 2009 SNU CSE Biointelligence Lab

Analysis on the Map of Cue Learners (C) 2009 SNU CSE Biointelligence Lab

Analysis on the Map of Cue Learners DO NOT BE PURPLEXED BY THE EQUATIONS when they are just about details of simple calculations. Directional change, or Irreversability… why?? (C) 2009 SNU CSE Biointelligence Lab

Investigation on the Fixed Points (C) 2009 SNU CSE Biointelligence Lab

(C) 2009 SNU CSE Biointelligence Lab Limiting Analysis Allowing the number of examples K goes infinite The dynamics of the finite sample case are qualitatively similar to the infinite sample case (C) 2009 SNU CSE Biointelligence Lab

Directional Changes in Linguistic Grammars A homogeneous population of L2 users will always remain stable and can never change to a population of L1 users A homogenous population of L1 users will remain stable only in a certain regime of p values. As p changes, the basin of attraction shrinks and after a critical value of p the population switches to a stable mode of L2 speakers A change from L1 to L2 is possible. The other way is never possible (C) 2009 SNU CSE Biointelligence Lab

An Example from Yiddish L1: INFL-final L2: INFL-medial Yiddish (literally "Jewish") is a non-territorial High German language of Jewish origin, spoken throughout the world. Unlike other Germanic languages, Yiddish is written with the Hebrew alphabet as opposed to a Latin alphabet. (C) 2009 SNU CSE Biointelligence Lab

(C) 2009 SNU CSE Biointelligence Lab Discussion (C) 2009 SNU CSE Biointelligence Lab

Reflection on General Findings with Learning Models (C) 2009 SNU CSE Biointelligence Lab

Reflection on General Findings with Learning Models (C) 2009 SNU CSE Biointelligence Lab

Reflection on General Findings with Learning Models (C) 2009 SNU CSE Biointelligence Lab

(C) 2009 SNU CSE Biointelligence Lab Major Insights (C) 2009 SNU CSE Biointelligence Lab

Future Directions – Relaxing Symplifying Assumptions Multiple languages Finite populations Generational structure Spatial population structure Multilingual acquisition Non-vertical and other nodes of transmission (C) 2009 SNU CSE Biointelligence Lab