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

2. (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
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3. Setting for Population Dynamics
Choices: K (maturation time), A (learning algorithm)
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4. 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
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5. Analysis on the Map of BE Learners
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6. Analysis on the Map of BE Learners
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7. 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
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8. Analysis on the Map of Cue Learners
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9. 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??
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10. Investigation on the Fixed Points
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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
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12. 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
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13. 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.
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Discussion
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15. Reflection on General Findings with Learning Models
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16. Reflection on General Findings with Learning Models
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17. Reflection on General Findings with Learning Models
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18. (C) 2009 SNU CSE Biointelligence Lab
Major Insights
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19. Future Directions – Relaxing Symplifying Assumptions
Multiple languages
Finite populations
Generational structure
Spatial population structure
Multilingual acquisition
Non-vertical and other nodes of transmission
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