Self-Sustaining Iterated Learning

Authors Bernard Chazelle, Chu Wang



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Bernard Chazelle
Chu Wang

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Bernard Chazelle and Chu Wang. Self-Sustaining Iterated Learning. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ITCS.2017.17

Abstract

An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the lengths of the training sessions ensures self-sustainability for any discrete language class. In the second part, we tackle the nondiscrete case and investigate self-sustainability for iterated linear regression. We discuss the implications of our findings to issues of non-equilibrium dynamics in natural algorithms.
Keywords
  • Iterated learning
  • language evolution
  • iterated Bayesian linear regression
  • non-equilibrium dynamics

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References

  1. FC Bartlett. Remembering: a study in experimental and social psychology.(1932). 317 pp. Google Scholar
  2. Aaron Beppu and Thomas L Griffiths. Iterated learning and the cultural ratchet. In Proceedings of the 31st annual conference of the cognitive science society, pages 2089-2094. Citeseer, 2009. Google Scholar
  3. A Bhattachayya. On a measure of divergence between two statistical population defined by their population distributions. Bulletin Calcutta Mathematical Society, 35:99-109, 1943. Google Scholar
  4. Dorin Comaniciu, Visvanathan Ramesh, and Peter Meer. Real-time tracking of non-rigid objects using mean shift. In Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on, volume 2, pages 142-149. IEEE, 2000. Google Scholar
  5. Kenneth R Davidson and Stanislaw J Szarek. Local operator theory, random matrices and banach spaces. Handbook of the geometry of Banach spaces, 1(317-366):131, 2001. Google Scholar
  6. Alan Edelman. Eigenvalues and condition numbers of random matrices. SIAM Journal on Matrix Analysis and Applications, 9(4):543-560, 1988. Google Scholar
  7. Thomas L Griffiths and Michael L Kalish. A bayesian view of language evolution by iterated learning. In Proceedings of the 27th annual conference of the cognitive science society, pages 827-832, 2005. Google Scholar
  8. Thomas L Griffiths and Michael L Kalish. Language evolution by iterated learning with bayesian agents. Cognitive Science, 31(3):441-480, 2007. Google Scholar
  9. Thomas L Griffiths, Michael L Kalish, and Stephan Lewandowsky. Theoretical and empirical evidence for the impact of inductive biases on cultural evolution. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 363(1509):3503-3514, 2008. Google Scholar
  10. Michiel Hazewinkel. Encyclopaedia of Mathematics. Springer Science &Business Media, 2013. Google Scholar
  11. Michael L Kalish, Thomas L Griffiths, and Stephan Lewandowsky. Iterated learning: Intergenerational knowledge transmission reveals inductive biases. Psychonomic Bulletin &Review, 14(2):288-294, 2007. Google Scholar
  12. Simon Kirby, Tom Griffiths, and Kenny Smith. Iterated learning and the evolution of language. Current opinion in neurobiology, 28:108-114, 2014. Google Scholar
  13. James R Norris. Markov chains. Cambridge university press, 1998. Google Scholar
  14. Amy Perfors and Daniel Navarro. Language evolution is shaped by the structure of the world: An iterated learning analysis. In Annual Conference, 2011. Google Scholar
  15. Anna N Rafferty, Thomas L Griffiths, and Dan Klein. Convergence bounds for language evolution by iterated learning. In Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society, 2009. Google Scholar
  16. Anna N Rafferty, Thomas L Griffiths, and Dan Klein. Analyzing the rate at which languages lose the influence of a common ancestor. Cognitive science, 38(7):1406-1431, 2014. Google Scholar
  17. Mark Rudelson and Roman Vershynin. Smallest singular value of a random rectangular matrix. Communications on Pure and Applied Mathematics, 62(12):1707-1739, 2009. Google Scholar
  18. Kenny Smith. Iterated learning in populations of bayesian agents. In Proceedings of the 31st annual conference of the cognitive science society, pages 697-702. Citeseer, 2009. Google Scholar
  19. Mónica Tamariz and Simon Kirby. Culture: copying, compression, and conventionality. Cognitive science, 39(1):171-183, 2015. Google Scholar
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