The performance of a linear learning algorithm for cross-situational vocabulary learning

Cross-situational learning is based on the idea that a learner can determine the meaning of a word by finding something in common across all observed uses of that word. Here we present the results of an extensive statistical analysis of the performance of a linear learning algorithm for learning a one-to-one mapping between N objects and N words based solely on the co-occurrence between objects and words. In particular, a learning trial in our cross-situational learning scenario consists of the presentation of C < N objects together with a word, which refers to one of the objects in the context. We find that the learning error ∊ decreases exponentially as the number of learning trials T increases, i.e., ∊ ∼ exp (−αT) where the learning rate is given by α = (N−C) / [N (N−1)].

[1]  Dirk Ifenthaler,et al.  Stochastic Models of Learning , 2012 .

[2]  P. Bloom.  How Children Learn the Meaning of Words and How LSA Does It ( Too ) , 2005 .

[3]  J.F. Fontanari,et al.  Integrating Language and Cognition: A Cognitive Robotics Approach , 2007, IEEE Computational Intelligence Magazine.

[4]  Michael C. Frank,et al.  A Bayesian Framework for Cross-Situational Word-Learning , 2007, NIPS.

[5]  Luc Steels,et al.  Spontaneous Lexicon Change , 1998, ACL.

[6]  E. Markman,et al.  When it is better to receive than to give: Syntactic and conceptual constraints on vocabulary growth , 1994 .

[7]  M. R. Manzini.  Learnability and Cognition , 1991 .

[8]  Ellen M. Markman,et al.  Constraints Children Place on Word Meanings , 1990, Cogn. Sci..

[9]  K. Tuyls,et al.  The evolutionary language game: an orthogonal approach. , 2005, Journal of theoretical biology.

[10]  Leonid I. Perlovsky,et al.  A game theoretical approach to the evolution of structured communication codes , 2008, Theory in Biosciences.

[11]  Simon Kirby,et al.  Iterated Learning: A Framework for the Emergence of Language , 2003, Artificial Life.

[12]  Kenny Smith,et al.  Learning Times for Large Lexicons Through Cross-Situational Learning , 2010, Cogn. Sci..

[13]  Angelo Cangelosi,et al.  2009 Special Issue: Cross-situational learning of object-word mapping using Neural Modeling Fields , 2009 .

[14]  Tony Belpaeme,et al.  A cross-situational learning algorithm for damping homonymy in the guessing game , 2006 .

[15]  J. Fodor.  The Mind Doesn't Work That Way : The Scope and Limits of Computational Psychology , 2000 .

[16]  Simon Kirby,et al.  Language as an evolutionary system , 2005 .

[17]  L. Steels.  Perceptually grounded meaning creation , 1996 .

[18]  Leonid I. Perlovsky,et al.  A computational model of adults' performance in naming objects using cross-situational learning , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[19]  M. Feldman,et al.  Cultural transmission and evolution: a quantitative approach. , 1981, Monographs in population biology.

[20]  J. Fontanari,et al.  Solvable null model for the distribution of word frequencies. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  James R. Hurford,et al.  Biological evolution of the Saussurean sign as a component of the language acquisition device , 1989 .

[22]  Chen Yu,et al.  Statistical Cross-Situational Learning to Build Word-to-World Mappings , 2006 .

[23]  José F. Fontanari.  Statistical analysis of discrimination games , 2006 .

[24]  S. Pinker,et al.  Natural language and natural selection , 1990, Behavioral and Brain Sciences.

[25]  J. Siskind.  A computational study of cross-situational techniques for learning word-to-meaning mappings , 1996, Cognition.

[26]  Leonid I. Perlovsky,et al.  How language can help discrimination in the Neural Modelling Fields framework , 2008, Neural Networks.

[27]  Leonid I. Perlovsky,et al.  Evolving Compositionality in Evolutionary Language Games , 2007, IEEE Transactions on Evolutionary Computation.

[28]  Andrew D. M. Smith,et al.  Semantic Generalisation and the Inference of Meaning , 2003, ECAL.