Critical behavior in a cross-situational lexicon learning scenario

Instituto de Física de São Carlos, Universidade de São Paulo - Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

Received: 12 June 2012
Accepted: 4 September 2012

Abstract

The associationist account for early word learning is based on the co-occurrence between referents and words. Here we introduce a noisy cross-situational learning scenario in which the referent of the uttered word is eliminated from the context with probability γ, thus modeling the noise produced by out-of-context words. We examine the performance of a simple associative learning algorithm and find a critical value of the noise parameter γ_c above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order τ^−1/2 about γ_c, where τ is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent −3/2 at the critical point.