Critical behavior in a cross-situational lexicon learning scenario

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 gamma, 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 gamma(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 tau(-1/2) about gamma(c), where tau 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. Copyright (C) EPLA, 2012Southern Office of Aerospace Research and Development (SOARD)Southern Office of Aerospace Research and Development (SOARD) [FA9550-10-1-0006]Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP