Minimal model of associative learning for cross-situational lexicon acquisition

TL;DR

This paper presents an analytical model of associative learning for cross-situational lexicon acquisition, demonstrating that simple algorithms can outperform human performance and are affected by discrimination limits and forgetting.

Contribution

It provides exact analytical results for a minimal associative learning model, revealing how learning times depend on context size and sequence type.

Findings

Learning times are exponentially distributed.

Learning rates depend on the ratio of objects to context size.

Discrimination limits and forgetting reduce performance to human levels.

Abstract

An explanation for the acquisition of word-object mappings is the associative learning in a cross-situational scenario. Here we present analytical results of the performance of a simple associative learning algorithm for acquiring 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 learning scenario consists of the presentation of $C + 1 < N$ objects together with a target word, which refers to one of the objects in the context. We find that the learning times are distributed exponentially and the learning rates are given by $\ln{[\frac{N(N-1)}{C + (N-1)^{2}}]}$ in the case the $N$ target words are sampled randomly and by $\frac{1}{N} \ln [\frac{N-1}{C}] $ in the case they follow a deterministic presentation sequence. This learning performance is much superior to those exhibited by humans and more realistic learning algorithms in cross-situational experiments. We show that introduction of discrimination limitations using Weber's law and forgetting reduce the performance of the associative algorithm to the human level.