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 ϵ decreases exponentially as the number of learning trials T increases, i.e., ϵ ~ exp (-αT) where the learning rate is given by α = (N-C) / [N (N-1)].