Stochastic dynamics of lexicon learning in an uncertain and nonuniform world

TL;DR

This paper analyzes how the process of lexicon learning is affected by nonuniform meaning distributions and assumptions about shared meanings, revealing phase transitions between efficient and inefficient learning regimes.

Contribution

It introduces a statistical mechanical framework to exactly analyze the dynamics of cross-situational learning under realistic conditions, highlighting phase transitions in learning efficiency.

Findings

Identifies a phase transition between efficient and inefficient learning regimes.

Shows that nonuniform meaning distributions can impair learning performance.

Provides exact solutions for the learning process using statistical mechanics.

Abstract

We study the time taken by a language learner to correctly identify the meaning of all words in a lexicon under conditions where many plausible meanings can be inferred whenever a word is uttered. We show that the most basic form of cross-situational learning - whereby information from multiple episodes is combined to eliminate incorrect meanings - can perform badly when words are learned independently and meanings are drawn from a nonuniform distribution. If learners further assume that no two words share a common meaning, we find a phase transition between a maximally-efficient learning regime, where the learning time is reduced to the shortest it can possibly be, and a partially-efficient regime where incorrect candidate meanings for words persist at late times. We obtain exact results for the word-learning process through an equivalence to a statistical mechanical problem of enumerating loops in the space of word-meaning mappings.