title: Stochastic dynamics of lexicon learning in an uncertain and nonuniform world.
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.
authors.affiliation: Physik-Department, Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany.
authors.forename: Rainer
authors.initials: R
authors.lastname: Reisenauer
authors.forename: Kenny
authors.initials: K
authors.lastname: Smith
authors.forename: Richard A
authors.initials: RA
authors.lastname: Blythe