Exact solution of a stochastic model for lexicon learning

I will discuss a stochastic model for learning the meanings of words where: (i) many meanings are plausible each time a word is uttered; (ii) incorrect "confounder" meanings appear with an arbitrary distribution; and (iii) learners compare instances of a word's use to eliminate uncertainty as to a word's intended meaning; with or without (iv) a "mutual exclusivity" constraint that eliminates the meanings of words that have already been learnt as potential meanings for other words. This latter constraint introduces highly nontrivial interactions ("avalanches") between words in the lexicon. Remarkably, one can obtain an exact expression for the probability that a lexicon has been learnt after a given time, which in turn reveals a phase transition in the learning time as a function of the difficulty of the learning problem.