Quantifying the impact of active choice in word learning

Past theoretical studies on word learning have offered simple sampling models as a means of explaining real word learning, with a particular goal of addressing the speed of word learning: people learn tens of thousands of words within their first 18 years. The present study revisits past theoretical claims by considering a more realistic word frequency distribution in which a large number of words are sampled with extremely small probabilities (e.g., according to Zipf’s law). Our new mathematical analysis of a recently-proposed simple learning model suggests that the model is unable to account for word learning in feasible time when the distribution of word frequency is Zipfian (i.e., power-law distributed). To ameliorate the difficulty of learning real-world word frequency distributions, we consider a type of active, selfdirected learning in which the learner can influence the construction of contexts from which they learn words. We show that active learners who choose optimal learning situations can learn words hundreds of times faster than passive learners faced with randomly-sampled situations. Thus, in agreement with past empirical studies, we find theoretical support for the idea that statistical structure in real-world situations–potentially structured for learning by both a self-directed learner, and by a beneficent teacher–is a potential remedy for the pathological case of learning words with Zipf-distributed frequency.