title: When learners surpass their models: mathematical modeling of learning from an inconsistent source.
abstract: It has been reported in the literature that both adults and children can, to a different degree, modify and regularize the often-inconsistent linguistic input they receive. We present a new algorithm to model and investigate the learning process of a learner mastering a set of (grammatical or lexical) forms from an inconsistent source. The algorithm is related to reinforcement learning and drift-diffusion models of decision making, and possesses several psychologically relevant properties such as fidelity, robustness, discounting, and computational simplicity. It demonstrates how a learner can successfully learn from or even surpass its imperfect source. We use the data collected by Singleton and Newport (Cognit Psychol 49(4):370-407, 2004) on the performance of a 7-year-boy Simon, who mastered the American Sign Language (ASL) by learning it from his parents, both of whom were imperfect speakers of ASL. We show that the algorithm possesses a frequency boosting property, whereby the frequency of the most common form of the source is increased by the learner. We also explain several key features of Simon's ASL.
authors.affiliation: Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA.
authors.forename: Yelena
authors.initials: Y
authors.lastname: Mandelshtam
authors.forename: Natalia L
authors.initials: NL
authors.lastname: Komarova
mesh_terms: D000328:Adult; D000465:Algorithms; D002648:Child; D005260:Female; D006801:Humans; D007802:Language; D007858:Learning; D008297:Male; D008962:Models, Theoretical