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When Learners Surpass Their Models: Mathematical Modeling of Learning from an Inconsistent Source

Bulletin of Mathematical Biology volume 76, pages 2198–2216 (2014)Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA

    Yelena Mandelshtam & Natalia L. Komarova

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  1. Yelena Mandelshtam
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  2. Natalia L. Komarova
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Correspondence to Natalia L. Komarova .

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Mandelshtam, Y., Komarova , N.L. When Learners Surpass Their Models: Mathematical Modeling of Learning from an Inconsistent Source. Bull Math Biol 76, 2198–2216 (2014). https://doi.org/10.1007/s11538-014-9990-2

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  • DOI: https://doi.org/10.1007/s11538-014-9990-2

Keywords

  • Language regularization
  • Boosting property
  • Reinforcement models
  • Frequency boosting
  • Frequency matching