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Research Article

Latent structure in random sequences drives neural learning toward a rational bias

Yanlong Sun, Randall C. O’Reilly, Rajan Bhattacharyya, Jack W. Smith, Xun Liu, and Hongbin Wang
  1. aCenter for Biomedical Informatics, Texas A&M University Health Science Center, Houston, TX 77030;
  2. bDepartment of Psychology and Neuroscience, University of Colorado, Boulder, CO 80309;
  3. cCenter for Neural and Emergent Systems, Information and System Sciences Lab, HRL Laboratories LLC, Malibu, CA 90265; and
  4. dKey Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Beijing, China 100101

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PNAS first published March 9, 2015; https://doi.org/10.1073/pnas.1422036112
Yanlong Sun
aCenter for Biomedical Informatics, Texas A&M University Health Science Center, Houston, TX 77030;
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  • For correspondence: ysun@tamhsc.edu hwang@tamhsc.edu
Randall C. O’Reilly
bDepartment of Psychology and Neuroscience, University of Colorado, Boulder, CO 80309;
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Rajan Bhattacharyya
cCenter for Neural and Emergent Systems, Information and System Sciences Lab, HRL Laboratories LLC, Malibu, CA 90265; and
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Jack W. Smith
aCenter for Biomedical Informatics, Texas A&M University Health Science Center, Houston, TX 77030;
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Xun Liu
dKey Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Beijing, China 100101
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Hongbin Wang
aCenter for Biomedical Informatics, Texas A&M University Health Science Center, Houston, TX 77030;
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  • For correspondence: ysun@tamhsc.edu hwang@tamhsc.edu
  1. Edited by Michael I. Posner, University of Oregon, Eugene, OR, and approved February 4, 2015 (received for review November 18, 2014)

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Significance

The human mind has a unique capacity to find order in chaos. The way the neocortex integrates information over time enables the mind to capture rich statistical structures embedded in random sequences. We show that a biologically motivated neural network model reacts to not only how often a pattern occurs (mean time) but also when a pattern is first encountered (waiting time). This behavior naturally produces the alternation bias in the gambler’s fallacy and provides a neural grounding for the Bayesian models of human behavior in randomness judgments. Our findings support a rational account for human probabilistic reasoning and a unifying perspective that connects the implicit learning without instruction with the generalization under structured and expressive rules.

Abstract

People generally fail to produce random sequences by overusing alternating patterns and avoiding repeating ones—the gambler’s fallacy bias. We can explain the neural basis of this bias in terms of a biologically motivated neural model that learns from errors in predicting what will happen next. Through mere exposure to random sequences over time, the model naturally develops a representation that is biased toward alternation, because of its sensitivity to some surprisingly rich statistical structure that emerges in these random sequences. Furthermore, the model directly produces the best-fitting bias-gain parameter for an existing Bayesian model, by which we obtain an accurate fit to the human data in random sequence production. These results show that our seemingly irrational, biased view of randomness can be understood instead as the perfectly reasonable response of an effective learning mechanism to subtle statistical structure embedded in random sequences.

  • gambler's fallacy
  • waiting time
  • neural network
  • temporal integration
  • Bayesian inference

Footnotes

  • ↵1To whom correspondence may be addressed. Email: ysun{at}tamhsc.edu or hwang{at}tamhsc.edu.
  • Author contributions: Y.S., R.C.O., and H.W. designed research; Y.S. and H.W. performed research; Y.S., R.C.O., J.W.S., and H.W. contributed new reagents/analytic tools; Y.S. and H.W. analyzed data; and Y.S., R.C.O., R.B., J.W.S., X.L., and H.W. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1422036112/-/DCSupplemental.

Freely available online through the PNAS open access option.

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Neural learning of waiting time
Yanlong Sun, Randall C. O’Reilly, Rajan Bhattacharyya, Jack W. Smith, Xun Liu, Hongbin Wang
Proceedings of the National Academy of Sciences Mar 2015, 201422036; DOI: 10.1073/pnas.1422036112

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Neural learning of waiting time
Yanlong Sun, Randall C. O’Reilly, Rajan Bhattacharyya, Jack W. Smith, Xun Liu, Hongbin Wang
Proceedings of the National Academy of Sciences Mar 2015, 201422036; DOI: 10.1073/pnas.1422036112
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