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A unifying theory explains seemingly contradictory biases in perceptual estimation

Abstract

Perceptual biases are widely regarded as offering a window into the neural computations underlying perception. To understand these biases, previous work has proposed a number of conceptually different, and even seemingly contradictory, explanations, including attraction to a Bayesian prior, repulsion from the prior due to efficient coding and central tendency effects on a bounded range. We present a unifying Bayesian theory of biases in perceptual estimation derived from first principles. We demonstrate theoretically an additive decomposition of perceptual biases into attraction to a prior, repulsion away from regions with high encoding precision and regression away from the boundary. The results reveal a simple and universal rule for predicting the direction of perceptual biases. Our theory accounts for, and yields, new insights regarding biases in the perception of a variety of stimulus attributes, including orientation, color and magnitude. These results provide important constraints on the neural implementations of Bayesian computations.

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Fig. 1: Overall theoretical framework.
Fig. 2: Illustration of the P/P ratio rule.
Fig. 3: Bias and variability in orientation estimation.
Fig. 4: Modeling the effect of perceptual learning on motion perception.
Fig. 5: Modeling central tendency effect in numerosity perception and time interval estimation.
Fig. 6: Bias and variability in color hue estimation.
Fig. 7: General insights gained across datasets.

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Data availability

No new experimental datasets were collected in this study. The datasets used in this study were all published previously. Datasets collected by ref. 41 and ref. 37 are publicly available. Requests for other datasets should be directed to the original authors who collected the data.

Code availability

The code, including instructions for using the fitting procedure for the Bayesian modeling developed in the paper, is freely available at https://gitlab.com/m-hahn/unifying-theory-biases.

References

  1. Jastrow, J. Studies from the University of Wisconsin: on the judgment of angles and positions of lines. Am. J. Psychol. 5, 214–248 (1892).

    Article  Google Scholar 

  2. Hollingworth, H. L. The central tendency of judgment. J. Philos. Psych. Sci. Methods 7, 461–469 (1910).

    Google Scholar 

  3. Sadi, R., Asl, H. G., Rostami, M. R., Gholipour, A. & Gholipour, F. Behavioral finance: the explanation of investors’ personality and perceptual biases effects on financial decisions. Int. J. Econ Finance 3, 234–241 (2011).

    Article  Google Scholar 

  4. Frydman, C. & Jin, L. J. Efficient coding and risky choice. Q. J. Econ. 137, 161–213 (2022).

    Article  Google Scholar 

  5. Lieder, I. et al. Perceptual bias reveals slow-updating in autism and fast-forgetting in dyslexia. Nat. Neurosci. 22, 256–264 (2019).

    Article  CAS  PubMed  Google Scholar 

  6. Horga, G. & Abi-Dargham, A. An integrative framework for perceptual disturbances in psychosis. Nat. Rev. Neurosci. 20, 763–778 (2019).

    Article  CAS  PubMed  Google Scholar 

  7. Von Helmholtz, H. Treatise on Physiological Optics, Vol. 3 (Optical Society of America, 1925).

  8. Knill, D. C. & Pouget, A. The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci. 27, 712–719 (2004).

    Article  CAS  PubMed  Google Scholar 

  9. Körding, K. P. & Wolpert, D. M. Bayesian integration in sensorimotor learning. Nature 427, 244–247 (2004).

    Article  PubMed  Google Scholar 

  10. Weiss, Y., Simoncelli, E. P. & Adelson, E. H. Motion illusions as optimal percepts. Nat. Neurosci. 5, 598–604 (2002).

    Article  CAS  PubMed  Google Scholar 

  11. Stocker, A. A. & Simoncelli, E. P. Noise characteristics and prior expectations in human visual speed perception. Nat. Neurosci. 9, 578–585 (2006).

    Article  CAS  PubMed  Google Scholar 

  12. Sun, J. & Perona, P. Where is the sun? Nat. Neurosci. 1, 183–184 (1998).

    Article  CAS  PubMed  Google Scholar 

  13. Adams, W. J., Graf, E. W. & Ernst, M. O. Experience can change the ‘light-from-above’ prior. Nat. Neurosci. 7, 1057–1058 (2004).

    Article  CAS  PubMed  Google Scholar 

  14. Huttenlocher, J., Hedges, L. V. & Duncan, S. Categories and particulars: prototype effects in estimating spatial location. Psychol. Rev. 98, 352 (1991).

    Article  CAS  PubMed  Google Scholar 

  15. Jazayeri, M. & Shadlen, M. N. Temporal context calibrates interval timing. Nat. Neurosci. 13, 1020–1026 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Wei, X.-X. & Stocker, A. A. Efficient coding provides a direct link between prior and likelihood in perceptual Bayesian inference. In Proc. Advances in Neural Information Processing Systems (NIPS 2012) (eds Pereira, F. et al.) 1313–1321 (Curran Associates, 2012).

  17. Wei, X.-X. & Stocker, A. A Bayesian observer model constrained by efficient coding can explain ‘anti-Bayesian’ percepts. Nat. Neurosci. 18, 1509–1517 (2015).

    Article  CAS  PubMed  Google Scholar 

  18. Barlow, H. B. et al. Possible principles underlying the transformation of sensory messages. Sensory Communication (ed. Rosenblith, W. A.) 217–233 (MIT Press, 1961).

  19. Laughlin, S. A simple coding procedure enhances a neuron’s information capacity. Z. Naturforsch. C 36, 910–912 (1981).

    Article  CAS  PubMed  Google Scholar 

  20. Linsker, R. Self-organization in a perceptual network. Computer 21, 105–117 (1988).

    Article  Google Scholar 

  21. Lennie, P. Distortions of perceived orientation. Nat. New Biol. 233, 155–156 (1971).

    Article  CAS  PubMed  Google Scholar 

  22. de Gardelle, V., Kouider, S. & Sackur, J. An oblique illusion modulated by visibility: non-monotonic sensory integration in orientation processing. J. Vision 10, 6 (2010).

    Article  Google Scholar 

  23. Coppola, D. M., Purves, H. R., McCoy, A. N. & Purves, D. The distribution of oriented contours in the real world. Proc. Natl Acad. Sci. USA 95, 4002–4006 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Girshick, A. R., Landy, M. S. & Simoncelli, E. P. Cardinal rules: visual orientation perception reflects knowledge of environmental statistics. Nat. Neurosci. 14, 926–932 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Körding, K. P. & Wolpert, D. M. The loss function of sensorimotor learning. Proc. Natl Acad. Sci. USA 101, 9839–9842 (2004).

    Article  PubMed  PubMed Central  Google Scholar 

  26. Bell, A. J. & Sejnowski, T. J. An information-maximization approach to blind separation and blind deconvolution. Neural Comput. 7, 1129–1159 (1995).

    Article  CAS  PubMed  Google Scholar 

  27. Polanía, R., Woodford, M. & Ruff, C. C. Efficient coding of subjective value. Nat. Neurosci. 22, 134–142 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  28. Wei, X.-X. & Stocker, A. Lawful relation between perceptual bias and discriminability. Proc. Natl Acad. Sci. USA 114, 10244–10249 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Petzschner, F. H. & Glasauer, S. Iterative Bayesian estimation as an explanation for range and regression effects: a study on human path integration. J. Neurosci. 31, 17220–17229 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Zhang, H., Ren, X. & Maloney, L. T. The bounded rationality of probability distortion. Proc. Natl Acad. Sci. USA 117, 22024–22034 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Prat-Carrabin, A. & Woodford, M. Bias and variance of the Bayesian-mean decoder. In Proc. Advances in Neural Information Processing Systems 34 (NeurIPS 2021) (eds Ranzata, M. et al.) 23793–23805 (Curran Associates, 2021).

  32. Stocker, A. A. & Simoncelli, E. Sensory adaptation within a Bayesian framework for perception. Advances in Neural Information Processing Systems 18. In Proc. Advances in Neural Information Processing Systems (NIPS 2005) (eds Weiss, Y. et al.) 1291–1298 (MIT, 2005).

  33. Morais, M. J. & Pillow, J. W. Power-law efficient neural codes provide general link between perceptual bias and discriminability. In Proc. Advances in Neural Information Processing Systems 31 (NuerIPS 2018) (eds Bengio, S. et al.) (Curran Associates, 2018).

  34. Ganguli, D. & Simoncelli, E. P. Implicit encoding of prior probabilities in optimal neural populations. Adv. Neural Inf. Process. Syst. 2010, 658–666 (2010).

    PubMed  PubMed Central  Google Scholar 

  35. Prat-Carrabin, A. & Woodford, M. Efficient coding of numbers explains decision bias and noise. Nat. Hum. Behav. 6, 1142–1152 (2022).

    Article  PubMed  Google Scholar 

  36. Wei, X.-X. & Stocker, A. Mutual information, Fisher information, and efficient coding. Neural Comput. 28, 305–326 (2016).

    Article  PubMed  Google Scholar 

  37. Remington, E. D., Parks, T. V. & Jazayeri, M. Late Bayesian inference in mental transformations. Nature Commun. 9, 4419 (2018).

    Article  Google Scholar 

  38. Tomassini, A., Morgan, M. J. & Solomon, J. A. Orientation uncertainty reduces perceived obliquity. Vision Res. 50, 541–547 (2010).

    Article  PubMed  Google Scholar 

  39. Olkkonen, M., McCarthy, P. & Allred, S. R. The central tendency bias in color perception: effects of internal and external noise. J. Vision 14, 5 (2014).

    Article  Google Scholar 

  40. Bae, G.-Y., Olkkonen, M., Allred, S. R. & Flombaum, J. I. Why some colors appear more memorable than others: a model combining categories and particulars in color working memory. J. Exp. Psychol. Gen. 144, 744–763 (2015).

    Article  PubMed  Google Scholar 

  41. Xiang, Y., Graeber, T., Enke, B. &Gershman, S. J. Confidence and central tendency in perceptual judgment.Atten. Percept. Psychophys. 83, 3024–3034 (2021).

    Article  PubMed  Google Scholar 

  42. Gekas, N., Chalk, M., Seitz, A. R. & Seriès, P. Complexity and specificity of experimentally induced expectations in motion perception. J. Vision 14, P355 (2013).

    Google Scholar 

  43. Van Bergen, R. S., Ji Ma, W., Pratte, M. S. & Jehee, J. F. Sensory uncertainty decoded from visual cortex predicts behavior. Nat. Neurosci. 18, 1728–1730 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  44. Appelle, S. Perception and discrimination as a function of stimulus orientation: the ‘oblique effect’ in man and animals. Psychol. Bull. 78, 266–278 (1972).

    Article  CAS  PubMed  Google Scholar 

  45. Mao, J. & Stocker, A. Holistic inference explains human perception of stimulus orientation. Preprint at bioRxiv https://doi.org/10.1101/2022.06.24.497534 (2022).

  46. Chalk, M., Seitz, A. R. & Seriès, P. Rapidly learned stimulus expectations alter perception of motion. J. Vision 10, 2 (2010).

    Article  Google Scholar 

  47. Gros, B. L., Blake, R. & Hiris, E. Anisotropies in visual motion perception: a fresh look. J. Opt. Soc. Am. A. Opt. Image Sci. Vis. 15, 2003–2011 (1998).

    Article  CAS  PubMed  Google Scholar 

  48. Krukowski, A. E. & Stone, L. S. Expansion of direction space around the cardinal axes revealed by smooth pursuit eye movements. Neuron 45, 315–323 (2005).

    Article  CAS  PubMed  Google Scholar 

  49. Stevens, S. S. & Greenbaum, H. B. Regression effect in psychophysical judgment. Percept. Psychophys. 1, 439–446 (1966).

    Article  Google Scholar 

  50. Huttenlocher, J., Hedges, L. V. & Vevea, J. L. Why do categories affect stimulus judgment?. J. Exp. Psychol. Gen. 129, 220–241 (2000).

    Article  CAS  PubMed  Google Scholar 

  51. Cicchini, G. M., Anobile, G. & Burr, D. C. Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform. Proc. Natl Acad. Sci. USA 111, 7867–7872 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Mamassian, P. & Goutcher, R. Prior knowledge on the illumination position. Cognition 81, B1–B9 (2001).

    Article  CAS  PubMed  Google Scholar 

  53. Noel, J.-P., Zhang, L.-Q., Stocker, A. A. & Angelaki, D. E. Individuals with autism spectrum disorder have altered visual encoding capacity. PLoS Biol. 19, e3001215 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Manning, T. S. et al. A general framework for inferring Bayesian ideal observer models from psychophysical data. eNeuro 10, ENEURO.0144-22.2022 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  55. Tversky, A. & Fox, C. R. Weighing risk and uncertainty. Psychol. Rev. 102, 269 (1995).

    Article  Google Scholar 

  56. Shenoy, P. & Yu, A. J. Strategic impatience in go/nogo versus forced-choice decision-making. In Proc. Advances in Neural Information Processing Systems (NIPS 2012) (eds Pereira, F. et al.) 2132–2140 (Curran Associates, 2012).

  57. Mamassian, P. Overconfidence in an objective anticipatory motor task. Psychol. Sci. 19, 601–606 (2008).

    Article  PubMed  Google Scholar 

  58. Hudson, T. E., Maloney, L. T. & Landy, M. S. Optimal compensation for temporal uncertainty in movement planning. PLoS Comput. Biol. 4, e1000130 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  59. Ganguli, D. & Simoncelli, E. P. Efficient sensory encoding and Bayesian inference with heterogeneous neural populations. Neural Comput. 26, 2103–2134 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Burge, J. & Geisler, W. S. Optimal defocus estimation in individual natural images. Proc. Natl Acad. Sci. USA 108, 16849–16854 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Park, I. M. & Pillow, J. W. Bayesian efficient coding. Preprint at bioRxiv https://doi.org/10.1101/178418 (2017).

  62. Młynarski, W. F. & Hermundstad, A. M. Efficient and adaptive sensory codes. Nat. Neurosci. 24, 998–1009 (2021).

    Article  PubMed  Google Scholar 

  63. Roach, N. W., McGraw, P. V., Whitaker, D. J. & Heron, J. Generalization of prior information for rapid Bayesian time estimation. Proc. Natl Acad. Sci. USA 114, 412–417 (2017).

    Article  CAS  PubMed  Google Scholar 

  64. Fritsche, M., Spaak, E. & de Lange, F. P. A Bayesian and efficient observer model explains concurrent attractive and repulsive history biases in visual perception. eLife 9, e55389 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  65. Gekas, N., McDermott, K. C. & Mamassian, P. Disambiguating serial effects of multiple timescales. J. Vision 19, 24–24 (2019).

    Article  Google Scholar 

  66. Fischer, J. & Whitney, D. Serial dependence in visual perception. Nat. Neurosci. 17, 738–743 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Ma, W. J., Beck, J. M., Latham, P. E. & Pouget, A. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9, 1432–1438 (2006).

    Article  CAS  PubMed  Google Scholar 

  68. Vilares, I., Howard, J. D., Fernandes, H. L., Gottfried, J. A. & Kording, K. P. Differential representations of prior and likelihood uncertainty in the human brain. Curr. Biol. 22, 1641–1648 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Funamizu, A., Kuhn, B. & Doya, K. Neural substrate of dynamic Bayesian inference in the cerebral cortex. Nat. Neurosci. 19, 1682–1689 (2016).

    Article  CAS  PubMed  Google Scholar 

  70. Wei, X.-X. & Stocker, A. A. Bayesian inference with efficient neural population codes. In Proc. Artificial Neural Networks and Machine Learning—ICANN 2012: 22nd International Conference on Artificial Neural Networks, Part I 22, (eds Villa, A. E. P. et al.) 523–530 (Springer, 2012).

  71. Fischer, B. J. & Peña, J. L. Owl’s behavior and neural representation predicted by Bayesian inference. Nat. Neurosci. 14, 1061–1066 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Notredame, C.-E., Pins, D., Denéve, S. & Jardri, R. What visual illusions teach us about schizophrenia. Front. Integr. Neurosci. 8, 63 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

This research uses data from a number of previously published studies. We would like to thank G.-Y. Bae, V. de Gardelle, N. Gekas, J. Solomon, R. Polania and C. Ruff for sharing their data with us, as well as the authors of several other studies for making their data publicly available. We thank A. Huttenlocher and M. Woodford for helpful discussions, along with B. Geisler, R. Goris, M. Hayhoe, N. Kriegeskorte, K. Kay, S. Gershman, G. de Hollander and L. Colgin for comments on earlier versions of this paper. X.-X.W. is supported by the startup funds provided by The University of Texas at Austin. M.H. gratefully acknowledges Saarland University for providing computing resources.

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M.H. and X.-X.W. conceived and designed the research. M.H. and X.-X.W. developed the theoretical framework. M.H. performed the theoretical, numerical and data analyses, with input from X.X.W. M.H. and X.-X.W. interpreted the results and wrote the paper.

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Correspondence to Michael Hahn or Xue-Xin Wei.

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Hahn, M., Wei, XX. A unifying theory explains seemingly contradictory biases in perceptual estimation. Nat Neurosci 27, 793–804 (2024). https://doi.org/10.1038/s41593-024-01574-x

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