Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Synaptic computation underlying probabilistic inference

Nature Neuroscience volume 13, pages 112–119 (2010)Cite this article

Abstract

We propose that synapses may be the workhorse of the neuronal computations that underlie probabilistic reasoning. We built a neural circuit model for probabilistic inference in which information provided by different sensory cues must be integrated and the predictive powers of individual cues about an outcome are deduced through experience. We found that bounded synapses naturally compute, through reward-dependent plasticity, the posterior probability that a choice alternative is correct given that a cue is presented. Furthermore, a decision circuit endowed with such synapses makes choices on the basis of the summed log posterior odds and performs near-optimal cue combination. The model was validated by reproducing salient observations of, and provides insights into, a monkey experiment using a categorization task. Our model thus suggests a biophysical instantiation of the Bayesian decision rule, while predicting important deviations from it similar to the 'base-rate neglect' observed in human studies when alternatives have unequal prior probabilities.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Schematic of the model and posterior computation by plastic synapses when a single cue is presented on each trial.
Figure 2: Posterior computation by plastic synapses when multiple cues are presented on each trial.
Figure 3: Choice behavior of the model and the subjective weight of evidence in the weather prediction task.
Figure 4: Model neural population activity during the weather prediction task.
Figure 5: Neural population activity is parametrically correlated with the log LR.
Figure 6: Effect of prior probability on the choice behavior and neural activity.

Similar content being viewed by others

References

  1. Knowlton, B.J., Squire, L.R. & Gluck, M.A. Probabilistic classification learning in amnesia. Learn. Mem. 1, 106–120 (1994).

    CAS  PubMed  Google Scholar 

  2. Knowlton, B.J., Mangels, J.A. & Squire, L.R. A neostriatal habit learning system in humans. Science 273, 1399–1402 (1996).

    Article  CAS  Google Scholar 

  3. Moody, T.D., Bookheimer, S.Y., Vanek, Z. & Knowlton, B.J. An implicit learning task activates medial temporal lobe in patients with Parkinson's disease. Behav. Neurosci. 118, 438–442 (2004).

    Article  Google Scholar 

  4. Fera, F. et al. Neural mechanisms underlying probabilistic category learning in normal aging. J. Neurosci. 25, 11340–11348 (2005).

    Article  CAS  Google Scholar 

  5. Ashby, F.G. & Maddox, W.T. Human category learning. Annu. Rev. Psychol. 56, 149–178 (2005).

    Article  Google Scholar 

  6. Yang, T. & Shadlen, M.N. Probabilistic reasoning by neurons. Nature 447, 1075–1080 (2007).

    Article  CAS  Google Scholar 

  7. Gold, J.I. & Shadlen, M. Neural computations that underlie decisions about sensory stimuli. Trends Cogn. Sci. 5, 10–16 (2001).

    Article  Google Scholar 

  8. Gold, J.I. & Shadlen, M.N. The neural basis of decision making. Annu. Rev. Neurosci. 30, 535–574 (2007).

    Article  CAS  Google Scholar 

  9. Soltani, A. & Wang, X.-J. A biophysically-based neural model of matching law behavior: melioration by stochastic synapses. J. Neurosci. 26, 3731–3744 (2006).

    Article  CAS  Google Scholar 

  10. Soltani, A., Lee, D. & Wang, X.-J. Neural mechanism for stochastic behavior during a competitive game. Neural Netw. 19, 1075–1090 (2006).

    Article  Google Scholar 

  11. Fusi, S., Asaad, W.F., Miller, E.K. & Wang, X.-J.Aneural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales. Neuron 54, 319–333 (2007).

    Article  CAS  Google Scholar 

  12. Fusi, S., Drew, P.J. & Abbott, L.F. Cascade models of synaptically stored memories. Neuron 45, 599–611 (2005).

    Article  CAS  Google Scholar 

  13. Fusi, S. & Abbott, L.F. Limits on the memory storage capacity of bounded synapses. Nat. Neurosci. 10, 485–493 (2007).

    Article  CAS  Google Scholar 

  14. Wang, X.-J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 955–968 (2002).

    Article  CAS  Google Scholar 

  15. Wong, K.-F. & Wang, X.-J. A recurrent network mechanism of time integration in perceptual decisions. J. Neurosci. 26, 1314–1328 (2006).

    Article  CAS  Google Scholar 

  16. Wong, K.-F., Huk, A.C., Shadlen, M.N. & Wang, X.-J. Neural circuit dynamics underlying accumulation of time-varying evidence during perceptual decision making. Front. Comput. Neurosci. 1, 6 (2007).

    Article  Google Scholar 

  17. Furman, M. & Wang, X.-J. Similarity effect and optimal control of multiple-choice decision making. Neuron 60, 1153–1168 (2008).

    Article  CAS  Google Scholar 

  18. Liu, F. & Wang, X.-J. A common cortical circuit mechanism for perceptual categorical discrimination and veridical judgment. PLOS Comput. Biol. 4, e1000253 (2008).

    Article  Google Scholar 

  19. Wang, X.-J. Decision making in recurrent neuronal circuits. Neuron 60, 215–234 (2008).

    Article  CAS  Google Scholar 

  20. Gluck, M.A. & Bower, G.H. From conditioning to category learning: an adaptive network model. J. Exp. Psychol. Gen. 117, 227–247 (1988).

    Article  CAS  Google Scholar 

  21. Amit, D.J. & Fusi, S. Dynamic learning in neural networks with material synapses. Neural Comput. 6, 957–982 (1994).

    Article  Google Scholar 

  22. Fusi, S. Hebbian spike-driven synaptic plasticity for learning patterns of mean firing rates. Biol. Cybern. 87, 459–470 (2002).

    Article  Google Scholar 

  23. Meeter, M., Myers, C.E., Shohamy, D., Hopkins, R.O. & Gluck, M.A. Strategies in probabilistic categorization: results from a new way of analyzing performance. Learn. Mem. 13, 230–239 (2006).

    Article  Google Scholar 

  24. Myers, J.L. Probability learning and sequence learning. in Handbook of Learning and Cognitive Processes (ed. Estes, W.K.) 171–205 (Erlbaum, Hillsdale, New Jersey, USA, 1976).

  25. Vulkan, N. An economist's perspective on probability matching. J. Econ. Surv. 14, 101–118 (2000).

    Article  Google Scholar 

  26. Shanks, D.R., Tunney, R.J. & McCarthy, J.D. A re-examination of probability matching and rational choice. J. Behav. Decis. Mak. 15, 233–250 (2002).

    Article  Google Scholar 

  27. Kahneman, D. & Tversky, A. On the psychology of prediction. Psychol. Rev. 80, 237–251 (1973).

    Article  Google Scholar 

  28. Tversky, A. & Kahneman, D. Evidential impact of base rates. in Judgment Under Uncertainty: Heuristics and Biases (eds. Kahneman, D., Slovic, P. & Tversky, A.) 153–160 (Cambridge Univ. Press, Cambridge, UK, 1982).

  29. Kruschke, J.K. ALCOVE: an exemplar-based connectionist model of category learning. Psychol. Rev. 99, 22–44 (1992).

    Article  CAS  Google Scholar 

  30. Glimcher, P.W. The neurobiology of visual-saccadic decision making. Annu. Rev. Neurosci. 26, 133–179 (2003).

    Article  CAS  Google Scholar 

  31. Sugrue, L.P., Corrado, G.C. & Newsome, W.T. Matching behavior and representation of value in parietal cortex. Science 304, 1782–1787 (2004).

    Article  CAS  Google Scholar 

  32. Sugrue, L.P., Corrado, G.S. & Newsome, W.T. Choosing the greater of two goods: neural currencies for valuation and decision making. Nat. Rev. Neurosci. 6, 363–375 (2005).

    Article  CAS  Google Scholar 

  33. Soltani, A. & Wang, X.-J. From biophysics to cognition: reward-dependent adaptive choice behavior. Curr. Opin. Neurobiol. 18, 209–216 (2008).

    Article  CAS  Google Scholar 

  34. 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  Google Scholar 

  35. Beck, J.M. et al. Probabilistic population codes for bayesian decision making. Neuron 60, 1142–1152 (2008).

    Article  CAS  Google Scholar 

  36. Ma, W.J., Beck, J.M. & Pouget, A. Spiking networks for bayesian inference and choice. Curr. Opin. Neurobiol. 18, 217–222 (2008).

    Article  CAS  Google Scholar 

  37. Rushworth, M.F.S. & Behrens, T.E.J. Choice, uncertainty and value in prefrontal and cingulate cortex. Nat. Neurosci. 11, 389–397 (2008).

    Article  CAS  Google Scholar 

  38. Lee, K.-M. & Keller, E.L. Neural activity in the frontal eye fields modulated by the number of alternatives in target choice. J. Neurosci. 28, 2242–2251 (2008).

    Article  CAS  Google Scholar 

  39. Lauwereyns, J., Watanabe, K., Coe, B. & Hikosaka, O. A neural correlate of response bias in monkey caudate nucleus. Nature 418, 413–417 (2002).

    Article  CAS  Google Scholar 

  40. Samejima, K., Ueda, Y., Doya, K. & Kimura, M. Representation of action-specific reward values in the striatum. Science 310, 1337–1340 (2005).

    Article  CAS  Google Scholar 

  41. Lau, B. & Glimcher, P.W. Value representations in the primate striatum during matching behavior. Neuron 58, 451–463 (2008).

    Article  CAS  Google Scholar 

  42. Reynolds, J.N., Hyland, B.I. & Wickens, J.R. A cellular mechanism of reward-related learning. Nature 413, 67–70 (2001).

    Article  CAS  Google Scholar 

  43. Shen, W., Flajolet, M., Greengard, P. & Surmeier, D.J. Dichotomous dopaminergic control of striatal synaptic plasticity. Science 321, 848–851 (2008).

    Article  CAS  Google Scholar 

  44. Schultz, W. Predictive reward signal of dopamine neurons. J. Neurophysiol. 80, 1–27 (1998).

    Article  CAS  Google Scholar 

  45. Schultz, W. Multiple dopamine functions at different time courses. Annu. Rev. Neurosci. 30, 259–288 (2007).

    Article  CAS  Google Scholar 

  46. Poldrack, R.A. et al. Interactive memory systems in the human brain. Nature 414, 546–550 (2001).

    Article  CAS  Google Scholar 

  47. Tanaka, K. Inferotemporal cortex and object vision. Annu. Rev. Neurosci. 19, 109–139 (1996).

    Article  CAS  Google Scholar 

  48. Tsunoda, K., Yamane, Y., Nishizaki, M. & Tanifuji, M. Complex objects are represented in macaque inferotemporal cortex by the combination of feature columns. Nat. Neurosci. 4, 832–838 (2001).

    Article  CAS  Google Scholar 

  49. Petersen, C.C., Malenka, R.C., Nicoll, R.A. & Hopfield, J.J. All-or-none potentiation at CA3–CA1 synapses. Proc. Natl. Acad. Sci. USA 95, 4732–4737 (1998).

    Article  CAS  Google Scholar 

  50. O'Connor, D.H., Wittenberg, G.M. & Wang, S.S.-H. Graded bidirectional synaptic plasticity is composed of switch-like unitary events. Proc. Natl. Acad. Sci. USA 102, 9679–9684 (2005).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by US National Institutes of Health grants 2-R01-MH062349 and MH073246. We are thankful to D. Andrieux, S. Ardid, A. Bernacchia and R. Wilson for comments on the manuscript.

Author information

Authors and Affiliations

  1. Department of Neurobiology and Kavli Institute of Neuroscience, Yale University School of Medicine, New Haven, Connecticut, USA

    Alireza Soltani & Xiao-Jing Wang

  2. Division of Biology, California Institute of Technology, Pasadena, California, USA

    Alireza Soltani

Authors
  1. Alireza Soltani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.S. and X.-J.W. conceived the problem and designed the model. A.S. performed model simulations and analyzed the data. A.S. and X.-J.W. wrote the paper.

Corresponding authors

Correspondence to Alireza Soltani or Xiao-Jing Wang.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–11, Supplementary Notes 1–5 and Supplementary Methods (PDF 1204 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Soltani, A., Wang, XJ. Synaptic computation underlying probabilistic inference. Nat Neurosci 13, 112–119 (2010). https://doi.org/10.1038/nn.2450

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn.2450

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing