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Towards a Mathematical Theory of Cortical Micro-circuits

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  • Dileep George
  • Jeff Hawkins

Abstract

The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.Author Summary: Understanding the computational and information processing roles of cortical circuitry is one of the outstanding problems in neuroscience. In this paper, we work from a theory of neocortex that models it as a spatio-temporal hierarchical system to derive a biological cortical circuit. This is achieved by combining the computational constraints provided by the inference equations for this spatio-temporal hierarchy with anatomical data. The result is a mathematically consistent biological circuit that can be mapped to the cortical laminae and matches many prominent features of the mammalian neocortex. The mathematical model can serve as a starting point for the construction of machines that work like the brain. The resultant biological circuit can be used for modeling physiological phenomena and for deriving testable predictions about the brain.

Suggested Citation

  • Dileep George & Jeff Hawkins, 2009. "Towards a Mathematical Theory of Cortical Micro-circuits," PLOS Computational Biology, Public Library of Science, vol. 5(10), pages 1-26, October.
    • Handle: RePEc:plo:pcbi00:1000532
    DOI: 10.1371/journal.pcbi.1000532
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    References listed on IDEAS

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    1. Karl Friston, 2008. "Hierarchical Models in the Brain," PLOS Computational Biology, Public Library of Science, vol. 4(11), pages 1-24, November.
    2. Nicolas Pinto & David D Cox & James J DiCarlo, 2008. "Why is Real-World Visual Object Recognition Hard?," PLOS Computational Biology, Public Library of Science, vol. 4(1), pages 1-6, January.
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    1. Adam Safron, 2019. "Multilevel evolutionary developmental optimization (MEDO): A theoretical framework for understanding preferences and selection dynamics," Papers 1910.13443, arXiv.org, revised Nov 2019.

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