[Comp-neuro] Mathematical theory of cortical microcircuits (New
dileepg at gmail.com
Sun Oct 18 20:34:35 CEST 2009
I would like to draw your attention to our recent paper describing a
mathematical theory for cortical microcircuits.
George D, Hawkins J
Towards a Mathematical Theory of Cortical Micro-circuits
PLoS Comput Biol 5(10: e1000532. doi:10.1371/journal.pcbi.1000532
The paper can be downloaded from http://www.ploscompbiol.org/doi/pcbi.1000532
Author summary and abstract are included below.
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.
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.
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