Systematic fluctuation expansion for neural network activity equations

Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into ac...

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Bibliographic Details
Published in:Neural computation Vol. 22; no. 2; p. 377
Main Authors: Buice, Michael A, Cowan, Jack D, Chow, Carson C
Format: Journal Article
Language:English
Published: United States 01.02.2010
Subjects:
Action Potentials - physiology
Algorithms
Animals
Artificial Intelligence
Brain - physiology
Humans
Mathematical Computing
Mathematical Concepts
Nerve Net - physiology
Neural Networks, Computer
Neurons - physiology
ISSN:1530-888X, 1530-888X
Online Access:Get more information
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Summary:Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Correspondence-1
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ISSN:1530-888X
1530-888X
DOI:10.1162/neco.2009.02-09-960