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Michael A. Buice
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2010) 22 (2): 377–426.
Published: 01 February 2010
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Abstract
View articletitled, Systematic Fluctuation Expansion for Neural Network Activity Equations
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for article titled, 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 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.