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.
Michael A
MA
Buice
Jack D
JD
Cowan
Carson C
CC
Chow
D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001185:Artificial Intelligence; D001921:Brain / Q000502:physiology*; D006801:Humans; D008432:Mathematical Computing; D055641:Mathematical Concepts; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*