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Solution of a chaotic neural network at fixed connectivity
1Center for Theoretical Neuroscience, Zuckerman Institute, Columbia University.
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We calculate the moments and response functions of a nonlinear random recurrent neural network in the large- limit using a diagrammatic technique. Our approach does not require averaging over synaptic weights and gives the first nontrivial term in a expansion of general intensive-order correlation functions, proving a recent conjecture by Shen and Hu as a special case. Our results provide an analytical link between synaptic connectivity, correlations in spontaneous activity, and the response of a network to small perturbations.
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