Solution of a chaotic neural network at fixed connectivity

Albert J. Wakhloo

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arXiv · 2604.24141

Solution of a chaotic neural network at fixed connectivity

Albert J. Wakhloo

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Abstract

We calculate the moments and response functions of a nonlinear random recurrent neural network in the large-$N$ limit using a diagrammatic technique. Our approach does not require averaging over synaptic weights and gives the first nontrivial term in a $1/\sqrt{N}$ 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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Albert J. Wakhloo. 2026-04-27. Solution of a chaotic neural network at fixed connectivity. https://arxiv.org/abs/2604.24141

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