Solution of a large nonlinear recurrent neural network at fixed connectivity
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918469609455616 |
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| author | Wakhloo, Albert J. |
| author_facet | Wakhloo, Albert J. |
| contents | We calculate the moments and response functions of a nonlinear random recurrent neural network in the large $N$ limit. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solution of a large nonlinear recurrent neural network at fixed connectivity Wakhloo, Albert J. Disordered Systems and Neural Networks Neurons and Cognition We calculate the moments and response functions of a nonlinear random recurrent neural network in the large $N$ limit. 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. |
| title | Solution of a large nonlinear recurrent neural network at fixed connectivity |
| topic | Disordered Systems and Neural Networks Neurons and Cognition |
| url | https://arxiv.org/abs/2604.24141 |