Dynamic Mean Field Theories for Nonlinear Noise in Recurrent Neuronal Networks
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917216773996544 |
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| author | Chipman, Shoshana Doiron, Brent |
| author_facet | Chipman, Shoshana Doiron, Brent |
| contents | Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that replaces nonlinear functions of Ornstein-Uhlenbeck (OU) noise with a Gaussian-equivalent process matched in mean and covariance, and combine this with a lognormal moment closure for expansive nonlinearities to derive a closed dynamical mean-field theory for recurrent neuronal networks. The resulting theory captures order-one transients, fixed points, and noise-induced shifts of bifurcation structure, and outperforms standard linearization-based approximations in the strong-fluctuation regime. More broadly, the approach applies whenever dynamics depend smoothly on OU processes via nonlinear transformations, offering a tractable route to noise-dependent phase diagrams in computational neuroscience models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamic Mean Field Theories for Nonlinear Noise in Recurrent Neuronal Networks Chipman, Shoshana Doiron, Brent Neurons and Cognition Dynamical Systems 60H10, 92C20, 37H20 Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that replaces nonlinear functions of Ornstein-Uhlenbeck (OU) noise with a Gaussian-equivalent process matched in mean and covariance, and combine this with a lognormal moment closure for expansive nonlinearities to derive a closed dynamical mean-field theory for recurrent neuronal networks. The resulting theory captures order-one transients, fixed points, and noise-induced shifts of bifurcation structure, and outperforms standard linearization-based approximations in the strong-fluctuation regime. More broadly, the approach applies whenever dynamics depend smoothly on OU processes via nonlinear transformations, offering a tractable route to noise-dependent phase diagrams in computational neuroscience models. |
| title | Dynamic Mean Field Theories for Nonlinear Noise in Recurrent Neuronal Networks |
| topic | Neurons and Cognition Dynamical Systems 60H10, 92C20, 37H20 |
| url | https://arxiv.org/abs/2601.15462 |