{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/characterizing-variability-in-nonlinear","title":"Characterizing variability in nonlinear recurrent neuronal networks","arxiv_id":"1610.03110","date":"2016-10-10","proceeding":null,"authors":[],"abstract":"In this note, we develop semi-analytical techniques to obtain the full\ncorrelational structure of a stochastic network of nonlinear neurons described\nby rate variables. Under the assumption that pairs of membrane potentials are\njointly Gaussian -- which they tend to be in large networks -- we obtain\ndeterministic equations for the temporal evolution of the mean firing rates and\nthe noise covariance matrix that can be solved straightforwardly given the\nnetwork connectivity. We also obtain spike count statistics such as Fano\nfactors and pairwise correlations, assuming doubly-stochastic action potential\nfiring. Importantly, our theory does not require fluctuations to be small, and\nworks for several biologically motivated, convex single-neuron nonlinearities.","url_abs":"http://arxiv.org/abs/1610.03110v1","url_pdf":"http://arxiv.org/pdf/1610.03110v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"characterizing-variability-in-nonlinear","repo_url":"https://github.com/dylanfesta/SSNVariability.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}