{"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/finite-size-effects-for-spiking-neural","title":"Finite size effects for spiking neural networks with spatially dependent coupling","arxiv_id":"1805.03601","date":"2018-05-09","proceeding":null,"authors":["Siwei Qiu","Carson Chow"],"abstract":"We study finite-size fluctuations in a network of spiking deterministic\nneurons coupled with non-uniform synaptic coupling. We generalize a previously\ndeveloped theory of finite size effects for uniform globally coupled neurons.\nIn the uniform case, mean field theory is well defined by averaging over the\nnetwork as the number of neurons in the network goes to infinity. However, for\nnonuniform coupling it is no longer possible to average over the entire network\nif we are interested in fluctuations at a particular location within the\nnetwork. We show that if the coupling function approaches a continuous function\nin the infinite system size limit then an average over a local neighborhood can\nbe defined such that mean field theory is well defined for a spatially\ndependent field. We then derive a perturbation expansion in the inverse system\nsize around the mean field limit for the covariance of the input to a neuron\n(synaptic drive) and firing rate fluctuations due to dynamical deterministic\nfinite-size effects.","url_abs":"http://arxiv.org/abs/1805.03601v3","url_pdf":"http://arxiv.org/pdf/1805.03601v3.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":"finite-size-effects-for-spiking-neural","repo_url":"https://github.com/qius5/FiniteSizeEffect","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}