{"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/low-dimensional-spike-rate-models-derived","title":"Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation","arxiv_id":"1611.07999","date":"2017-07-19","proceeding":null,"authors":[],"abstract":"The spiking activity of single neurons can be well described by a nonlinear\nintegrate-and-fire model that includes somatic adaptation. When exposed to\nfluctuating inputs sparsely coupled populations of these model neurons exhibit\nstochastic collective dynamics that can be effectively characterized using the\nFokker-Planck equation. [...] Here we derive from that description four simple\nmodels for the spike rate dynamics in terms of low-dimensional ordinary\ndifferential equations using two different reduction techniques: one uses the\nspectral decomposition of the Fokker-Planck operator, the other is based on a\ncascade of two linear filters and a nonlinearity, which are determined from the\nFokker-Planck equation and semi-analytically approximated. We evaluate the\nreduced models for a wide range of biologically plausible input statistics and\nfind that both approximation approaches lead to spike rate models that\naccurately reproduce the spiking behavior of the underlying adaptive\nintegrate-and-fire population. [...] The low-dimensional models also well\nreproduce stable oscillatory spike rate dynamics that is generated by recurrent\nsynaptic excitation and neuronal adaptation. [...] We have made available\nimplementations that allow to numerically integrate the low-dimensional spike\nrate models as well as the Fokker-Planck partial differential equation in\nefficient ways for arbitrary model parametrizations as open source software.\nThe derived spike rate descriptions retain a direct link to the properties of\nsingle neurons, allow for convenient mathematical analyses of network states,\nand are well suited for application in neural mass/mean-field based brain\nnetwork models.","url_abs":"http://arxiv.org/abs/1611.07999v2","url_pdf":"http://arxiv.org/pdf/1611.07999v2.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":"low-dimensional-spike-rate-models-derived","repo_url":"https://github.com/neuromethods/fokker-planck-based-spike-rate-models","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1611.07999","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1611.07999"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/neuromethods/fokker-planck-based-spike-rate-models","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"01a1adaa69b04350","entry":"get_v","repo":"neuromethods/fokker-planck-based-spike-rate-models","repo_kind":"official","path":"models/fp/fokker_planck_model.py","file_url":"https://github.com/neuromethods/fokker-planck-based-spike-rate-models/blob/HEAD/models/fp/fokker_planck_model.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"01a1adaa69b04350"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}