{"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/towards-a-general-theory-of-infinite-width","title":"Towards a General Theory of Infinite-Width Limits of Neural Classifiers","arxiv_id":"2003.05884","date":"2020-03-12","proceeding":"ICML 2020 1","authors":["Eugene. A. Golikov"],"abstract":"Obtaining theoretical guarantees for neural networks training appears to be a hard problem in a general case. Recent research has been focused on studying this problem in the limit of infinite width and two different theories have been developed: a mean-field (MF) and a constant kernel (NTK) limit theories. We propose a general framework that provides a link between these seemingly distinct theories. Our framework out of the box gives rise to a discrete-time MF limit which was not previously explored in the literature. We prove a convergence theorem for it and show that it provides a more reasonable approximation for finite-width nets compared to the NTK limit if learning rates are not very small. Also, our framework suggests a limit model that coincides neither with the MF limit nor with the NTK one. We show that for networks with more than two hidden layers RMSProp training has a non-trivial discrete-time MF limit but GD training does not have one. Overall, our framework demonstrates that both MF and NTK limits have considerable limitations in approximating finite-sized neural nets, indicating the need for designing more accurate infinite-width approximations for them.","url_abs":"https://arxiv.org/abs/2003.05884v3","url_pdf":"https://arxiv.org/pdf/2003.05884v3.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":"towards-a-general-theory-of-infinite-width","repo_url":"https://github.com/deepmipt/infinite-width_nets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"ntk","method_name":"NTK"},{"method_slug":"rmsprop","method_name":"RMSProp"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2003.05884","atlas_url":"https://app.syntology.ai/?focus=2003.05884","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2003.05884"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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":"deterministic:regex_extraction","url":"https://github.com/deepmipt/research","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/deepmipt/infinite-width_nets","reach":null}],"summary":{"ran":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":"2572ab529244fdec","entry":"LinearizedModel","repo":"deepmipt/infinite-width_nets","repo_kind":"official","path":"utils/models.py","file_url":"https://github.com/deepmipt/infinite-width_nets/blob/HEAD/utils/models.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"2572ab529244fdec"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}