{"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/mean-field-limit-of-the-learning-dynamics-of","title":"Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks","arxiv_id":"1902.02880","date":"2019-02-07","proceeding":null,"authors":["Phan-Minh Nguyen"],"abstract":"Can multilayer neural networks -- typically constructed as highly complex\nstructures with many nonlinearly activated neurons across layers -- behave in a\nnon-trivial way that yet simplifies away a major part of their complexities? In\nthis work, we uncover a phenomenon in which the behavior of these complex\nnetworks -- under suitable scalings and stochastic gradient descent dynamics --\nbecomes independent of the number of neurons as this number grows sufficiently\nlarge. We develop a formalism in which this many-neurons limiting behavior is\ncaptured by a set of equations, thereby exposing a previously unknown operating\nregime of these networks. While the current pursuit is mathematically\nnon-rigorous, it is complemented with several experiments that validate the\nexistence of this behavior.","url_abs":"http://arxiv.org/abs/1902.02880v1","url_pdf":"http://arxiv.org/pdf/1902.02880v1.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":"mean-field-limit-of-the-learning-dynamics-of","repo_url":"https://github.com/npminh12/multilayer-mean-field","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.02880","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1902.02880"}},"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/npminh12/multilayer-mean-field","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"listed":{"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":0,"samples":[{"code_sha256_prefix":"dc27f27a37006650","entry":"load_pickle","repo":"npminh12/multilayer-mean-field","repo_kind":"listed","path":"nnet_tensorflow_compact.py","file_url":"https://github.com/npminh12/multilayer-mean-field/blob/HEAD/nnet_tensorflow_compact.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"dc27f27a37006650"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}