{"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/spurious-local-minima-are-common-in-two-layer","title":"Spurious Local Minima are Common in Two-Layer ReLU Neural Networks","arxiv_id":"1712.08968","date":"2017-12-24","proceeding":"ICML 2018 7","authors":["Itay Safran","Ohad Shamir"],"abstract":"We consider the optimization problem associated with training simple ReLU\nneural networks of the form $\\mathbf{x}\\mapsto\n\\sum_{i=1}^{k}\\max\\{0,\\mathbf{w}_i^\\top \\mathbf{x}\\}$ with respect to the\nsquared loss. We provide a computer-assisted proof that even if the input\ndistribution is standard Gaussian, even if the dimension is arbitrarily large,\nand even if the target values are generated by such a network, with orthonormal\nparameter vectors, the problem can still have spurious local minima once $6\\le\nk\\le 20$. By a concentration of measure argument, this implies that in high\ninput dimensions, \\emph{nearly all} target networks of the relevant sizes lead\nto spurious local minima. Moreover, we conduct experiments which show that the\nprobability of hitting such local minima is quite high, and increasing with the\nnetwork size. On the positive side, mild over-parameterization appears to\ndrastically reduce such local minima, indicating that an over-parameterization\nassumption is necessary to get a positive result in this setting.","url_abs":"http://arxiv.org/abs/1712.08968v3","url_pdf":"http://arxiv.org/pdf/1712.08968v3.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":"spurious-local-minima-are-common-in-two-layer","repo_url":"https://github.com/ItaySafran/OneLayerGDconvergence","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1712.08968","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}