{"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/error-bounds-for-approximations-with-deep","title":"Error bounds for approximations with deep ReLU networks","arxiv_id":"1610.01145","date":"2016-10-03","proceeding":null,"authors":["Dmitry Yarotsky"],"abstract":"We study expressive power of shallow and deep neural networks with piece-wise\nlinear activation functions. We establish new rigorous upper and lower bounds\nfor the network complexity in the setting of approximations in Sobolev spaces.\nIn particular, we prove that deep ReLU networks more efficiently approximate\nsmooth functions than shallow networks. In the case of approximations of 1D\nLipschitz functions we describe adaptive depth-6 network architectures more\nefficient than the standard shallow architecture.","url_abs":"http://arxiv.org/abs/1610.01145v3","url_pdf":"http://arxiv.org/pdf/1610.01145v3.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":"error-bounds-for-approximations-with-deep","repo_url":"https://github.com/arsenal9971/TUB_MoDL","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"error-bounds-for-approximations-with-deep","repo_url":"https://github.com/jmaces/mfo_dl_seminar_2018","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.01145","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}