{"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/on-dropout-and-nuclear-norm-regularization","title":"On Dropout and Nuclear Norm Regularization","arxiv_id":"1905.11887","date":"2019-05-28","proceeding":null,"authors":["Poorya Mianjy","Raman Arora"],"abstract":"We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.","url_abs":"https://arxiv.org/abs/1905.11887v1","url_pdf":"https://arxiv.org/pdf/1905.11887v1.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":"on-dropout-and-nuclear-norm-regularization","repo_url":"https://github.com/r3831/dln_dropout","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"dropout","method_name":"Dropout"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.11887","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}