{"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/understanding-deep-learning-requires","title":"Understanding deep learning requires rethinking generalization","arxiv_id":"1611.03530","date":"2016-11-10","proceeding":null,"authors":["Chiyuan Zhang","Samy Bengio","Moritz Hardt","Benjamin Recht","Oriol Vinyals"],"abstract":"Despite their massive size, successful deep artificial neural networks can\nexhibit a remarkably small difference between training and test performance.\nConventional wisdom attributes small generalization error either to properties\nof the model family, or to the regularization techniques used during training.\n  Through extensive systematic experiments, we show how these traditional\napproaches fail to explain why large neural networks generalize well in\npractice. Specifically, our experiments establish that state-of-the-art\nconvolutional networks for image classification trained with stochastic\ngradient methods easily fit a random labeling of the training data. This\nphenomenon is qualitatively unaffected by explicit regularization, and occurs\neven if we replace the true images by completely unstructured random noise. We\ncorroborate these experimental findings with a theoretical construction showing\nthat simple depth two neural networks already have perfect finite sample\nexpressivity as soon as the number of parameters exceeds the number of data\npoints as it usually does in practice.\n  We interpret our experimental findings by comparison with traditional models.","url_abs":"http://arxiv.org/abs/1611.03530v2","url_pdf":"http://arxiv.org/pdf/1611.03530v2.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":"understanding-deep-learning-requires","repo_url":"https://github.com/2xic/notebooks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/KellyHwong/rethinking_generalization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/aaronpeikert/methods-meetup","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Unlicense"}},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/glouppe/info8010-deep-learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/jessemzhang/dl_spectral_normalization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/mdv3101/Rethinking_Generalization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"understanding-deep-learning-requires","repo_url":"https://github.com/pluskid/fitting-random-labels","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1611.03530","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}