{"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/a-surprising-linear-relationship-predicts","title":"A Surprising Linear Relationship Predicts Test Performance in Deep Networks","arxiv_id":"1807.09659","date":"2018-07-25","proceeding":null,"authors":["Qianli Liao","Brando Miranda","Andrzej Banburski","Jack Hidary","Tomaso Poggio"],"abstract":"Given two networks with the same training loss on a dataset, when would they\nhave drastically different test losses and errors? Better understanding of this\nquestion of generalization may improve practical applications of deep networks.\nIn this paper we show that with cross-entropy loss it is surprisingly simple to\ninduce significantly different generalization performances for two networks\nthat have the same architecture, the same meta parameters and the same training\nerror: one can either pretrain the networks with different levels of\n\"corrupted\" data or simply initialize the networks with weights of different\nGaussian standard deviations. A corollary of recent theoretical results on\noverfitting shows that these effects are due to an intrinsic problem of\nmeasuring test performance with a cross-entropy/exponential-type loss, which\ncan be decomposed into two components both minimized by SGD -- one of which is\nnot related to expected classification performance. However, if we factor out\nthis component of the loss, a linear relationship emerges between training and\ntest losses. Under this transformation, classical generalization bounds are\nsurprisingly tight: the empirical/training loss is very close to the\nexpected/test loss. Furthermore, the empirical relation between classification\nerror and normalized cross-entropy loss seem to be approximately monotonic","url_abs":"http://arxiv.org/abs/1807.09659v1","url_pdf":"http://arxiv.org/pdf/1807.09659v1.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":"a-surprising-linear-relationship-predicts","repo_url":"https://github.com/brando90/Generalization-Puzzles-in-Deep-Networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-surprising-linear-relationship-predicts","repo_url":"https://github.com/brando90/overparam_experiments","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-surprising-linear-relationship-predicts","repo_url":"https://github.com/liaoq/Generalization-Puzzles-in-Deep-Networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"generalization-bounds","task_name":"Generalization Bounds"}],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.09659","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}