{"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/are-saddles-good-enough-for-deep-learning","title":"Are Saddles Good Enough for Deep Learning?","arxiv_id":"1706.02052","date":"2017-06-07","proceeding":null,"authors":["Adepu Ravi Sankar","Vineeth N. Balasubramanian"],"abstract":"Recent years have seen a growing interest in understanding deep neural\nnetworks from an optimization perspective. It is understood now that converging\nto low-cost local minima is sufficient for such models to become effective in\npractice. However, in this work, we propose a new hypothesis based on recent\ntheoretical findings and empirical studies that deep neural network models\nactually converge to saddle points with high degeneracy. Our findings from this\nwork are new, and can have a significant impact on the development of gradient\ndescent based methods for training deep networks. We validated our hypotheses\nusing an extensive experimental evaluation on standard datasets such as MNIST\nand CIFAR-10, and also showed that recent efforts that attempt to escape\nsaddles finally converge to saddles with high degeneracy, which we define as\n`good saddles'. We also verified the famous Wigner's Semicircle Law in our\nexperimental results.","url_abs":"http://arxiv.org/abs/1706.02052v1","url_pdf":"http://arxiv.org/pdf/1706.02052v1.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":"are-saddles-good-enough-for-deep-learning","repo_url":"https://github.com/ravisankaradepu/degenerate_saddle","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.02052","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}