{"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/escaping-from-saddle-points-online-stochastic","title":"Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition","arxiv_id":"1503.02101","date":"2015-03-06","proceeding":null,"authors":["Rong Ge","Furong Huang","Chi Jin","Yang Yuan"],"abstract":"We analyze stochastic gradient descent for optimizing non-convex functions.\nIn many cases for non-convex functions the goal is to find a reasonable local\nminimum, and the main concern is that gradient updates are trapped in saddle\npoints. In this paper we identify strict saddle property for non-convex problem\nthat allows for efficient optimization. Using this property we show that\nstochastic gradient descent converges to a local minimum in a polynomial number\nof iterations. To the best of our knowledge this is the first work that gives\nglobal convergence guarantees for stochastic gradient descent on non-convex\nfunctions with exponentially many local minima and saddle points. Our analysis\ncan be applied to orthogonal tensor decomposition, which is widely used in\nlearning a rich class of latent variable models. We propose a new optimization\nformulation for the tensor decomposition problem that has strict saddle\nproperty. As a result we get the first online algorithm for orthogonal tensor\ndecomposition with global convergence guarantee.","url_abs":"http://arxiv.org/abs/1503.02101v1","url_pdf":"http://arxiv.org/pdf/1503.02101v1.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":"escaping-from-saddle-points-online-stochastic","repo_url":"https://github.com/Jasmine216/Fine-grained-image-classification-Dog-Breeds","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1503.02101","atlas_url":"https://app.syntology.ai/?focus=1503.02101","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}