{"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-the-role-of-momentum-in-non","title":"Momentum via Primal Averaging: Theoretical Insights and Learning Rate Schedules for Non-Convex Optimization","arxiv_id":"2010.00406","date":"2020-10-01","proceeding":null,"authors":["Aaron Defazio"],"abstract":"Momentum methods are now used pervasively within the machine learning community for training non-convex models such as deep neural networks. Empirically, they out perform traditional stochastic gradient descent (SGD) approaches. In this work we develop a Lyapunov analysis of SGD with momentum (SGD+M), by utilizing a equivalent rewriting of the method known as the stochastic primal averaging (SPA) form. This analysis is much tighter than previous theory in the non-convex case, and due to this we are able to give precise insights into when SGD+M may out-perform SGD, and what hyper-parameter schedules will work and why.","url_abs":"https://arxiv.org/abs/2010.00406v4","url_pdf":"https://arxiv.org/pdf/2010.00406v4.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-the-role-of-momentum-in-non","repo_url":"https://github.com/facebookresearch/madgrad","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"single-particle-analysis","task_name":"Single Particle Analysis"}],"methods":[{"method_slug":"sgd","method_name":"SGD"},{"method_slug":"sgd-with-momentum","method_name":"SGD with Momentum"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2010.00406","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}