{"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/maximum-principle-based-algorithms-for-deep","title":"Maximum Principle Based Algorithms for Deep Learning","arxiv_id":"1710.09513","date":"2017-10-26","proceeding":null,"authors":["Qianxiao Li","Long Chen","Cheng Tai","Weinan E"],"abstract":"The continuous dynamical system approach to deep learning is explored in\norder to devise alternative frameworks for training algorithms. Training is\nrecast as a control problem and this allows us to formulate necessary\noptimality conditions in continuous time using the Pontryagin's maximum\nprinciple (PMP). A modification of the method of successive approximations is\nthen used to solve the PMP, giving rise to an alternative training algorithm\nfor deep learning. This approach has the advantage that rigorous error\nestimates and convergence results can be established. We also show that it may\navoid some pitfalls of gradient-based methods, such as slow convergence on flat\nlandscapes near saddle points. Furthermore, we demonstrate that it obtains\nfavorable initial convergence rate per-iteration, provided Hamiltonian\nmaximization can be efficiently carried out - a step which is still in need of\nimprovement. Overall, the approach opens up new avenues to attack problems\nassociated with deep learning, such as trapping in slow manifolds and\ninapplicability of gradient-based methods for discrete trainable variables.","url_abs":"http://arxiv.org/abs/1710.09513v4","url_pdf":"http://arxiv.org/pdf/1710.09513v4.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":"maximum-principle-based-algorithms-for-deep","repo_url":"https://github.com/foxycharm/E-MSA","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"maximum-principle-based-algorithms-for-deep","repo_url":"https://github.com/huisun317/snn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.09513","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}