{"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/an-optimal-control-approach-to-deep-learning","title":"An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks","arxiv_id":"1803.01299","date":"2018-03-04","proceeding":"ICML 2018 7","authors":["Qianxiao Li","Shuji Hao"],"abstract":"Deep learning is formulated as a discrete-time optimal control problem. This\nallows one to characterize necessary conditions for optimality and develop\ntraining algorithms that do not rely on gradients with respect to the trainable\nparameters. In particular, we introduce the discrete-time method of successive\napproximations (MSA), which is based on the Pontryagin's maximum principle, for\ntraining neural networks. A rigorous error estimate for the discrete MSA is\nobtained, which sheds light on its dynamics and the means to stabilize the\nalgorithm. The developed methods are applied to train, in a rather principled\nway, neural networks with weights that are constrained to take values in a\ndiscrete set. We obtain competitive performance and interestingly, very sparse\nweights in the case of ternary networks, which may be useful in model\ndeployment in low-memory devices.","url_abs":"http://arxiv.org/abs/1803.01299v2","url_pdf":"http://arxiv.org/pdf/1803.01299v2.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":"an-optimal-control-approach-to-deep-learning","repo_url":"https://github.com/LiQianxiao/discrete-MSA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.01299","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}