{"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/proximal-backpropagation","title":"Proximal Backpropagation","arxiv_id":"1706.04638","date":"2017-06-14","proceeding":"ICLR 2018 1","authors":["Thomas Frerix","Thomas Möllenhoff","Michael Moeller","Daniel Cremers"],"abstract":"We propose proximal backpropagation (ProxProp) as a novel algorithm that\ntakes implicit instead of explicit gradient steps to update the network\nparameters during neural network training. Our algorithm is motivated by the\nstep size limitation of explicit gradient descent, which poses an impediment\nfor optimization. ProxProp is developed from a general point of view on the\nbackpropagation algorithm, currently the most common technique to train neural\nnetworks via stochastic gradient descent and variants thereof. Specifically, we\nshow that backpropagation of a prediction error is equivalent to sequential\ngradient descent steps on a quadratic penalty energy, which comprises the\nnetwork activations as variables of the optimization. We further analyze\ntheoretical properties of ProxProp and in particular prove that the algorithm\nyields a descent direction in parameter space and can therefore be combined\nwith a wide variety of convergent algorithms. Finally, we devise an efficient\nnumerical implementation that integrates well with popular deep learning\nframeworks. We conclude by demonstrating promising numerical results and show\nthat ProxProp can be effectively combined with common first order optimizers\nsuch as Adam.","url_abs":"http://arxiv.org/abs/1706.04638v3","url_pdf":"http://arxiv.org/pdf/1706.04638v3.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":"proximal-backpropagation","repo_url":"https://github.com/tfrerix/proxprop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"adam","method_name":"Adam"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.04638","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}