{"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/backprop-as-functor-a-compositional","title":"Backprop as Functor: A compositional perspective on supervised learning","arxiv_id":"1711.10455","date":"2017-11-28","proceeding":null,"authors":["Brendan Fong","David I. Spivak","Rémy Tuyéras"],"abstract":"A supervised learning algorithm searches over a set of functions $A \\to B$\nparametrised by a space $P$ to find the best approximation to some ideal\nfunction $f\\colon A \\to B$. It does this by taking examples $(a,f(a)) \\in\nA\\times B$, and updating the parameter according to some rule. We define a\ncategory where these update rules may be composed, and show that gradient\ndescent---with respect to a fixed step size and an error function satisfying a\ncertain property---defines a monoidal functor from a category of parametrised\nfunctions to this category of update rules. This provides a structural\nperspective on backpropagation, as well as a broad generalisation of neural\nnetworks.","url_abs":"http://arxiv.org/abs/1711.10455v3","url_pdf":"http://arxiv.org/pdf/1711.10455v3.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":"backprop-as-functor-a-compositional","repo_url":"https://github.com/TomohikoK/backprop-as-functor","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"backprop-as-functor-a-compositional","repo_url":"https://github.com/darrenjw/isba2021","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"backprop-as-functor-a-compositional","repo_url":"https://github.com/vonpost/HLearn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.10455","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}