{"id":766339,"date":"2021-08-11T07:40:01","date_gmt":"2021-08-11T14:40:01","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=766339"},"modified":"2022-01-03T10:54:32","modified_gmt":"2022-01-03T18:54:32","slug":"provably-correct-asymptotically-efficient-higher-order-reverse-mode-automatic-differentiation","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/provably-correct-asymptotically-efficient-higher-order-reverse-mode-automatic-differentiation\/","title":{"rendered":"Provably Correct, Asymptotically Efficient, Higher-Order Reverse-Mode Automatic Differentiation"},"content":{"rendered":"<p><span class=\"fontstyle0\">In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.<\/span><\/p>\n<p>Here is a <a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" rel=\"noopener noreferrer\" target=\"_blank\" href=\"https:\/\/www.youtube.com\/watch?v=EPGqzkEZWyw\">video of Simon giving a talk about the paper<span class=\"sr-only\"> (opens in new tab)<\/span><\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"POPL 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