{"paper":{"title":"Categorical semantics of a simple differential programming language","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"math.CT","authors_text":"Dorette Pronk, Geoffrey Cruttwell, Jonathan Gallagher","submitted_at":"2021-01-26T00:08:48Z","abstract_excerpt":"With the increased interest in machine learning, and deep learning in particular,  the use of automatic differentiation has become more wide-spread in computation.  There have been two recent developments to provide the theoretical support for this types of structure.  One approach, due to Abadi and Plotkin, provides a simple differential programming language.  Another approach is the notion of a reverse differential category.  In the present paper we bring these two approaches together.  In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's langua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.10491","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.10491/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}