{"ID":2865879,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.20931","arxiv_id":"2509.20931","title":"Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories","abstract":"Reverse differentiation is an essential operation for automatic differentiation. Cartesian reverse differential categories axiomatize reverse differentiation in a categorical framework, where one of the primary axioms is the reverse chain rule, which is the formula that expresses the reverse derivative of a composition. Here, we present the reverse differential analogue of Faa di Bruno's Formula, which gives a higher-order reverse chain rule in a Cartesian reverse differential category. To properly do so, we also define partial reverse derivatives and higher-order reverse derivatives in a Cartesian reverse differential category.","short_abstract":"Reverse differentiation is an essential operation for automatic differentiation. Cartesian reverse differential categories axiomatize reverse differentiation in a categorical framework, where one of the primary axioms is the reverse chain rule, which is the formula that expresses the reverse derivative of a composition...","url_abs":"https://arxiv.org/abs/2509.20931","url_pdf":"https://arxiv.org/pdf/2509.20931v1","authors":"[\"Aaron Biggin\",\"Jean-Simon Pacaud Lemay\"]","published":"2025-09-25T09:16:45Z","proceeding":"cs.LO","tasks":"[\"cs.LO\",\"cs.LG\"]","methods":"[]","has_code":false}