Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.20931 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912604531720192 |
|---|---|
| author | Biggin, Aaron Lemay, Jean-Simon Pacaud |
| author_facet | Biggin, Aaron Lemay, Jean-Simon Pacaud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories Biggin, Aaron Lemay, Jean-Simon Pacaud Logic in Computer Science Machine Learning F.4.1; G.1.4 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. |
| title | Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories |
| topic | Logic in Computer Science Machine Learning F.4.1; G.1.4 |
| url | https://arxiv.org/abs/2509.20931 |