Compositional Taylor expansion in cartesian differential categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915297256013824 |
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| author | Walch, Aymeric |
| author_facet | Walch, Aymeric |
| contents | This paper provides a compositional approach to Taylor expansion, in the setting of cartesian differential categories. Taylor expansion is captured here by a functor that generalizes the tangent bundle functor to higher order derivatives. The fundamental properties of Taylor expansion then boils down to naturality equations that turns this functor into a monad. This monad provides a categorical approach to higher order dual numbers and the jet bundle construction used in automated differentiation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compositional Taylor expansion in cartesian differential categories Walch, Aymeric Logic in Computer Science This paper provides a compositional approach to Taylor expansion, in the setting of cartesian differential categories. Taylor expansion is captured here by a functor that generalizes the tangent bundle functor to higher order derivatives. The fundamental properties of Taylor expansion then boils down to naturality equations that turns this functor into a monad. This monad provides a categorical approach to higher order dual numbers and the jet bundle construction used in automated differentiation. |
| title | Compositional Taylor expansion in cartesian differential categories |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2502.09066 |