English

Reverse Tangent Categories

Category Theory 2023-11-27 v2

Abstract

Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based learning for functions between more general spaces such as smooth manifolds. In this paper, we propose a setting to handle this, which we call reverse tangent categories: tangent categories with an involution operation for their differential bundles.

Keywords

Cite

@article{arxiv.2308.01131,
  title  = {Reverse Tangent Categories},
  author = {Geoffrey Cruttwell and Jean-Simon Pacaud Lemay},
  journal= {arXiv preprint arXiv:2308.01131},
  year   = {2023}
}

Comments

Accepted and published in the proceedings of CSL2024

R2 v1 2026-06-28T11:46:25.369Z