2023/08/02 by G. S. H. Cruttwell, Geoffrey Cruttwell, Jean-Simon Pacaud Lemay +2 · 3 voices · 1 citation
Computer Science · Engineering · Mathematics · #18F40 #Advanced Numerical Analysis Techniques #Category Theory (math.CT) #D.3.1 #F.3.2 #FOS: Mathematics #Image Retrieval and Classification Techniques #Neural Networks and Applications #math.CT
paper · pdf · doi:10.48550/arxiv.2308.01131
openalex publication_date 2023/08/02 · arxiv published 2023/08/02 · arxiv updated 2023/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.