Reverse Tangent Categories
Geoffrey Cruttwell, Jean-Simon Pacaud Lemay

TL;DR
This paper introduces reverse tangent categories, extending reverse differential categories to more general spaces like smooth manifolds, enabling gradient-based learning in broader mathematical contexts.
Contribution
The paper proposes reverse tangent categories, a new framework that generalizes reverse differential categories to include smooth manifolds with an involution operation.
Findings
Defines reverse tangent categories with involution on differential bundles.
Extends gradient-based learning to functions on smooth manifolds.
Provides a categorical framework for advanced geometric learning methods.
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.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Image Retrieval and Classification Techniques · Neural Networks and Applications
