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Category Theory × Machine Learning


Reverse tangent categories

Geoffrey Cruttwell, Jean-Simon Pacaud Lemay

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.