21 citations · 24 across the 3 of their papers we have counts for
5 papers
Monoidal Reverse Differential Categories
Geoffrey Cruttwell, Jonathan Gallagher, Jean-Simon Pacaud Lemay +1
Cartesian reverse differential categories (CRDCs) are a recently defined structure which categorically model the reverse differentiation operations used in supervised learning. Her…
Categorical semantics of a simple differential programming language
Geoffrey Cruttwell, Jonathan Gallagher, Dorette Pronk
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been t…
Latent Fibrations: Fibrations for Categories of Partial Maps
Robin Cockett, Geoff Cruttwell, Jonathan Gallagher +1
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the…
Reverse derivative categories
Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher +4
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivativ…
Differential restriction categories
J. R. B. Cockett, G. S. H. Cruttwell, J. D. Gallagher
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on o…