18 citations · 35 across the 7 of their papers we have counts for
7 papers
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 differenti…
Categorical Foundations of Gradient-Based Learning
G. S. H. Cruttwell, Bruno Gavranović, Neil Ghani +2
We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides…
Differential equations in a tangent category I: Complete vector fields, flows, and exponentials
J. R. B. Cockett, G. S. H. Cruttwell, J. -S. P. Lemay
This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differ…
Connections in Tangent Categories
J. R. B. Cockett, G. S. H. Cruttwell
Connections are an important tool of differential geometry. This paper investigates their definition and structure in the abstract setting of tangent categories. At this level of a…
A simplicial foundation for differential and sector forms in tangent categories
G. S. H. Cruttwell, Rory B. B. Lucyshyn-Wright
Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abs…
Differential bundles and fibrations for tangent categories
J. R. B. Cockett, G. S. H. Cruttwell
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the c…
A unified framework for generalized multicategories
G. S. H. Cruttwell, Michael A. Shulman
Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular oper…