2 papers
math.CT2024
A Fibrational Theory of First Order Differential Structures
Matteo Capucci, Geoffrey S. H. Cruttwell, Neil Ghani +1
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of…
cs.LG2024
Deep Learning with Parametric Lenses
Geoffrey S. H. Cruttwell, Bruno Gavranovic, Neil Ghani +2
We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful expla…