Monoidal reverse differential categories

Geoff S. H. Cruttwell, Jonathan Gallagher, Jean-Simon Pacaud Lemay, Dorette Pronk

Abstract: Cartesian reverse differential categories (CRDCs) are a recently defined structure which categorically model the reverse differentiation operations used in supervised learning. Here, we define a related structure called a monoidal reverse differential category, prove important results about its relationship to CRDCs, and provide examples of both structures, including examples coming from models of quantum computation.