Monoidal Reverse Differential Categories

TL;DR

This paper introduces monoidal reverse differential categories, explores their relationship with Cartesian reverse differential categories, and provides examples including models from quantum computation, advancing the categorical understanding of reverse differentiation.

Contribution

It defines monoidal reverse differential categories, establishes their connection to CRDCs, and offers new examples, notably from quantum computation models.

Findings

Monoidal reverse differential categories are formally defined.

Key relationships between monoidal and Cartesian reverse differential categories are established.

Examples from quantum computation models are provided.

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.