Work

Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories

Year: 2025

Type: article

Abstract: Reverse differentiation is an essential operation for automatic differentiation.Cartesian reverse differential categories axiomatize reverse differentiation in a categorical framework, where one of the primary axioms is the reverse chain rule, which is the formula that expresses the reverse derivative of a composition.Here, we present the reverse differential analogue of Faà di Bruno's Formula, which gives a higher-order reverse chain rule in a Cartesian reverse differential category.To properly do so, we also define partial reverse derivatives and higher-order reverse derivatives in a Cartesian reverse differential category.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.429.6

Authors: Aaron Biggin, Jean-Simon Pacaud Lemay

Institution: Macquarie University

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Macquarie University, Australian Research Council, Air Force Office of Scientific Research

Awards: G1523888516, G3262544604, New Foundations for Algebraic Geometry