Jean-Simon Pacaud Lemay

Amar Hadzihasanovic, Jean-Simon Pacaud Lemay

The Eight International Conference on Applied Category Theory took place at the University of Florida on June 2-6 2025. The conference consisted of 2 plenary invited talks, 28 contributed talks, an online community meeting, a general community meeting, and 4 talks by junior researchers who attended the Adjoint School to present the results of their research at the school. Information regarding the conference may be found at https://gataslab.org/act2025/act2025.html. Submission to ACT2025 had three tracks: extended abstracts, software demonstrations, and proceedings. Accepted proceed track submissions are included in this volume. The contributions to ACT2025 ranged from pure to applied and included contributions in a wide range of disciplines. ACT2025 included talks related to computer science, probability theory, chemistry, string diagrams, game semantics, quantum computation, and more.

Aaron Biggin, Jean-Simon Pacaud Lemay

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 Faa 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.