It's rare to see a CS paper, let alone a CS paper with category theory, with 7 authors!
It's fairly mathematical, so I'm going to quote the abstract for some context as to why you might care about this:
The reverse derivative[0] is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure[1] on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.
It's fairly mathematical, so I'm going to quote the abstract for some context as to why you might care about this:
The reverse derivative[0] is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure[1] on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.
[0] This is usually called the reverse mode of differentiation in the automatic differentiation literature: https://en.wikipedia.org/wiki/Automatic_differentiation#The_...
[1] https://ncatlab.org/nlab/show/dagger+category