Categorical semantics of a simple differential programming language

Geoffrey Cruttwell
Jonathan Gallagher
Dorette Pronk

With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support for this types of structure. One approach, due to Abadi and Plotkin, provides a simple differential programming language. Another approach is the notion of a reverse differential category. In the present paper we bring these two approaches together. In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's language, and describe how this categorical model allows one to consider potential improvements to the operational semantics of the language.

In David I. Spivak and Jamie Vicary: Proceedings of the 3rd Annual International Applied Category Theory Conference 2020 (ACT 2020), Cambridge, USA, 6-10th July 2020, Electronic Proceedings in Theoretical Computer Science 333, pp. 289–310.
Published: 8th February 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.333.20 bibtex PDF

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