@inproceedings{bfc6e62698ba4979a2e7e268fd02ddde,
title = "Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing",
abstract = "We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.",
author = "Mathieu Huot and Sam Staton and Matthijs V{\'a}k{\'a}r",
year = "2020",
month = apr,
day = "17",
doi = "10.1007/978-3-030-45231-5_17",
language = "English",
isbn = "978-3-030-45230-8",
volume = "12077",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "319--338",
editor = "Jean Goubault-Larrecq and Barbara K{\"o}nig",
booktitle = "Foundations of Software Science and Computation Structures - 23rd International Conference, FOSSACS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25-30, 2020, Proceedings",
}