A simple differentiable programming language

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear---...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages 2020-01, Vol.4 (POPL), p.1-28
Main Authors: Abadi, Martín, Plotkin, Gordon D.
Format: Article
Language:English
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Summary:Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear---discrepancies can arise, sometimes inadvertently. In order to study automatic differentiation in such programming contexts, we define a small but expressive programming language that includes a construct for reverse-mode differentiation. We give operational and denotational semantics for this language. The operational semantics employs popular implementation techniques, while the denotational semantics employs notions of differentiation familiar from real analysis. We establish that these semantics coincide.
ISSN:2475-1421
2475-1421
DOI:10.1145/3371106