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Higher Order Automatic Differentiation of Higher Order Functions

Logical methods in computer science, 2022-01, Vol.18, Issue 1 [Peer Reviewed Journal]

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Title:
Higher Order Automatic Differentiation of Higher Order Functions
Author: Huot, Mathieu ; Staton, Sam ; Vákár, Matthijs
Subjects: computer science - logic in computer science ; computer science - programming languages
Is Part Of: Logical methods in computer science, 2022-01, Vol.18, Issue 1
Description: 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. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.
Publisher: Logical Methods in Computer Science e.V
Language: English
Identifier: ISSN: 1860-5974
EISSN: 1860-5974
DOI: 10.46298/lmcs-18(1:41)2022
Source: Alma/SFX Local Collection
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