文章基本信息

标题：HIGHER ORDER AUTOMATIC DIFFERENTIATION OF HIGHER ORDER FUNCTIONS
本地全文：下载
作者：Mathieu Huot ; Sam Staton ; Matthijs Vákár 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2022
卷号：18
期号：1
页码：1-34
DOI：10.46298/lmcs-18(1:41)2022
语种：English
出版社：Technical University of Braunschweig
摘要：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.
关键词：automatic differentiation;software correctness;denotational semantics