Siskind, Jeffrey Mark and Pearlmutter, Barak A. (2008) Nesting forward-mode AD in a functional framework. Higher-Order and Symbolic Computation, 21 (4). pp. 361-376. ISSN 1388-3690

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Abstract

We discuss the augmentation of a functional-programming language with a derivative-taking operator implemented with forward-mode automatic differentiation (AD). The primary technical difficulty in doing so lies in ensuring correctness in the face of nested invocation of that operator, due to the need to distinguish perturbations introduced by distinct invocations. We exhibit a series of implementations of a referentially-transparent forward-mode-AD derivative-taking operator, each of which uses a different non-referentially-transparent mechanism to distinguish perturbations. Even though the forward-mode-AD derivative-taking operator is itself referentially transparent, we hypothesize that one cannot correctly formulate this operator as a function definition in current pure dialects of Haskell.

Item Type:	Article
Additional Information:	Cite as: Siskind, J.M. & Pearlmutter, B.A. Higher-Order Symb Comput (2008) 21: 361. https://doi.org/10.1007/s10990-008-9037-1
Keywords:	Automatic differentiation; Applicative (functional) languages; Referential transparency; Multiple transformation;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	10236
Identification Number:	https://doi.org/10.1007/s10990-008-9037-1
Depositing User:	Barak Pearlmutter
Date Deposited:	21 Nov 2018 15:35
Journal or Publication Title:	Higher-Order and Symbolic Computation
Publisher:	Springer US
Refereed:	Yes
Funders:	National Science Foundation, US (NSF), Science Foundation Ireland (SFI), Higher Education Authority (HEA)
URI:	https://link.springer.com
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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