Provably correct, asymptotically efficient, higher-order reverse-mode automatic differentiation

Author:

Krawiec Faustyna1ORCID,Peyton Jones Simon2ORCID,Krishnaswami Neel1ORCID,Ellis Tom2ORCID,Eisenberg Richard A.3ORCID,Fitzgibbon Andrew2ORCID

Affiliation:

1. University of Cambridge, UK

2. Microsoft Research, UK

3. Tweag, France

Abstract

In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

Publisher

Association for Computing Machinery (ACM)

Subject

Safety, Risk, Reliability and Quality,Software

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