Pearlmutter, Barak A. and Siskind, Jeffrey Mark (2008) Using programming language theory to make automatic differentiation sound and efficient. Advances in Automatic Differentiation. ISSN 1439-7358

Download (92kB)

Abstract

This paper discusses a new Automatic Differentiation (AD) system that correctly and automatically accepts nested and dynamic use of the AD operators, without any manual intervention. The system is based on a new formulation of AD as highly generalized firstclass citizens in a λ- calculus, which is briefly described. Because the λ-calculus is the basis for modern programming-language implementation techniques, integration of AD into the λ-calculus allows AD to be integrated into an aggressive compiler. We exhibit a research compiler which does this integration. Using novel analysis techniques, it accepts source code involving free use of a first-class forward AD operator and generates object code which attains numerical performance comparable to, or better than, the most aggressive existing AD systems.

Item Type:	Article
Keywords:	Nesting; Lambda calculus; Multiple transformation; Forward mode; optimization; Hamilton Institute.
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	1730
Depositing User:	Hamilton Editor
Date Deposited:	10 Dec 2009 15:11
Journal or Publication Title:	Advances in Automatic Differentiation
Publisher:	Springer
Refereed:	Yes
URI:
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

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads