Siskind, Jeffrey Mark and Pearlmutter, Barak A. (2005) Perturbation Confusion and Referential Transparency: Correct Functional Implementation of Forward-Mode AD. In: 17th International Workshop, IFL'05 (2005).

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Abstract

It is tempting to incorporate dierentiation operators into functional-programming languages. Making them rst-class citizens, however, is an enterprise fraught with danger. We discuss a potential problem with forward-mode AD common to many AD systems, including all attempts to integrate a forward-mode AD operator into Haskell. In particular, we show how these implementations fail to preserve referential transparency, and can compute grossly incorrect results when the dierentiation operator is applied to a function that itself uses that operator. The underlying cause of this problem is perturbation confusion, a failure to distinguish between distinct perturbations introduced by distinct invocations of the dierentiation operator. We then discuss how perturbation confusion can be avoided.

Item Type:	Conference or Workshop Item (Other)
Keywords:	Perturbation; Referential Transparency; Forward-Mode AD;
Academic Unit:	Faculty of Science and Engineering > Computer Science
Item ID:	566
Depositing User:	Barak Pearlmutter
Date Deposited:	15 Jun 2007
Publisher:	Springer
Refereed:	No
URI:	http://www.springer.com/uk/home?searchKe...
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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