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Perturbation Confusion and Referential Transparency: Correct Functional Implementation of Forward-Mode AD

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;
Subjects: Science & Engineering > Computer Science
Item ID: 566
Depositing User: Dr. Barak Pearlmutter
Date Deposited: 15 Jun 2007
Publisher: Springer
Refereed: No
URI:

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