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Perturbation Confusion and Referential Transparency: Correct Functional Implementation of Forward-Mode AD
Siskind, Jeffrey Mark; Pearlmutter, Barak A.
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.
Keyword(s): Computer Science; Perturbation; Referential Transparency; Forward-Mode AD
Publication Date:
2005
Type: Conference item
Peer-Reviewed: No
Contributor(s): Siskind, Jerey Mark; Pearlmutter, Barak A.
Institution: Maynooth University
Citation(s): 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).
Publisher(s): Springer
File Format(s): application/pdf
Related Link(s): http://eprints.maynoothuniversity.ie/566/1/Perturbation.pdf
First Indexed: 2014-09-21 05:16:53 Last Updated: 2018-11-30 06:20:23