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    Using programming language theory to make automatic differentiation sound and efficient

    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

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    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
      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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