Certification of Directional Derivatives Computed by Automatic Differentiation

Mauricio Araya-Polo Laurent Hascoët (INRIA, BP93, 06902 Sophia-Antipolis, France)

Article in WSEAS Transactions on Circuits and Systems, WSEAS, 2005 (6 pages)

Abstract: Automatic Differentiation (AD) tools assume differentiability of the function implemented by the given program. However, due to switches in the control flow, most programs are only piecewise differentiable. Thereby sometimes the derivatives are wrong. Unfortunately this fact is overlooked by everyday use of AD. There exist extended models of AD that return useful generalized derivatives for some classes of piecewise differentiable functions,but there is little hope of doing so for all cases. In contrast, our goal is to evaluate, along with the derivative, the size of the differentiable neighborhood around the current input. This ``safe neighborhood'' is essential to use the derivatives consistently. We investigate several models to compute this neighborhood and study their complexity. We propose one model of acceptable cost. We present a first implementation and experiments made with our AD tool TAPENADE.

Keywords: Automatic Differentiation, Piecewise Differentiability

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@article{Araya05CoD,
  author = {Araya-Polo, M. and Hasco\"et, L.},
  title = {Certification of Directional Derivatives Computed by Automatic Differentiation},
  journal = {WSEAS Transactions on Circuits and Systems},
  publisher = {WSEAS},
  year = 2005
}