Project : tropics

Section: New Results

Keywords : discontinuities, validity of derivatives.

Automatic estimation of the validity domain of derivatives

Participants : Mauricio Araya-Polo, Laurent Hascoët.

Automatic Differentiation gives analytical derivatives, e.g. gradients, based on local properties of the function at the given input point. These derivatives are then used to extrapolate the behavior of the function around this point. Since the analysis is local, these derivatives do not take into account discontinuities that may occur in the neighborhood of the current point. These discontinuities basically correspond to conditionals in the source program.

At the end of last year research, we proposed an algorithm to evaluate the size of the neighborhood around the current point, in which the function remains differentiable. This algorithm is very expensive. We proposed and implemented a limited algorithm that evaluates this size only in one dimension, which could be the descent direction in gradient-based optimization.

This year we made further experiments on larger applications. Mauricio Araya presented his results at the French-Latin American congress on Applied Mathematics in Santiago, Chile [20]. He made a deeper presentation at the WSEAS'05 conference in Cancún, Mexico. We are pleased to highlight that he won the best student paper award. His presentation was then made an article in the ``WSEAS transactions on circuits and systems'' journal [12].

Mauricio Araya's algorithm is now implemented as a standard differentiation mode in tapenade version 2.1.