Seminar

A mathematical model for nonsmooth algorithmic differentiation with applications to machine learning.

Edouard Pauwels (IRIT, Université Toulouse 3 Paul Sabatier,)

September 24, 2020, 11:00–12:15

Toulouse

Room Auditorium 5 (2°floor)

MAD-Stat. Seminar

Abstract

We are interested in nonsmooth analysis of algorithmic differentiation, a central building block of the learning phase implemented in modern deep learning software librairies, such as Tensorflow or Pytorch. First I will illustrate how blind application of differential calculus to nonsmooth objects can be problematic, requiring a proper mathematical model. Then I will introduce a weak notion of generalized derivative, named conservativity, and illustrate how it complies with calculus and optimization for well structured objects. We provide stability results for empirical risk minimization similar as in the smooth setting for the combination of nonsmooth automatic differentiation, minibatch stochastic approximation and first order optimization. This is joint work with Jérôme Bolte. References: Bolte, J., Pauwels, E. (2020). Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning. Math. Program. Bolte, J., & Pauwels, E. (2020). A mathematical model for automatic differentiation in machine learning. arXiv preprint arXiv:2006.02080.