Le jeudi 30 mai de 15h00 à 16h00, en salle M7-315 (au 3ème étage) de l’ENS de Lyon, nous aurons le plaisir d’écouter, dans le cadre des séminaires de la Fédération Informatique de Lyon (FIL), Laurent Feuilloley (CR CNRS, LIRIS) et Michele Pagani  (PR ENSL, LIP). Vous trouverez titres et résumés de leurs présentations ci-dessous.

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Laurent Feuilloley
Title: Local certification: distributed computing lenses on graph theory
Abstract:
Graphs are a classic mathematical objects to represent networks (communication networks, social networks etc.). A large fraction of the research in graph theory is about graph classes (e.g. planar graphs): how to characterize/decompose/recognize these. In this talk I will introduce local certification, a notion originating from distributed computing, which gives a new point of view on graph classes, that I have been studying for some time. In a nutshell, the graph is seen as a network, and the nodes want to check collectively whether the network belongs to a given class, with some external help.

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Michele Pagani
Titre: Applying Programming Language Theory to Automatic Differentiation
Abstract:
Automatic Differentiation (AD) transforms a numerical program into one computing the gradient of the function computed by the program: in many implementations this transformation is defined on the top of a kind of execution-flow graph called computational graph. It is a fundamental tool in several fields, most notably machine learning, where it is the key for efficiently training (deep) neural networks.

We study the correctness of AD in the context of a higher-order, Turing-complete programming language, both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive functions included in the language, AD is almost everywhere correct, that is, it computes the derivative or gradient of the program under consideration except for a set of Lebesgue measure zero. Stated otherwise, there are inputs on which AD is incorrect, but the probability of randomly choosing one such input is zero.