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NeurIPS paper+talk: A Shooting Formulation of Deep Learning

Oct. 2020: The visit of Marc Niethammer in 2019 led to a result, obtained jointly with François-Xavier Vialard (LIGM, Bézout Labex) and other colleagues, to be presented at NeurIPS 2020 as an oral (top 1.1% of submissions).

Deep learning usually has a large number of layers and thus a large number of parameters, which are optimized for the given learning task. Questions raised in this work are: Is it possible to parametrize deep neural network with much less parameters, and to control the complexity of the resulting deep neural network maps ? This work leverages optimal control ideas to answer positively to both questions. The authors use a regularization on the parameters and by optimizing only on the “optimal paths” in the parameter space, they are able to parametrize the network using only “initial conditions” and the complexity of the map is controlled explicitly in terms of these initial conditions. They show promising experiments. This work may open up a new fertile area of research in deep learning parametrization.

ANR Project MinMax accepted

ANR (the French National Research Agency) will support the ANR project “MinMax” on min-max constructions, waist estimates, and related aspects in geometry and topology, minimal surface theory and geometric analysis, and computational geometry and algorithms. The project is led by Stéphane Sabourau (LAMA) and will involve members from LAMA, LIGM, as well as participants from Montpellier, Nancy, Grenoble, and Tours. It fits within the Images and Geometry research area of the Labex, and many aspects of the project have been discussed in the Labex working group Min-max theory and computational geometry.

Course “Discrete topology and geometry and applications”

May-June 2018: A course “Discrete topology and geometry and applications” is starting. It is aimed at a broad audience, so everyone’s welcome!

The course will cover some discrete theorems in topology (Sperner and Tucker) and geometry (Helly and Carathéodory) as well as several of their applications.

We will illustrate how these theorems offer elementary gateways to a diversity of results in game theory and fair division, in graph theory, in optimization and in geometric data analysis. We will start assuming only a general background in mathematics (continuity, vector spaces, etc.).

The course consists in six 2h lectures, one per week, it will start on Thursday, 24th of May, 2018 to end of June. Lectures will take place on Thursdays from 10am to noon, in the Coriolis building on the Descartes site.

All details can be found on the course webpage: http://monge.univ-mlv.fr/~goaoc/tgda2018.html

Everyone’s welcome!