Éric Colin de Verdière

30 posts

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; 22,000 participants).

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.

Meeting of the Scientific Board

January 10, 2020 — The scientific board of the Bézout Labex will be gathered for a one-day meeting, with an extensive presentation of the Labex and scientific talks.  This event will take place from 9:30am to 6pm in the Copernic building (RER A stop “Noisy-Champs”, exit at the head of the train from Paris and to the right, then walk 10 minutes); see the access map.

Members

The members of the scientific board are:

(Probably final) program

This meeting will take place in the Copernic building, in room 0B120 (at street level, close to the elevators), except for the events marked with a star, which will take place on the 4th floor (room 4B107, or in the common areas for the lunch).

09:30 for the scientific board members only: welcome coffee (*)
10:00 presentation of the Labex, past and present (Éric Colin de Verdière)
10:40 research area 1 “images and geometry” (Alfredo Hubard, Yukiko Kenmochi)
11:05 research area 2 “discrete mathematics and algorithms” (Matthieu Fradelizi)
11:30 break
11:50 research area 3 “stochastic and deterministic models” (Étienne Sandier)
12:15 research area 4 “high-dimensional phenomena” (Jamal Najim)
12:40 lunch (*) (registration is closed)
14:00 research area 5 “smart cities” (Laurent Hauswirth, Rami Langar)
14:25 scientific talk 1 (Arnaud de Mesmay: “From Riemannian geometry to graph theory and back”)
14:55 scientific talk 2 (Pierre-André Zitt: “Understanding a self-repelling Monte Carlo algorithm”)
15:25 the future of the Labex (Éric Colin de Verdière)
15:45 break internal to the scientific board members (*)
16:05 discussion with the persons in charge of the master’s programs (*)
16:30 discussion with the direction of the Labex and the three laboratories (*)
17:15 internal discussion of the scientific board (*)
18:00 the end

Professor János Pach, Bézout chair

October 2019: We are delighted to announce that János Pach has been awarded the Bézout chair! He will visit the Bézout Labex, hosted by Frédéric Meunier (CERMICS) and Nabil Mustafa (LIGM), between October 15, 2019 and November 15, 2019, and also for two months in 2020.

His Bézout lecture will be jointly organized with CERMICS’ Colloquium and take place on November 12 at 2pm in the seminar room of CERMICS (Cité Descartes, Coriolis building, left aisle, 2nd floor). See below for a title and abstract.

Professor Pach is currently affiliated with the Renyi Institute Budapest and MIPT Moscow. He has received many distinctions in his research carrier, including membership at the Hungarian Academy of Sciences. He is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.

Title: How to escape the curse of dimensionality in combinatorics
Abstract: According to Gelfand, “at the bottom of most deep mathematical questions there is a combinatorial problem.” Combinatorics, once viewed as “the slums of topology,” has come a long way during the past century. It has its own powerful techniques and close ties to algebra, topology, information theory, and several other disciplines. Nevertheless, many basic combinatorial problems, including ones needed for applications, are wide open, partially due to a phenomenon called “combinatorial explosion” or the “curse of dimension.” In this talk, we will illustrate how to solve some notoriously difficult open problems by restricting our attention to certain combinatorial structures arising in geometric, algebraic, and practical applications. The talk will be entirely self-contained, and no previous knowledge of the subject will be assumed.

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.

Meeting of the Bézout Labex

December 4, 2018: A one-day meeting of the Bézout Labex is organized on the site of Marne-la-Vallée. It will be the opportunity to:

  • briefly present the past and future actions in the Labex, at the occasion of the change of head of the Labex (still to be confirmed by ANR),
  • welcome three new members of the research units of the Bézout Labex: Claire Lacour, Yohann De Castro, and François-Xavier Vialard, who will all give a talk,
  • see an overview of ongoing research from the research areas of the Labex.

How to come

The meeting will take place in the auditorium of bibliothèque Georges Perec:

Program

10:30 Philippe Loubaton and Éric Colin de Verdière (introduction)
10:50 François-Xavier Vialard (slides)
11:35 Olivier Guédon (high-dimensional phenomena)
11:50 Renaud Marlet (smart cities)
12:05 lunch (registration is closed)
13:45 Claire Lacour (slides)
14:30 François Bouchut, Bernard Lapeyre, Béatrice de Tilière (deterministic and stochastic models) – (slides)
14:45 Frédéric Meunier (slides)
15:00 Stéphane Sabourau (images and geometry) – (slides)
15:15 break
15:45 Yohann De Castro (see below) – (slides)
16:30 the end

Abstracts

(Most talks are likely to be in French.)

François-Xavier Vialard (LIGM): An overview of unbalanced optimal transport: theory and applications

In this talk, we present an equivalent of the L2 Wasserstein metric to the space of positive Radon measures. After the presentation of standard optimal transport, static and dynamic formulations, we introduce the new model and show the corresponding static and dynamic formulations. Then, we briefly present the link with a fluid dynamic model and show applications in medical imaging. Last, we present a new similarity between measures, based on regularized optimal transport.

Claire Lacour (LAMA): Méthode de comparaison pénalisée pour la sélection d’estimateurs

En statistiques ou en apprentissage, il est courant que les prédicteurs ou les estimateurs dépendent d’un paramètre à ajuster au mieux par l’utilisateur. Par exemple, on cherche à retrouver la distribution des données, et on fournit une densité approchée avec un paramètre de lissage. Ou encore, on produit une classification des données, mais qui dépend du nombre de classes voulues.

On présentera dans cet exposé une nouvelle méthode de sélection d’estimateurs, qui utilise une comparaison pénalisée à l’estimateur de surapprentissage. On présentera des résultats théoriques dans le cas de l’estimation de densité par noyau, ainsi que des simulations numériques.

Yohann De Castro (CERMICS): On Representer Theorems and Convex Regularization

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of « atoms ». These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem.