Publications

Mathematics

Convergence rates and approximation results for SGD and its continuous-time counterpart

This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous Stochastic…

Xavier Fontaine, Valentin de Bortoli, Alain Durmus

Mathematics

Polynomial approximations in a generalized Nyman–Beurling criterion

François Alouges, Sébastien Darses, Erwan Hillion

Journal de Théorie des Nombres de Bordeaux - 2023

Machine Learning

Barycentric embeddings for geometric manifold learning

An MRI image has over 60,000 pixels. The largest known human protein consists of around 30,000 amino acids. We call such data high-dimensional. In practice, most high-dimensional data is high-dimensional only artificially. For example, of all the…

Elodie Maignant

Santé publique et épidémiologie

RADIO-AIDE : une modélisation spatio-temporelle des effets secondaires cognitifs observés dans les suites de la radiothérapie cérébrale

Introduction et but de l’étude La radiothérapie est un traitement majeur des tumeurs du système nerveux central. L’altération des fonctions cognitives, fréquemment observée dans les suites d’une radiothérapie cérébrale, peut être en rapport avec la…

Julian Jacob, Sarah Amrani Joutei, Monica Ribeiro, Georges Noël, Florence Forbes, Michel Dojat, Marie-Odile Bernier, Cecilia Damon, Alan Tucholka, Catherine Jenny, Alice Bressand, Philippe Maingon, Lucia Nichelli, Nadya Pyatigorskaya, Alice Thomas-Joulié, Dimitri Psimaras, Khe Hoang-Xuan, Cyrus Chargari, Jean-Marc Simon, Sophie Ancelet, Damien Ricard

34ème congrès de la SFRO - 2023

Neural and Evolutionary Computing

An in-depth study of the deep learning pipeline

Despite the tremendous success of neural networks in many applications, progress in understanding their performance and limits is slow. While universal approximation theorems bring the promise of machines capable of approximating any complex mapping…

Adrien Courtois

Mathematics

Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics

This paper is motivated by the study of Lyapunov functionals for four equations describing free surface flows in fluid dynamics: the Hele-Shaw and Mullins-Sekerka equations together with their lubrication approximations, the Boussinesq and thin-film…

Thomas Alazard, Didier Bresch

Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications - 2023

Mathematics

Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension

We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The model…

Thomas Alazard, Martina Magliocca, Nicolas Meunier

Physics

Localization landscape for interacting Bose gases in one-dimensional speckle potentials

While the properties and the shape of the ground state of a gas of ultracold bosons are well understood in harmonic potentials, they remain for a large part unknown in the case of random potentials. Here we use localization-landscape (LL) theory to…

Filippo Stellin, Marcel Filoche, Frédéric Dias

Physical Review A - 2023

Statistics

On quantitative Laplace-type convergence results for some exponential probability measures, with two applications

Laplace-type results characterize the limit of sequence of measures $(\pi_\varepsilon)_{\varepsilon >0}$ with density w.r.t the Lebesgue measure $(\mathrm{d} \pi_\varepsilon / \mathrm{d} \mathrm{Leb})(x) \propto \exp[-U(x)/\varepsilon]$ when the…

Valentin de Bortoli, Agnès Desolneux

Life Sciences

Innovative multidimensional gait evaluation using IMU in multiple sclerosis: introducing the semiogram

Background Quantifying gait using inertial measurement units has gained increasing interest in recent years. Highly degraded gaits, especially in neurological impaired patients, challenge gait detection algorithms and require specific segmentation…

Cyril Voisard, Nicolas de l'Escalopier, Aliénor Vienne-Jumeau, Albane Moreau, Flavien Quijoux, Flavie Bompaire, Magali Sallansonnet, Marie-Laure Brechemier, Irina Taifas, Camille Tafani, Eve Drouard, Nicolas Vayatis, Damien Ricard, Laurent Oudre

Frontiers in Neurology - 2023