113 citations · 638 across the 37 of their papers we have counts for
47 papers
A Unified Dual Method for Matching Problems
Guillaume Houry, Ferdinand Genans, Jean Feydy +1
Matching problems are ubiquitous in data science as they enable the alignment of structured objects and distributions. While existing solvers are often tailored to specific matchin…
Gauss-Newton drifting extends natural gradient descent
Théo Dumont, Théo Lacombe, François-Xavier Vialard
Drifting methods have recently been introduced as a promising new paradigm for training generative models, and have attracted a lot of attention so far. In this work, we focus on h…
Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport
Ferdinand Genans, Antoine Godichon-Baggioni, François-Xavier Vialard +1
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a…
Stochastic Optimization in Semi-Discrete Optimal Transport: Convergence Analysis and Minimax Rate
Ferdinand Genans, Antoine Godichon-Baggioni, François-Xavier Vialard +1
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure is transported to a discrete target measure , with particular attention to…
Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regime
Raphaël Barboni, Gabriel Peyré, François-Xavier Vialard
We study the convergence of gradient methods for the training of mean-field single-hidden-layer neural networks with square loss. For this high-dimensional and non-convex optimizat…
Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
Flavien Léger, Gabriele Todeschi, François-Xavier Vialard
Nonnegative cross-curvature (NNCC) is a geometric property of a cost function defined on a product space that originates in optimal transportation and the Ma-Trudinger-Wang theory.…
multiGradICON: A Foundation Model for Multimodal Medical Image Registration
Basar Demir, Lin Tian, Thomas Hastings Greer +7
Modern medical image registration approaches predict deformations using deep networks. These approaches achieve state-of-the-art (SOTA) registration accuracy and are generally fast…
CARL: A Framework for Equivariant Image Registration
Hastings Greer, Lin Tian, Francois-Xavier Vialard +3
Image registration estimates spatial correspondences between a pair of images. These estimates are typically obtained via numerical optimization or regression by a deep network. A…
uniGradICON: A Foundation Model for Medical Image Registration
Lin Tian, Hastings Greer, Roland Kwitt +5
Conventional medical image registration approaches directly optimize over the parameters of a transformation model. These approaches have been highly successful and are used generi…
Understanding the training of infinitely deep and wide ResNets with Conditional Optimal Transport
Raphaël Barboni, Gabriel Peyré, François-Xavier Vialard
We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training con…
Inverse Consistency by Construction for Multistep Deep Registration
Hastings Greer, Lin Tian, Francois-Xavier Vialard +5
Inverse consistency is a desirable property for image registration. We propose a simple technique to make a neural registration network inverse consistent by construction, as a con…
A geometric Laplace method
Flavien Léger, François-Xavier Vialard
A classical tool for approximating integrals is the Laplace method. The first-order, as well as the higher-order Laplace formula is most often written in coordinates without any ge…
Unbalanced Optimal Transport, from Theory to Numerics
Thibault Séjourné, Gabriel Peyré, François-Xavier Vialard
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions.…
On the existence of Monge maps for the Gromov-Wasserstein problem
Théo Dumont, Théo Lacombe, François-Xavier Vialard
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipp…
Toric Geometry of Entropic Regularization
Bernd Sturmfels, Simon Telen, François-Xavier Vialard +1
Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at th…
Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe
Thibault Séjourné, François-Xavier Vialard, Gabriel Peyré
Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applica…
Parameter tuning and model selection in optimal transport with semi-dual Brenier formulation
Adrien Vacher, François-Xavier Vialard
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples a…
Global convergence of ResNets: From finite to infinite width using linear parameterization
Raphaël Barboni, Gabriel Peyré, François-Xavier Vialard
Overparametrization is a key factor in the absence of convexity to explain global convergence of gradient descent (GD) for neural networks. Beside the well studied lazy regime, inf…
ICON: Learning Regular Maps Through Inverse Consistency
Hastings Greer, Roland Kwitt, Francois-Xavier Vialard +1
Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformat…
A Dimension-free Computational Upper-bound for Smooth Optimal Transport Estimation
Adrien Vacher, Boris Muzellec, Alessandro Rudi +2
It is well-known that plug-in statistical estimation of optimal transport suffers from the curse of dimensionality. Despite recent efforts to improve the rate of estimation with th…
The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
Thibault Séjourné, François-Xavier Vialard, Gabriel Peyré
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between su…
A Shooting Formulation of Deep Learning
François-Xavier Vialard, Roland Kwitt, Susan Wei +1
Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Altho…
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
Lenaic Chizat, Pierre Roussillon, Flavien Léger +2
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimat…
Sinkhorn Divergences for Unbalanced Optimal Transport
Thibault Séjourné, Jean Feydy, François-Xavier Vialard +2
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the…