249 citations · 744 across the 13 of their papers we have counts for
16 papers
Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings
Lénaïc Chizat, Alex Delalande, Tomas Vaškevičius
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, , admits a densit…
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations
Lénaïc Chizat, Tomas Vaškevičius
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. P…
On the symmetries in the dynamics of wide two-layer neural networks
Karl Hajjar, Lenaic Chizat
We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on t…
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…
Statistical and Topological Properties of Sliced Probability Divergences
Kimia Nadjahi, Alain Durmus, Lénaïc Chizat +3
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and…
Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss
Lenaic Chizat, Francis Bach
Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towar…
Sparse Optimization on Measures with Over-parameterized Gradient Descent
Lenaic Chizat
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training.…
HexaShrink, an exact scalable framework for hexahedral meshes with attributes and discontinuities: multiresolution rendering and storage of geoscience models
Jean-Luc Peyrot, Laurent Duval, Frédéric Payan +4
With huge data acquisition progresses realized in the past decades and acquisition systems now able to produce high resolution grids and point clouds, the digitization of physical…
On Lazy Training in Differentiable Programming
Lenaic Chizat, Edouard Oyallon, Francis Bach
In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero…
Sample Complexity of Sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach +2
Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn div…
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport
Lenaic Chizat, Francis Bach
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural netw…
Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
Alexis Thibault, Lénaïc Chizat, Charles Dossal +1
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative…
Quantum Optimal Transport for Tensor Field Processing
Gabriel Peyré, Lenaïc Chizat, François-Xavier Vialard +1
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formu…
Scaling Algorithms for Unbalanced Transport Problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only…
Unbalanced Optimal Transport: Dynamic and Kantorovich Formulation
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative…
An Interpolating Distance between Optimal Transport and Fisher-Rao
Lenaic Chizat, Bernhard Schmitzer, Gabriel Peyré +1
This paper defines a new transport metric over the space of non-negative measures. This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and general…