1 code implementation • 16 Nov 2022 • 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 the learned parameters and predictors.
no code implementations • NeurIPS 2020 • Lenaic Chizat, Pierre Roussillon, Flavien Léger, François-Xavier Vialard, Gabriel Peyré
We also propose and analyze an estimator based on Richardson extrapolation of the Sinkhorn divergence which enjoys improved statistical and computational efficiency guarantees, under a condition on the regularity of the approximation error, which is in particular satisfied for Gaussian densities.
1 code implementation • 11 Feb 2020 • Lenaic Chizat, Francis Bach
Neural networks trained to minimize the logistic (a. k. a.
1 code implementation • 24 Jul 2019 • 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.
1 code implementation • NeurIPS 2019 • 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 training loss, with their parameters hardly varying.
no code implementations • NeurIPS 2018 • Lenaic Chizat, Francis Bach
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure.
3 code implementations • 20 Jul 2016 • Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport.
Optimization and Control 65K10
1 code implementation • 21 Aug 2015 • Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard
These distances are defined by two equivalent alternative formulations: (i) a "fluid dynamic" formulation defining the distance as a geodesic distance over the space of measures (ii) a static "Kantorovich" formulation where the distance is the minimum of an optimization program over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures.
Optimization and Control
1 code implementation • 22 Jun 2015 • Lenaic Chizat, Bernhard Schmitzer, Gabriel Peyré, François-Xavier Vialard
This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses.
Analysis of PDEs