research
∙
06/30/2023
Abide by the Law and Follow the Flow: Conservation Laws for Gradient Flows
Understanding the geometric properties of gradient descent dynamics is a...
share
research
∙
02/02/2023
Fast, Differentiable and Sparse Top-k: a Convex Analysis Perspective
The top-k operator returns a k-sparse vector, where the non-zero values ...
research
∙
11/16/2022
Unbalanced Optimal Transport, from Theory to Numerics
Optimal Transport (OT) has recently emerged as a central tool in data sc...
research
∙
05/29/2022
Do Residual Neural Networks discretize Neural Ordinary Differential Equations?
Neural Ordinary Differential Equations (Neural ODEs) are the continuous ...
research
∙
05/03/2022
Smooth over-parameterized solvers for non-smooth structured optimization
Non-smooth optimization is a core ingredient of many imaging or machine ...
research
∙
01/03/2022
Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe
Unbalanced optimal transport (UOT) extends optimal transport (OT) to tak...
research
∙
12/10/2021
Global convergence of ResNets: From finite to infinite width using linear parameterization
Overparametrization is a key factor in the absence of convexity to expla...
research
∙
11/25/2021
Randomized Stochastic Gradient Descent Ascent
An increasing number of machine learning problems, such as robust or adv...
research
∙
10/22/2021
Sinkformers: Transformers with Doubly Stochastic Attention
Attention based models such as Transformers involve pairwise interaction...
research
∙
06/02/2021
Smooth Bilevel Programming for Sparse Regularization
Iteratively reweighted least square (IRLS) is a popular approach to solv...
research
∙
06/02/2021
Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs
The ability to compare and align related datasets living in heterogeneou...
research
∙
03/08/2021
Low-Rank Sinkhorn Factorization
Several recent applications of optimal transport (OT) theory to machine ...
research
∙
02/15/2021
Momentum Residual Neural Networks
The training of deep residual neural networks (ResNets) with backpropaga...
research
∙
02/15/2021
Fast and accurate optimization on the orthogonal manifold without retraction
We consider the problem of minimizing a function over the manifold of or...
research
∙
02/11/2021
Unsupervised Ground Metric Learning using Wasserstein Eigenvectors
Optimal Transport (OT) defines geometrically meaningful "Wasserstein" di...
research
∙
09/09/2020
The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
Comparing metric measure spaces (i.e. a metric space endowed with a prob...
research
∙
06/24/2020
Distribution-Based Invariant Deep Networks for Learning Meta-Features
Recent advances in deep learning from probability distributions enable t...
research
∙
06/15/2020
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
The squared Wasserstein distance is a natural quantity to compare probab...
research
∙
03/03/2020
Online Sinkhorn: optimal transportation distances from sample streams
Optimal Transport (OT) distances are now routinely used as loss function...
research
∙
02/11/2020
Wasserstein Control of Mirror Langevin Monte Carlo
Discretized Langevin diffusions are efficient Monte Carlo methods for sa...
research
∙
02/10/2020
Super-efficiency of automatic differentiation for functions defined as a minimum
In min-min optimization or max-min optimization, one has to compute the ...
research
∙
11/08/2019
Degrees of freedom for off-the-grid sparse estimation
A central question in modern machine learning and imaging sciences is to...
research
∙
11/08/2019
Ground Metric Learning on Graphs
Optimal transport (OT) distances between probability distributions are p...
research
∙
10/28/2019
Sinkhorn Divergences for Unbalanced Optimal Transport
This paper extends the formulation of Sinkhorn divergences to the unbala...
research
∙
05/15/2019
Geometric Losses for Distributional Learning
Building upon recent advances in entropy-regularized optimal transport, ...
research
∙
05/13/2019
Universal Invariant and Equivariant Graph Neural Networks
Graph Neural Networks (GNN) come in many flavors, but should always be e...
research
∙
11/19/2018
Stochastic Deep Networks
Machine learning is increasingly targeting areas where input data cannot...
research
∙
11/13/2018
Semi-dual Regularized Optimal Transport
Variational problems that involve Wasserstein distances and more general...
research
∙
10/18/2018
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
Comparing probability distributions is a fundamental problem in data sci...
research
∙
10/08/2018
Support Localization and the Fisher Metric for off-the-grid Sparse Regularization
Sparse regularization is a central technique for both machine learning (...
research
∙
10/05/2018
Sample Complexity of Sinkhorn divergences
Optimal transport (OT) and maximum mean discrepancies (MMD) are now rout...
research
∙
03/01/2018
Computational Optimal Transport
Optimal Transport (OT) is a mathematical gem at the interface between pr...
research
∙
02/23/2018
A Dual Certificates Analysis of Compressive Off-the-Grid Recovery
Many problems in machine learning and imaging can be framed as an infini...
research
∙
12/23/2017
A Low-Rank Approach to Off-The-Grid Sparse Deconvolution
We propose a new solver for the sparse spikes deconvolution problem over...
research
∙
08/07/2017
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning
This article introduces a new non-linear dictionary learning method for ...
research
∙
07/11/2017
Sensitivity Analysis for Mirror-Stratifiable Convex Functions
This paper provides a set of sensitivity analysis and activity identific...
research
∙
06/06/2017
GAN and VAE from an Optimal Transport Point of View
This short article revisits some of the ideas introduced in arXiv:1701.0...
research
∙
06/01/2017
Learning Generative Models with Sinkhorn Divergences
The ability to compare two degenerate probability distributions (i.e. tw...
research
∙
12/20/2016
Quantum Optimal Transport for Tensor Field Processing
This article introduces a new notion of optimal transport (OT) between t...
research
∙
11/02/2016
Bayesian Modeling of Motion Perception using Dynamical Stochastic Textures
A common practice to account for psychophysical biases in vision is to f...
research
∙
11/09/2015
Biologically Inspired Dynamic Textures for Probing Motion Perception
Perception is often described as a predictive process based on an optima...
research
∙
03/30/2015
Fast Optimal Transport Averaging of Neuroimaging Data
Knowing how the Human brain is anatomically and functionally organized a...
research
∙
03/09/2015
A Smoothed Dual Approach for Variational Wasserstein Problems
Variational problems that involve Wasserstein distances have been recent...
research
∙
07/07/2014
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemp...
research
∙
05/05/2014
Model Consistency of Partly Smooth Regularizers
This paper studies least-square regression penalized with partly smooth ...
research
∙
07/21/2013
Regularized Discrete Optimal Transport
This article introduces a generalization of the discrete optimal transpo...
research
∙
05/07/2012
Risk estimation for matrix recovery with spectral regularization
In this paper, we develop an approach to recursively estimate the quadra...
research
∙
01/27/2011