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07/25/2023
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations
We study the computation of doubly regularized Wasserstein barycenters, ...
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05/26/2023
Local Convergence of Gradient Methods for Min-Max Games under Partial Curvature
We study the convergence to local Nash equilibria of gradient methods fo...
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03/31/2023
On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks
In supervised learning, the regularization path is sometimes used as a c...
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03/21/2023
Doubly Regularized Entropic Wasserstein Barycenters
We study a general formulation of regularized Wasserstein barycenters th...
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11/29/2022
Infinite-width limit of deep linear neural networks
This paper studies the infinite-width limit of deep linear neural networ...
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11/16/2022
On the symmetries in the dynamics of wide two-layer neural networks
We consider the idealized setting of gradient flow on the population ris...
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11/02/2022
An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Games
We consider the problem of computing mixed Nash equilibria of two-player...
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05/14/2022
Trajectory Inference via Mean-field Langevin in Path Space
Trajectory inference aims at recovering the dynamics of a population fro...
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10/29/2021
Training Integrable Parameterizations of Deep Neural Networks in the Infinite-Width Limit
To theoretically understand the behavior of trained deep neural networks...
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10/15/2021
Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization
Many supervised machine learning methods are naturally cast as optimizat...
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06/15/2020
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
The squared Wasserstein distance is a natural quantity to compare probab...
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03/12/2020
Statistical and Topological Properties of Sliced Probability Divergences
The idea of slicing divergences has been proven to be successful when co...
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02/11/2020
Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss
Neural networks trained to minimize the logistic (a.k.a. cross-entropy) ...
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07/24/2019
Sparse Optimization on Measures with Over-parameterized Gradient Descent
Minimizing a convex function of a measure with a sparsity-inducing penal...
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03/16/2019
HexaShrink, an exact scalable framework for hexahedral meshes with attributes and discontinuities: multiresolution rendering and storage of geoscience models
With huge data acquisition progresses realized in the past decades and a...
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12/19/2018
A Note on Lazy Training in Supervised Differentiable Programming
In a series of recent theoretical works, it has been shown that strongly...
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10/05/2018
Sample Complexity of Sinkhorn divergences
Optimal transport (OT) and maximum mean discrepancies (MMD) are now rout...
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05/24/2018
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport
Many tasks in machine learning and signal processing can be solved by mi...
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12/20/2016