Christophe Vauthier

collaborators

3 papers

math.OC2025

Variational Analysis in the Wasserstein Hierarchy

Christophe Vauthier

Let $M$ be a complete connected Riemannian manifold. For $n \geq 0$ , we endow the Wasserstein space $P_{2}^{(n)} (M) = P_{2} (\dots P_{2} (M) \dots)$ , equipped with the Wasserstein distanc…

cs.LG2025

Flowing Datasets with Wasserstein over Wasserstein Gradient Flows

Clément Bonet, Christophe Vauthier, Anna Korba

Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable grad…

stat.ML2025

Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis

Christophe Vauthier, Anna Korba, Quentin Mérigot

In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the…