4 citations · 11 across the 15 of their papers we have counts for
15 papers
The Wasserstein--Ebin Metric: A Geometric Lift of Unbalanced Optimal Transport to the space of Riemannian metrics
Martin Bauer, Peter W. Michor, François-Xavier Vialard
We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first co…
Learning Monge maps with constrained drifting models
Théo Dumont, Théo Lacombe, François-Xavier Vialard
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold.…
Gromov-Wasserstein at Scale, Beyond Squared Norms
Guillaume Houry, Jean Feydy, François-Xavier Vialard
A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity cons…
Sliced ReLU attention: Quasi-linear contextual expressivity via sorting
François-Xavier Vialard, Siwan Boufadène
We introduce sliced ReLU attention, a new attention mechanism that departs structurally from both softmax and its approximation alternatives. Instead of applying a nonlinearity to…
Fast Large Deformation Matching with the Energy Distance Kernel
Siwan Boufadene, François-Xavier Vialard, Jean Feydy
We propose an efficient framework for point cloud and measure registration using bi-Lipschitz homeomorphisms, achieving O(n log n) complexity, where n is the number of points. By l…
Entropic Semi-Martingale Optimal Transport
Jean-David Benamou, Guillaume Chazareix, Marc Hoffmann +2
Entropic Optimal Transport (EOT), also referred to as the Schrödinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative en…