8 papers
Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge
Titouan Vayer
These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard t…
Path-conditioned training: a principled way to rescale ReLU neural networks
Arthur Lebeurrier, Titouan Vayer, Rémi Gribonval
Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters. While two properly rescal…
On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport plans
Titouan Vayer
This note gives a self-contained overview of some important properties of the Gromov-Wasserstein (GW) distance, compared with the standard linear optimal transport (OT) framework.…
Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Pierre Houedry, Nicolas Courty, Florestan Martin-Baillon +2
Trees and the associated shortest-path tree metrics provide a powerful framework for representing hierarchical and combinatorial structures in data. Given an arbitrary metric space…
Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein
Hugues Van Assel, Cédric Vincent-Cuaz, Nicolas Courty +3
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR)…
PASCO (PArallel Structured COarsening): an overlay to speed up graph clustering algorithms
Etienne Lasalle, Rémi Vaudaine, Titouan Vayer +4
Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spe…