6 citations · 9 across the 4 of their papers we have counts for
9 papers · 1 filter
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…
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.…
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…
A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
Titouan Vayer, Etienne Lasalle
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with en…
Compressive Recovery of Sparse Precision Matrices
Titouan Vayer, Etienne Lasalle, Rémi Gribonval +1
We consider the problem of learning a graph modeling the statistical relations of the variables from a dataset with samples . Standard approa…
A contribution to Optimal Transport on incomparable spaces
Titouan Vayer
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of po…