5 papers
GradRig: Differentiable Weights for Skinned Gaussian Splat Deformation
Nina Vesseron, Élie Michel
Skinned deformation is a common framework to turn a 3D shape from its rest pose into a dynamic pose through the deformation of a coarser kinematic structure, called rig. When appli…
On the Wasserstein Geodesic Principal Component Analysis of probability measures
Nina Vesseron, Elsa Cazelles, Alice Le Brigant +1
This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesi…
Sample and Map from a Single Convex Potential: Generation using Conjugate Moment Measures
Nina Vesseron, Louis Béthune, Marco Cuturi
The canonical approach in generative modeling is to split model fitting into two blocks: define first how to sample noise (e.g. Gaussian) and choose next what to do with it (e.g. u…
On a Neural Implementation of Brenier's Polar Factorization
Nina Vesseron, Marco Cuturi
In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices -- factored as PSD unitary -- to any vector field $F:\mathbb{R}^d\rightarrow…
Deep Neural Networks Are Congestion Games: From Loss Landscape to Wardrop Equilibrium and Beyond
Nina Vesseron, Ievgen Redko, Charlotte Laclau
The theoretical analysis of deep neural networks (DNN) is arguably among the most challenging research directions in machine learning (ML) right now, as it requires from scientists…