255 citations · 949 across the 71 of their papers we have counts for
65 papers · 1 filter
Diffusion annealed Langevin dynamics: a theoretical study
Patrick Cattiaux, Paula Cordero-Encinar, Arnaud Guillin
In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative t…
Some remarks on the effect of the Random Batch Method on phase transition
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
In this article, we focus on two toy models : the Curie-Weiss model and the system of particles in linear interactions in a double well confining potential. Both models, which…
Law of large numbers and central limit theorem for wide two-layer neural networks: the mini-batch and noisy case
Arnaud Descours, Arnaud Guillin, Manon Michel +1
In this work, we consider a wide two-layer neural network and study the behavior of its empirical weights under a dynamics set by a stochastic gradient descent along the quadratic…
On systems of particles in singular repulsive interaction in dimension one : log and Riesz gas
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that co…
Sticky nonlinear SDEs and convergence of McKean-Vlasov equations without confinement
Alain Durmus, Andreas Eberle, Arnaud Guillin +1
We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for t…
Uniform in time propagation of chaos for the 2D vortex model and other singular stochastic systems
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
In this article, we adapt the work of Jabin and Wang (2018) to show the first result of uniform in time propagation of chaos for a class of singular interaction kernels. In particu…