Abstract Retrieval Augmented Generation (RAG) is emerging as a flexible and robust
technique to adapt models to private users data without training to handle credit attribution …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

For the task of sampling from a density $\pi\propto\exp (-V) $ on $\R^ d $, where $ V $ is
possibly non-convex but $ L $-gradient Lipschitz, we prove that averaged Langevin Monte …

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics
recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide …

Abstract Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from
unnormalized densities by leveraging the momentum of a particle moving in a potential well …

Langevin diffusions are rapidly convergent under appropriate functional inequality
assumptions. Hence, it is natural to expect that with additional smoothness conditions to …

We propose a sampling algorithm that achieves superior complexity bounds in all the
classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI) …

Sampling from a high-dimensional distribution is a fundamental task in statistics,
engineering, and the sciences. A canonical approach is the Langevin Algorithm, ie, the …

Despite its success in a wide range of applications, characterizing the generalization
properties of stochastic gradient descent (SGD) in non-convex deep learning problems is …