The paper proves quantitative convergence to the target distribution and uniform‑in‑time propagation of chaos for Langevin‑regularized Stein variational gradient descent (SVGD). It shows that both the Stein interaction and the Langevin drift dissipate the same relative entropy, yielding exponential convergence under a log‑Sobolev inequality and providing finite‑particle entropy identities for empirical measures. Two finite‑time approaches—synchronous coupling and moving‑product entropy—are developed to give explicit Wasserstein, kernel Stein discrepancy, and total variation bounds, leading to polynomial uniform‑in‑time propagation of chaos rates.
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
arXiv:2609.40193v1 Announce Type: new Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
arXiv:2511. 05940v3 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains.
arXiv:2607. 14527v1 Announce Type: cross Abstract: Stein variational gradient descent (SVGD) transports interacting particles toward a target distribution through deterministic kernelized dynamics.
arXiv:2608.25279v1 Announce Type: cross Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...
arXiv:2602.13960v2 Announce Type: replace Abstract: Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency, yet the distribution of the iterates is ty...
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
arXiv:2610. 29007v1 Announce Type: cross Abstract: We study a jump-modified Wasserstein gradient flow of the squared maximum mean discrepancy generated by the energy kernels $K(z)=-|z|^q$, $0<q<2$, in every dimension $d\ge2$ as well as the one-dimensional range $1\le q<2$.
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
arXiv:2407.05790v4 Announce Type: replace-cross Abstract: This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIP...
arXiv:2405. 15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains.