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.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
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.
By Sayan Banerjee, Dohyeon Kim
arXiv:2508. 01392v2 Announce Type: replace Abstract: Gibbs measures, such as Coulomb gases, are popular in modelling systems of interacting particles.
By Martin Rouault, R\'emi Bardenet, Myl\`ene Ma\"ida
arXiv:2604. 24196v4 Announce Type: replace-cross Abstract: A drifting model is a one-step generator trained by moving each sample along a field of kernel-weighted attraction toward data samples and repulsion between model samples; training halts once this field vanishes.
By HakGeun Lee, Hyonho Chun
arXiv:2609.37787v1 Announce Type: new
Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
By Ruinan Jin, Difei Cheng, Ling Chen, Jun Luo, Hao Zhou, Youzhi Zhang
The paper investigates the mixing time of weighted Dikin walks used for sampling from exponential distributions on polytopes and truncated positive-semidefinite cones. It presents a general total-variation mixing bound under conditions of strong self-concordance, ν-symmetry, and mixed-trace regularity, achieving an “~O(d^2)" bound for polytopes and “~O(d^4)" for truncated PSD cones. A second result introduces a fourth-order bootstrap condition that yields stronger χ^2-divergence guarantees and an improved “~O(d^2)" mixing bound for a scaled Lee–Sidford metric.
By Yuansi Chen, Yunbum Kook