We study uniform-in-time propagation-of-chaos for continuous-time Stein Variational Gradient Descent (SVGD). Classical finite-time propagation-of-chaos estimates for mean-field systems typically deteriorate rapidly with time and therefore do not directly explain the long-time relation between the finite-particle system and its mean-field limit. We obtain two complementary classes of uniform-in-time propagation-of-chaos results. For broad distributional metrics, we introduce a cutoff strategy which combines finite-time propagation-of-chaos estimates up to an $N$-dependent horizon with independent quantitative long-time convergence estimates for the finite-particle and mean-field SVGD flows. This yields uniform-in-averaging-time propagation-of-chaos bounds in Langevin kernel Stein discrepancy, Wasserstein-1 distance, and Wasserstein-2 distance, with logarithmic or iterated-logarithmic rates depending on the metric, target and kernel class. We also develop a finite-dimensional theory for matrix-valued finite-rank kernels. For Gaussian targets with bilinear kernels, the SVGD dynamics close exactly on first and second moments, yielding genuine uniform-in-physical-time parametric propagation-of-chaos rates in finite-dimensional Stein-feature metrics. We then prove a conjugacy principle showing that these feature-level estimates transfer to conjugate target-kernel pairs under orientation-preserving diffeomorphisms, thereby extending the theory to broad classes of nonlinear, including multimodal, targets. Together, these results highlight the contrast between generic distributional metrics, for which our general approach yields logarithmic rates, and closed finite-dimensional Stein observables, for which parametric $N^{-1/2}$ propagation-of-chaos rates persist uniformly in time.

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For instance, in the synthetic example for E2ST model shown in Section 5.1,ˆβl can573 be estimated forβl since the edge, 2Star and triangle statistics are specified.

D 2 N, define [ D ]: = { 1,...,D } . The symbol & indicates greater than up to a universal constant.

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of kernel discrepancies, selecting an m-element subset from a large population of size $n \gg m$. We introduce a novel subset selection algorithm applicable to general kernel discrepancies to efficiently generate low-discrepancy samples from both the uniform distribution on the unit hypercube, the traditional setting of classical QMC, and from more general distributions $F$ with known density functions by employing the kernel Stein discrepancy. We also explore the relationship between the classical $L_2$ star discrepancy and its $L_\infty$ counterpart.