Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent

• URL: http://arxiv.org/abs/2607.00149v1
• Date: Tue, 30 Jun 2026 20:27:39 GMT
• Title: Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent
• Abstract summary: We study uniform-in-time propagation-of-chaos for continuous-time Stein Variational Gradient Descent flows.<n>For broad distributional metrics, we introduce a cutoff strategy which combines finite-time propagation-of-chaos estimates up to an $N$-dependent horizon.<n>We also develop a finite-dimensional theory for matrix-valued finite-rank kernels.
• Score: 16.01291417072387
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD [2.457924087844968]
  We show convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein descent.<n>For propagation of chaos, we develop two complementary finite-time approaches.
  arXiv  Detail & Related papers  (2026-08-28T19:56:49Z)
• Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limits [9.465013037575494]
  Stein variational gradient descent (SVGD) transports interacting particles toward a target distribution through deterministic kernelized dynamics.<n>We study periodic Riesz SVGD with self-interaction removed and prove a many-particle, long-time sampling singularity theorem.
  arXiv  Detail & Related papers  (2026-07-16T03:30:20Z)
• Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts [60.95873409673775]
  identifiability in continuous-time latent differential equation models remains largely open.<n>We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism.<n>We propose a two-stage estimator for latent disentanglement and optional graph recovery.
  arXiv  Detail & Related papers  (2026-06-26T16:18:28Z)
• Uniform-in-time concentration in two-layer neural networks via transportation inequalities [1.873444918172383]
  We prove uniform-in-time concentration of the empirical parameter measure around its mean-field limit in the Wasserstein distance W 1.<n>We also derive analogous concentration bounds in the sliced-Wasserstein distance SW 1.
  arXiv  Detail & Related papers  (2026-03-02T13:19:59Z)
• Finite-Particle Rates for Regularized Stein Variational Gradient Descent [9.824622287505454]
  We derive finite-particle rates for the regularized Stein variational descent gradient (R-SVGD) algorithm introduced by He et al.<n>For the resulting interacting $N$-particle system, we establish explicit non-asymptotic bounds for time-averaged (annealed) empirical measures.<n>Our analysis covers both continuous- and discrete-time dynamics and yields principled tuning rules for the regularization parameter, step size, and averaging horizon.
  arXiv  Detail & Related papers  (2026-02-05T01:00:00Z)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework.<n>We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points.<n>Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent [14.890609936348277]
  We provide finite-particle convergence rates for the Stein Variational Gradient Descent algorithm in the Kernelized Stein Discrepancy ($mathsfKSD$) and Wasserstein-2 metrics.<n>Our key insight is that the time derivative of the relative entropy between the joint density of $N$ particle locations splits into a dominant negative part' proportional to $N$ times the expected $mathsfKSD2$ and a smaller positive part'
  arXiv  Detail & Related papers  (2024-09-13T01:49:19Z)
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity [1.7620619500719317]
  We analyze the time-convolutionless (TCL) master equation, expanded to order 2n.<n>We show that while van Kampensants suppress early-time secular growth, they ultimately diverge at long times.<n>For exponentially decaying correlations, the method recovers a proper Markovian limit below a critical coupling threshold.
  arXiv  Detail & Related papers  (2024-06-16T22:15:07Z)
• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.