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

arXiv:2607.00149 · math.PR, stat.ML · Submitted 2026-06-30 · Read on arXiv

Krishnakumar Balasubramanian, Sayan Banerjee, Anna Korba

math.PR, stat.ML

Submitted: 2026-06-30

Comments: 56 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Stein Variational Gradient Descent — 17× in this paper
• Gradient Flow — 14× in this paper · explained in 2 episodes
• Mean-Field Limit — 12× in this paper · explained in 2 episodes
• Kernel Stein Discrepancy — 7× in this paper
• Initial Data — 5× in this paper · explained in 2 episodes
• Lyapunov function — 4× in this paper · explained in 2 episodes
• Mean-Field Dynamics — 4× in this paper · explained in 2 episodes
• Wasserstein Distance — 4× in this paper · explained in 6 episodes
• Exchangeability — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 14 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space — 2× in this paper
• Score Function — 2× in this paper · explained in 4 episodes
• Clarity — 1× in this paper · explained in 3 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 4 episodes
• Localization — 1× in this paper · explained in 2 episodes
• National Science Foundation — 1× in this paper
• Preconditioning — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 7 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models
• Flocking under Fast and Large Jumps: Stability, Chaos, and Traveling Waves
• Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences
• The Stein-log-Sobolev inequality and the exponential rate of convergence for the continuous Stein variational gradient descent method
• Stein Variational Gradient Descent dynamics for highly concentrated kernels
• Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
• Generative Modeling via Drifting
• Learning to Draw Samples with Amortized Stein Variational Gradient Descent
• Drifting Fields are not Conservative
• Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
• On the Wasserstein Gradient Flow Interpretation of Drifting Models
• Finite-Particle Rates for Regularized Stein Variational Gradient Descent
• Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective

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