Abstract: Stein Variational Gradient Descent (SVGD) is a deterministic, interacting particle-based algorithm for nonparametric variational inference, yet its theoretical properties remain challenging to fully understand. This talk presents two complementary perspectives on SVGD. First, we introduce Gaussian-SVGD, a framework that projects SVGD onto the family of Gaussian distributions using a bilinear kernel. We establish rigorous convergence results for both mean-field dynamics and finite-particle systems, proving linear convergence to equilibrium in strongly log-concave settings. This framework also unifies recent algorithms for…