Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
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Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
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Sobolev Regularized MMD Gradient Flow
Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
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Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.