Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
arXiv preprint arXiv:2410.20622 , year=
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Geometric tempering yields exponential convergence bounds for both Wasserstein and Fisher-Rao flows but produces no speedup in the Fisher-Rao metric, with new adaptive schedules derived from the tempered dynamics.
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
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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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Properties and limitations of geometric tempering for gradient flow dynamics
Geometric tempering yields exponential convergence bounds for both Wasserstein and Fisher-Rao flows but produces no speedup in the Fisher-Rao metric, with new adaptive schedules derived from the tempered dynamics.
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Weighted quantization using MMD: From mean field to mean shift via gradient flows
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.