Finite-width shallow networks remain within poly(d) m^{-min(1,c/6)} of their mean-field limit uniformly in time when mean-field excess loss decays as t^{-c} under standard regularity and an integral condition on the loss.
Quantita- tive convergence of wasserstein gradient flows of kernel mean discrepancies.arXiv preprint arXiv:2603.01977
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Introduces WSFN, a Newton-type method on Wasserstein space that escapes saddle points in polynomial time and achieves linear convergence to global minimizers under benign landscape assumptions.
Sobolev regularization on the witness function enables global convergence of MMD gradient flows for both sampling and generative modeling without isoperimetric assumptions.
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.
citing papers explorer
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Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
Finite-width shallow networks remain within poly(d) m^{-min(1,c/6)} of their mean-field limit uniformly in time when mean-field excess loss decays as t^{-c} under standard regularity and an integral condition on the loss.
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From Saddle Points Toward Global Minima: A Newton-Type Method on Wasserstein Space
Introduces WSFN, a Newton-type method on Wasserstein space that escapes saddle points in polynomial time and achieves linear convergence to global minimizers under benign landscape assumptions.
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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.
- Sharp Rates of MMD Empirical Estimation with Power Kernels