Empirical two-sample error for powered even-order Gromov-Wasserstein functionals is bounded by n^{-2/max{min(d_x,d_y),4}} up to logs when min dimension equals 4.
Villani.Optimal Transport: Old and New
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Proximal stochastic spectral preconditioning converges for nonconvex constrained objectives under heavy-tailed noise, with a variance-reduced version achieving faster rates and a refined analysis of Muon iterations.
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Empirical Convergence of Even-Order Gromov-Wasserstein Functionals
Empirical two-sample error for powered even-order Gromov-Wasserstein functionals is bounded by n^{-2/max{min(d_x,d_y),4}} up to logs when min dimension equals 4.
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Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives
Proximal stochastic spectral preconditioning converges for nonconvex constrained objectives under heavy-tailed noise, with a variance-reduced version achieving faster rates and a refined analysis of Muon iterations.