Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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12 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 12representative citing papers
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
A Gaussian-kernel diffusion operator on feature clouds yields closed-form class affinities and spectra in Gaussian models, with provably smooth observables under perturbations.
Derives Õ(d β² A² / ε⁴) oracle complexity for AIS estimating normalizing constant Z to relative error ε and introduces reverse diffusion sampler for geometric paths with large action.
Bilinear generating function for Wronskians of Hermite polynomials equals the Mehler kernel times a polynomial.
Proves log-Sobolev inequality with explicit constant for Wolff dynamics on 1D Ising model and confirms its use in spectral analysis of eigen microstate condensation matches simulations.
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
A regularity theorem establishes that sufficiently regular stationary measures for a variational eigenvalue problem on manifolds are absolutely continuous with densities induced by harmonic maps.
An optimal transport method is proposed to construct confidence intervals with improved coverage, including theoretical consistency results, error bounds, and simulation comparisons.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
Training a mean-field Transformer under L2 regularization induces an escape from attention-driven token clustering in later layers after initial clustering.
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.