Smoothness assumptions on graphical model kernels produce Wasserstein estimation rates determined by local graph structure rather than ambient dimension.
arXiv preprint arXiv:2407.18163 , year =
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Entropic OT with non-product Gaussian references reduces to a matrix optimization problem yielding complete primal-dual solutions that enable coherent continuous-time processes from time marginals.
Develops the first provably convergent stochastic fixed-point algorithm for free-support 2-Wasserstein barycenters of continuous measures under Caffarelli regularity, using a modified entropic OT map estimator.
Provides asymptotic distributions for entropic OT plans and potentials under vanishing regularization and links self-transport barycentric projections to score functions.
Systematic experiments reveal that activation steering trades fluency for concept control, is less effective on instruction-tuned models, and that prompting/SFT excel at injection but not removal, with textual metrics correlating to LLM judges.
Constructive isometry of tangent spaces along lifted geodesics equates local HK Riemannian geometry with Wasserstein geometry on the cone, enabling approximation of HK parallel transport.
Transfer learning achieves sample complexity O(m^{-(α+1)/d}) for d>3 via optimal transport, outperforming direct learning's O(m^{-p/d}) when target models are not smooth.
A grid-sketching technique enables ε-accurate estimation of W₂² between α-Hölder smooth distributions on (0,1)^d in time ε^{-max(2, (d+1+o(1))/(1+α))}.
dFlowGRPO is a new rate-aware RL method for discrete flow models that outperforms prior GRPO approaches on image generation and matches continuous flow models while supporting broad probability paths.
A nonparametric estimator for Wasserstein barycenters achieves improved convergence rates by incorporating smoothness via density estimation and Sobolev geometry.
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
A tractable mean-field model casts self-organized robustness as meta-optimization, producing a self-consistent seascape whose shape accelerates relaxation via optimized Wasserstein gradient flow and preferentially encodes slow or frequently perturbed modes under limited communication.
Score-based diffusion sampling is shown to be adiabatic ground-state transport for a Score Hamiltonian, with error floor equal to terminal score-matching error over the square root of the spectral gap.
Mean-field transformer models synchronize to a Dirac point mass exponentially fast with explicit quantitative rates under suitable parameter assumptions.
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