Category: math.AP
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Radon–Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions
Radon–Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions arXiv:2602.05227v1 Announce Type: new Abstract: Gradient flows of the Kullback–Leibler (KL) divergence, such as the Fokker–Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density known only up to a normalizing constant. We introduce new gradient flows of the KL divergence with…
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Implicit Bias of the JKO Scheme
Implicit Bias of the JKO Scheme arXiv:2511.14827v1 Announce Type: new Abstract: Wasserstein gradient flow provides a general framework for minimizing an energy functional $J$ over the space of probability measures on a Riemannian manifold $(M,g)$. Its canonical time-discretization, the Jordan-Kinderlehrer-Otto (JKO) scheme, produces for any step size $eta>0$ a sequence of probability distributions $rho_k^eta$ that…
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A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions
A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions arXiv:2508.16306v1 Announce Type: new Abstract: Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through reverse SDEs or Probability Flow ODEs. The best known guarantees,…
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Central limit theorems for the eigenvalues of graph Laplacians on data clouds
Central limit theorems for the eigenvalues of graph Laplacians on data clouds arXiv:2507.18803v1 Announce Type: new Abstract: Given i.i.d. samples $X_n ={ x_1, dots, x_n }$ from a distribution supported on a low dimensional manifold ${M}$ embedded in Eucliden space, we consider the graph Laplacian operator $Delta_n$ associated to an $varepsilon$-proximity graph over $X_n$ and…
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Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds arXiv:2506.00171v1 Announce Type: new Abstract: We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution $rho$ supported on a manifold $M$. The operators discussed in the paper are relevant in unsupervised learning and in particular are…