arXiv Machine Learning By Zhengjiang Lin, Philippe Rigollet

Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies

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arXiv:2609. 27008v1 Announce Type: cross Abstract: We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[\mu] = \frac12\iint_{M\times M}K(x,y)\,\mathrm d\mu(x)\,\mathrm d\mu(y) \] on a closed manifold $M$.

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arXiv Machine Learning
Aug 10

Free Denoising Diffusion Models

arXiv:2510. 22778v3 Announce Type: replace-cross Abstract: We develop a free-probabilistic framework for denoising diffusion, in which the data is a self-adjoint operator and its law a spectral distribution.

By Swagatam Das
arXiv Machine Learning
Jul 22

Linear convergence of proximal descent schemes on the Wasserstein space

arXiv:2411. 15067v2 Announce Type: replace-cross Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space.

By Razvan-Andrei Lascu, Mateusz B. Majka, David \v{S}i\v{s}ka, {\L}ukasz Szpruch