Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
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Sobolev-ball constraints on the hypothesis class achieve minimax rates for score estimation on the torus and, under conjecture, for generative modeling.
Established mathematical bottlenecks in representation, optimization, complexity, and high-dimensional learning aligned with the central disappointments of early AI research periods.
citing papers explorer
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Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
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Optimal score function estimation via derivatives constraints
Sobolev-ball constraints on the hypothesis class achieve minimax rates for score estimation on the torus and, under conjecture, for generative modeling.
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The Mathematics of AI Winters: The mathematical Taxonomy of Paradigm Fragility in AI Winter
Established mathematical bottlenecks in representation, optimization, complexity, and high-dimensional learning aligned with the central disappointments of early AI research periods.