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A Slightly Improved Bound for the KLS Constant
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We refine the recent breakthrough technique of Klartag and Lehec to obtain an improved polylogarithmic bound for the KLS constant.
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Cited by 4 Pith papers
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The KLS constant is $O(\log^{1/4} n)$
Every isotropic log-concave measure satisfies a quadratic-form Poincaré inequality with constant 2, which implies the KLS constant is at most C log^{1/4} n.
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Push-forwards of Gaussian or log-concave latent variables through Lipschitz neural networks are always sub-Gaussian or sub-exponential, so common deep generative models cannot generate heavy-tailed distributions.
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