Paper recorded by Signals 4 on 2026-09-24 in cs.LG. Abstract reproduced from arXiv; link to the original below.
Published 2026-09-24 on arXiv · recorded by Signals 4 on 2026-09-25
Category: cs.LG · 机器学习 · first seen 2026-09-25
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.07465), recovering the optimal moment bounds for