arXiv AI By Guangyi Zou, Roman Vershynin

On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note

Read the original on arXiv AI →

The paper establishes a bounded‑differences inequality for functions of non‑isotropic Gaussian vectors, showing that the concentration bound depends on the condition number of the covariance matrix. It applies this result to demonstrate the subgaussianity of sign‑quantized linear maps, addressing a question posed by Simone Bombari. The authors also correct attribution to earlier work by Barber and Kolar and highlight the role of AI assistance in the discovery process.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv Machine Learning
Jun 26

Gradient Testing and Estimation by Comparisons

arXiv:2405. 11454v3 Announce Type: replace Abstract: We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value.

By Xiwen Tao, Chenyi Zhang, Helin Wang, Yexin Zhang, Tongyang Li
arXiv Machine Learning
Sep 25

On the SoS Certifiability of Log-Concave Distributions

arXiv:2609. 30105v1 Announce Type: new Abstract: 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.

By Aleksandr Storozhenko
Hugging Face Trending Papers
Sep 24

On the SoS Certifiability of Log-Concave Distributions

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.

arXiv Machine Learning
Aug 26

Provable Quantum--Classical Separation for Continuous Gibbs Sampling

arXiv:2608.24527v1 Announce Type: cross Abstract: We prove the first quantum--classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$...

By Enrico Olivucci, Mariia Sobchuk, Sehmimul Hoque, Jeffrey Hnybida, Kyungho W. Kim, Ala Shayeghi, Pooya Ronagh