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

Abstract

We prove an elementary bounded-differences inequality for functions of non-isotropic Gaussian vectors. Specifically, if $f$ has bounded coordinate differences and $X\sim\mathcal N(\mu,\Sigma)$, then the resulting concentration bound depends on the condition number $\kappa(\Sigma)$. As an application, we answer a question of Simone Bombari concerning the subgaussianity of sign-quantized linear maps $Y=\mathrm{sgn}(Wx)$. In the special case where $f$ is the coordinatewise sign function, an argument was initially suggested to us by Gemini 3.5 Flash without attribution. We subsequently discovered that it closely resembles an earlier argument of Barber and Kolar [Ann. Statist. 46 (2018), Lemma 4.5]. This revision corrects the attribution and documents the episode as an instance of AI-assisted mathematical discovery.