math.PRMay 26, 2026

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

Authors: Guangyi Zou, Roman Vershynin

Organizations: Department of Mathematics, University of California, Irvine

Abstract

This short note presents a dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear mappings. Discovered by Gemini 3.5 Flash, this result applies to any bounded function under a well-conditioned covariance. We apply this tool to answer a question of Simone Bombari on sign-quantized linear maps Y=sgn(Wx)Y = \text{sgn}(Wx).

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