On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note
arXiv:2605.2756366.3h-index: 2
AI Analysis
Provides a theoretical tool for analyzing quantized linear maps, relevant to researchers in high-dimensional probability and signal processing.
This note proves a dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear mappings, and applies it to show that sign-quantized linear maps satisfy a subgaussian property.
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 $Y = \text{sgn}(Wx)$.