量化线性映射的子高斯性：一份AI辅助笔记 / On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note
1️⃣ 一句话总结
这篇短文证明了高斯向量在经过任意有界坐标变换后，仍具有与维度无关的子高斯集中性质，并用这个结论解释了为什么对高斯向量进行符号量化（只保留正负号）后得到的向量，也能保持良好的统计特性。
arXiv 提交日期: 2026-05-26
Abstract - On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note
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 $Y = \text{sgn}(Wx)$.
源自 arXiv: 2605.27563