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

arXiv: https://arxiv.org/abs/2605.27563 · HTML: https://mlsanity.com/paper/2605.27563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 4 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 1 of 1)

- [ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models](https://mlsanity.com/paper/1502.07641/) (2015)

## Built on by (most cited first, 1 of 1)

- [On McDiarmid's Inequality under Dependence via Approximate Tensorization of Entropy](https://mlsanity.com/paper/2606.12720/) (2026)

## Abstract (arXiv)

We prove an elementary bounded-differences inequality for functions of non-isotropic Gaussian vectors. Specifically, if f has bounded coordinate differences and X~mathcal N(μ,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=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.