# Notes on Sampled Gaussian Mechanism

arXiv: https://arxiv.org/abs/2409.04636 · HTML: https://mlsanity.com/paper/2409.04636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 1 references that are in the map.
- First posted on arXiv 6 Sep 2024.

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

- [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimisation](https://mlsanity.com/paper/2402.03990/) (2024)

## Abstract (arXiv)

In these notes, we prove a recent conjecture posed in the paper by R"ais"a, O. et al. [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimization (2024)]. Theorem 6.2 of the paper asserts that for the Sampled Gaussian Mechanism - a composition of subsampling and additive Gaussian noise, the effective noise level, σeff = fracσ(q)q, decreases as a function of the subsampling rate q. Consequently, larger subsampling rates are preferred for better privacy-utility trade-offs. Our notes provide a rigorous proof of Conjecture 6.3, which was left unresolved in the original paper, thereby completing the proof of Theorem 6.2.