# Beyond Laplace and Gaussian: Exploring the Generalized Gaussian Mechanism for Private Machine Learning

arXiv: https://arxiv.org/abs/2506.12553 · HTML: https://mlsanity.com/paper/2506.12553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Scalable Private Learning with PATE](https://mlsanity.com/paper/1802.08908/) (2018)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [R'enyi Differential Privacy of the Sampled Gaussian Mechanism](https://mlsanity.com/paper/1908.10530/) (2019)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Hyperparameter Tuning with Renyi Differential Privacy](https://mlsanity.com/paper/2110.03620/) (2021)
- [Deep Roto-Translation Scattering for Object Classification](https://mlsanity.com/paper/1412.8659/) (2014)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [Certifiably Robust Interpretation via Renyi Differential Privacy](https://mlsanity.com/paper/2107.01561/) (2021)
- [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021)
- [Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacy](https://mlsanity.com/paper/2206.04572/) (2022)
- [Privately Answering Counting Queries with Generalized Gaussian Mechanisms](https://mlsanity.com/paper/2010.01457/) (2020)
- [Cactus Mechanisms: Optimal Differential Privacy Mechanisms in the Large-Composition Regime](https://mlsanity.com/paper/2207.00420/) (2022)
- [The Podium Mechanism: Improving on the Laplace and Staircase Mechanisms](https://mlsanity.com/paper/1905.00191/) (2019)

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

- [Mind the Gap: Mixtures of Gaussians in Approximate Differential Privacy](https://mlsanity.com/paper/2605.28078/) (2026)

## Abstract (arXiv)

Differential privacy (DP) is obtained by randomizing a data analysis algorithm, which necessarily introduces a tradeoff between its utility and privacy. Many DP mechanisms are built upon one of two underlying tools: Laplace and Gaussian additive noise mechanisms. We expand the search space of algorithms by investigating the Generalized Gaussian (GG) mechanism, which samples the additive noise term x with probability proportional to e^-frac| x |σβ  for some β ≥ 1 (denoted GGβ, σ(f,D)). The Laplace and Gaussian mechanisms are special cases of GG for β=1 and β=2, respectively. We prove that the full GG family satisfies differential privacy and extend the PRV accountant to support privacy loss computation for these mechanisms. We then instantiate the GG mechanism in two canonical private learning pipelines, PATE and DP-SGD. Empirically, we explore PATE and DP-SGD with the GG mechanism across the computationally feasible values of β: β ∈ [1,2] for DP-SGD and β ∈ [1,4] for PATE. For both mechanisms, we find that β=2 (Gaussian) performs as well as or better than other values in their computational tractable domains.This provides justification for the widespread adoption of the Gaussian mechanism in DP learning.