# Not all noise is accounted equally: How differentially private learning benefits from large sampling rates

arXiv: https://arxiv.org/abs/2110.06255 · HTML: https://mlsanity.com/paper/2110.06255/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [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)
- [Tempered Sigmoid Activations for Deep Learning with Differential Privacy](https://mlsanity.com/paper/2007.14191/) (2020)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Individual Privacy Accounting via a Renyi Filter](https://mlsanity.com/paper/2008.11193/) (2020)
- [Improving Deep Learning with Differential Privacy using Gradient Encoding and Denoising](https://mlsanity.com/paper/2007.11524/) (2020)
- [An Empirical Study of Large-Batch Stochastic Gradient Descent with Structured Covariance Noise](https://mlsanity.com/paper/1902.08234/) (2019)
- [Stochastic Adaptive Line Search for Differentially Private Optimization](https://mlsanity.com/paper/2008.07978/) (2020)

## Built on by (most cited first, 21 of 21)

- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Differentially Private Diffusion Models](https://mlsanity.com/paper/2210.09929/) (2022)
- [Large Scale Transfer Learning for Differentially Private Image Classification](https://mlsanity.com/paper/2205.02973/) (2022)
- [Differentially private training of residual networks with scale normalisation](https://mlsanity.com/paper/2203.00324/) (2022)
- [Nearly Tight Black-Box Auditing of Differentially Private Machine Learning](https://mlsanity.com/paper/2405.14106/) (2024)
- [Differentially Private Image Classification by Learning Priors from Random Processes](https://mlsanity.com/paper/2306.06076/) (2023)
- [Unlocking Accuracy and Fairness in Differentially Private Image Classification](https://mlsanity.com/paper/2308.10888/) (2023)
- [Differentially Private Video Activity Recognition](https://mlsanity.com/paper/2306.15742/) (2023)
- [Differentially Private Image Classification from Features](https://mlsanity.com/paper/2211.13403/) (2022)
- [To Shuffle or not to Shuffle: Auditing DP-SGD with Shuffling](https://mlsanity.com/paper/2411.10614/) (2024)
- [Sparsity-Preserving Differentially Private Training of Large Embedding Models](https://mlsanity.com/paper/2311.08357/) (2023)
- [Equivariant Differentially Private Deep Learning: Why DP-SGD Needs Sparser Models](https://mlsanity.com/paper/2301.13104/) (2023)
- [SmoothNets: Optimizing CNN architecture design for differentially private deep learning](https://mlsanity.com/paper/2205.04095/) (2022)
- [Activity Recognition on Avatar-Anonymized Datasets with Masked Differential Privacy](https://mlsanity.com/paper/2410.17098/) (2024)
- [R+R:Understanding Hyperparameter Effects in DP-SGD](https://mlsanity.com/paper/2411.02051/) (2024)
- [The Impact of Generalization Techniques on the Interplay Among Privacy, Utility, and Fairness in Image Classification](https://mlsanity.com/paper/2412.11951/) (2024)
- [Kernel Normalized Convolutional Networks for Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2210.00053/) (2022)
- [Protecting Confidentiality, Privacy and Integrity in Collaborative Learning](https://mlsanity.com/paper/2412.08534/) (2024)
- [Forward Learning with Differential Privacy](https://mlsanity.com/paper/2504.00411/) (2025)
- [Towards Reliable and Generalizable Differentially Private Machine Learning (Extended Version)](https://mlsanity.com/paper/2508.15141/) (2025)
- [Rethinking Benchmarks for Differentially Private Image Classification](https://mlsanity.com/paper/2601.17189/) (2026)

## Abstract (arXiv)

Learning often involves sensitive data and as such, privacy preserving extensions to Stochastic Gradient Descent (SGD) and other machine learning algorithms have been developed using the definitions of Differential Privacy (DP). In differentially private SGD, the gradients computed at each training iteration are subject to two different types of noise. Firstly, inherent sampling noise arising from the use of minibatches. Secondly, additive Gaussian noise from the underlying mechanisms that introduce privacy. In this study, we show that these two types of noise are equivalent in their effect on the utility of private neural networks, however they are not accounted for equally in the privacy budget. Given this observation, we propose a training paradigm that shifts the proportions of noise towards less inherent and more additive noise, such that more of the overall noise can be accounted for in the privacy budget. With this paradigm, we are able to improve on the state-of-the-art in the privacy/utility tradeoff of private end-to-end CNNs.