# Correlating Cross-Iteration Noise for DP-SGD using Model Curvature

arXiv: https://arxiv.org/abs/2510.05416 · HTML: https://mlsanity.com/paper/2510.05416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 62 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [ChestX-ray8: Hospital-scale Chest X-ray Database and Benchmarks on Weakly-Supervised Classification and Localization of Common Thorax Diseases](https://mlsanity.com/paper/1705.02315/) (2017)
- [Large Language Models Can Be Strong Differentially Private Learners](https://mlsanity.com/paper/2110.05679/) (2021)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Bypassing the Ambient Dimension: Private SGD with Gradient Subspace Identification](https://mlsanity.com/paper/2007.03813/) (2020)
- [Automatic Clipping: Differentially Private Deep Learning Made Easier and Stronger](https://mlsanity.com/paper/2206.07136/) (2022)
- [Toward Training at ImageNet Scale with Differential Privacy](https://mlsanity.com/paper/2201.12328/) (2022)
- [Do Not Let Privacy Overbill Utility: Gradient Embedding Perturbation for Private Learning](https://mlsanity.com/paper/2102.12677/) (2021)
- [Differentially Private Optimization on Large Model at Small Cost](https://mlsanity.com/paper/2210.00038/) (2022)
- [Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams](https://mlsanity.com/paper/2202.08312/) (2022)
- [(Amplified) Banded Matrix Factorization: A unified approach to private training](https://mlsanity.com/paper/2306.08153/) (2023)
- [Multi-Epoch Matrix Factorization Mechanisms for Private Machine Learning](https://mlsanity.com/paper/2211.06530/) (2022)

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

- [DP-λCGD: Efficient Noise Correlation for Differentially Private Model Training](https://mlsanity.com/paper/2601.22334/) (2026)

## Abstract (arXiv)

Differentially private stochastic gradient descent (DP-SGD) offers the promise of training deep learning models while mitigating many privacy risks. However, there is currently a large accuracy gap between DP-SGD and normal SGD training. This has resulted in different lines of research investigating orthogonal ways of improving privacy-preserving training. One such line of work, known as DP-MF, correlates the privacy noise across different iterations of stochastic gradient descent -- allowing later iterations to cancel out some of the noise added to earlier iterations. In this paper, we study how to improve this noise correlation. We propose a technique called NoiseCurve that uses model curvature, estimated from public unlabeled data, to improve the quality of this cross-iteration noise correlation. Our experiments on various datasets, models, and privacy parameters show that the noise correlations computed by NoiseCurve offer consistent and significant improvements in accuracy over the correlation scheme used by DP-MF.