Differentially private stochastic gradient descent (DP-SGD) is the gold standard for training machine learning models with formal differential privacy guarantees. Several recent extensions improve its accuracy by introducing correlated noise across training iterations. Matrix factorization mechanisms are a prominent example, but they correlate noise across many iterations and require storing previously added noise vectors, leading to substantial memory overhead in some settings. In this work, we propose a new noise correlation strategy that correlates noise only with the immediately preceding iteration and cancels a controlled portion of it. Our method relies on noise regeneration using a pseudorandom noise generator, eliminating the need to store past noise. As a result, it requires no additional memory beyond standard DP-SGD. We show that the computational overhead is minimal and empirically demonstrate improved accuracy over DP-SGD.
@article{arxiv.2601.22334,
title = {DP-{\lambda}CGD: Efficient Noise Correlation for Differentially Private Model Training},
author = {Nikita P. Kalinin and Ryan McKenna and Rasmus Pagh and Christoph H. Lampert},
journal= {arXiv preprint arXiv:2601.22334},
year = {2026}
}