From Privacy to Generalization: Linear Max-Information Bounds for DP-SGD

Christoph H. Lampert; Hossein Zakerinia

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arXiv · 2605.26222

From Privacy to Generalization: Linear Max-Information Bounds for DP-SGD

Christoph H. Lampert·Hossein Zakerinia

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Abstract

Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent (DP-SGD). In this work we make progress on this persistent open problem by proving a finite-sample bound on the approximate max-information of DP-SGD that exhibits scaling properties comparable with (Dwork et al, 2015)'s classic result for $\epsilon$-differentially private algorithms, namely at most linear in the dataset size. From our result we obtain a general-purpose PAC-Bayes generalization bound in which the necessary prior distribution can be learned by DP-SGD, as well as a generalization bound for DP-SGD-trained models themselves, with a complexity term that is fully explicit and controlled by the optimization hyperparameters.

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Christoph H. Lampert, Hossein Zakerinia. 2026-05-25. From Privacy to Generalization: Linear Max-Information Bounds for DP-SGD. https://arxiv.org/abs/2605.26222

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