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Correlated Noise Mechanisms for Differentially Private Learning

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arxiv 2506.08201 v1 pith:FST2K7CT submitted 2025-06-09 cs.LG cs.CR

Correlated Noise Mechanisms for Differentially Private Learning

classification cs.LG cs.CR
keywords mechanismsnoiselearningcorrelatedprivacyprivatestepstraining
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This monograph explores the design and analysis of correlated noise mechanisms for differential privacy (DP), focusing on their application to private training of AI and machine learning models via the core primitive of estimation of weighted prefix sums. While typical DP mechanisms inject independent noise into each step of a stochastic gradient (SGD) learning algorithm in order to protect the privacy of the training data, a growing body of recent research demonstrates that introducing (anti-)correlations in the noise can significantly improve privacy-utility trade-offs by carefully canceling out some of the noise added on earlier steps in subsequent steps. Such correlated noise mechanisms, known variously as matrix mechanisms, factorization mechanisms, and DP-Follow-the-Regularized-Leader (DP-FTRL) when applied to learning algorithms, have also been influential in practice, with industrial deployment at a global scale.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise

    cs.LG 2026-05 unverdicted novelty 8.0

    First population risk bounds for KANs under mini-batch DP-SGD with correlated noise, using a new non-convex optimization analysis combined with stability-based generalization.

  2. Improved Error Bounds for Pure Differentially Private Continual Counting via Matrix Factorization

    cs.DS 2026-07 accept novelty 7.0

    Recursive matrix factorization from optimized low-dimensional bases yields pure-DP continual counting with MaxSE ≤ 0.0778 log^{3}_{2} n/ε^{2} and MeanSE ≤ 0.0710 log^{3}_{2} n/ε^{2}, plus Ω(log^{3} n) lower bounds for...

  3. Local Differential Privacy with Correlated Noise Achieves Central-DP Optimal Cost

    cs.IT 2026-05 unverdicted novelty 7.0

    Correlated local noise under pure ε-DP achieves central-DP optimal estimation cost for sums up to arbitrarily small error.

  4. CityOS: Privacy Architecture for Urban Sensing

    cs.OS 2026-05 unverdicted novelty 7.0

    CityOS is an edge runtime that enforces a three-tier privacy API for urban sensors: local raw data, differentially private single-location stats, and cross-location aggregates with per-user budgets enforced on devices.

  5. Privacy, Prediction, and Allocation

    cs.CR 2026-04 unverdicted novelty 7.0

    Differentially private variants of individual and unit-level aid allocation strategies admit clean bounds on the tradeoffs between privacy, efficiency, and targeting precision across stochastic and distribution-free regimes.

  6. Correlating Cross-Iteration Noise for DP-SGD using Model Curvature

    cs.LG 2025-10 conditional novelty 7.0

    Using Hessian eigenvalues from public data to design correlated noise for DP-SGD improves accuracy by 1–4% over current DP-MF methods.

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

    cs.LG 2026-05 unverdicted novelty 6.0

    Proves linear max-information bound for DP-SGD and derives explicit PAC-Bayes generalization bounds with learnable prior and hyperparameter-controlled complexity term.

  8. Limits of Personalizing Differential Privacy Budgets

    cs.CR 2026-05 unverdicted novelty 6.0

    For mean estimation, a simple thresholding operator on privacy budgets matches the performance of fully personalized differential privacy mechanisms up to constant factors.

  9. Privacy, Prediction, and Allocation

    cs.CR 2026-04 unverdicted novelty 6.0

    Private variants of individual and unit-level aid allocation admit interpretable bounds trading privacy, efficiency, and targeting precision in stochastic and distribution-free settings.