mlsanityData to 7 Oct 2026

Optimal Accounting of Differential Privacy via Characteristic Function

arXiv 2106.08567 ↗First posted 16 Jun 2021cs.LG cs.CRcited by 83

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Abstract (arXiv)

Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, f-DP and the PLD formalism) via the characteristic function (φ-function) of a certain dominating privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and f-DP, thus providing (ε,δ)-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the complex logarithm of φ-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments.

Key facts. Cited by 83 papers in the map (data through 7 Oct 2026). Builds on 16 of its 54 references that are in the map. First posted on arXiv 16 Jun 2021.

Builds on

16 of 54 references.

References · 16

  1. 2016Deep Learning with Differential Privacycited by 2,682
  2. 2017Renyi Differential Privacycited by 643
  3. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  4. 2013The Composition Theorem for Differential Privacycited by 290
  5. 2014RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Responsecited by 262
  6. 2018Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergencescited by 237
  7. 2018Subsampled R'enyi Differential Privacy and Analytical Moments Accountantcited by 234
  8. 2018Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoisingcited by 216
  9. 2021Numerical Composition of Differential Privacycited by 174
  10. 2020The Discrete Gaussian for Differential Privacycited by 134
  11. 2014Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Boundscited by 104
  12. 2019Hypothesis Testing Interpretations and Renyi Differential Privacycited by 84
4 more
  1. 2015Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlocited by 61
  2. 2020Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFTcited by 43
  3. 2020Three Variants of Differential Privacy: Lossless Conversion and Applicationscited by 25
  4. 2021Computing Differential Privacy Guarantees for Heterogeneous Compositions Using FFTcited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 15; 2023: 15; 2024: 23; 2025: 14; 2026: 11.

83 papers.

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  1. 2023Privacy Auditing with One (1) Training Runcited by 119
  2. 2022Automatic Clipping: Differentially Private Deep Learning Made Easier and Strongercited by 87
  3. 2022Differentially Private Optimization on Large Model at Small Costcited by 65
  4. 2022Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributionscited by 50
  5. 2022Composition of Differential Privacy & Privacy Amplification by Subsamplingcited by 42
  6. 2023Bounding Training Data Reconstruction in DP-SGDcited by 42
  7. 2024Private Fine-tuning of Large Language Models with Zeroth-order Optimizationcited by 41
  8. 2021Dynamic Differential-Privacy Preserving SGDcited by 29
  9. 2024Fine-Tuning Large Language Models with User-Level Differential Privacycited by 28
  10. 2024Auditing f-Differential Privacy in One Runcited by 28
  11. 2022FLUTE: A Scalable, Extensible Framework for High-Performance Federated Learning Simulationscited by 27
  12. 2022Fully Adaptive Composition in Differential Privacycited by 22
38 more
  1. 2024How Private are DP-SGD Implementations?cited by 22
  2. 2022Individual Privacy Accounting with Gaussian Differential Privacycited by 19
  3. 2023Practical Differentially Private Hyperparameter Tuning with Subsamplingcited by 19
  4. 2023Privacy Amplification for Matrix Mechanismscited by 17
  5. 2024Scalable DP-SGD: Shuffling vs. Poisson Subsamplingcited by 16
  6. 2022Edgeworth Accountant: An Analytical Approach to Differential Privacy Compositioncited by 14
  7. 2022Faster Privacy Accounting via Evolving Discretizationcited by 14
  8. 2023Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacycited by 14
  9. 2023Unified Enhancement of Privacy Bounds for Mixture Mechanisms via f-Differential Privacycited by 13
  10. 2024Balls-and-Bins Sampling for DP-SGDcited by 13
  11. 2025Privacy amplification by random allocationcited by 13
  12. 2024Avoiding Pitfalls for Privacy Accounting of Subsampled Mechanisms under Compositioncited by 12
  13. 2023A Randomized Approach for Tight Privacy Accountingcited by 11
  14. 2023Improving the Privacy and Practicality of Objective Perturbation for Differentially Private Linear Learnerscited by 11
  15. 2024Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimisationcited by 11
  16. 2023Privacy Loss of Noisy Stochastic Gradient Descent Might Converge Even for Non-Convex Lossescited by 10
  17. 2025InvisibleInk: High-Utility and Low-Cost Text Generation with Differential Privacycited by 10
  18. 2022Differentially Private Bootstrap: New Privacy Analysis and Inference Strategiescited by 9
  19. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  20. 2024Neural Collapse Meets Differential Privacy: Curious Behaviors of NoisyGD with Near-perfect Representation Learningcited by 8
  21. 2024Beyond the Calibration Point: Mechanism Comparison in Differential Privacycited by 8
  22. 2024A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theoremcited by 8
  23. 2021Generalization in the Face of Adaptivity: A Bayesian Perspectivecited by 7
  24. 2023On the accuracy and efficiency of group-wise clipping in differentially private optimizationcited by 7
  25. 2023Zero redundancy distributed learning with differential privacycited by 7
  26. 2024Differentially Private Stochastic Gradient Descent with Fixed-Size Minibatches: Tighter RDP Guarantees with or without Replacementcited by 7
  27. 2021Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliabilitycited by 6
  28. 2021DP-FP: Differentially Private Forward Propagation for Large Modelscited by 6
  29. 2024Auditing Differential Privacy Guarantees Using Density Estimationcited by 6
  30. 2024Attack-Aware Noise Calibration for Differential Privacycited by 6
  31. 2024To Shuffle or not to Shuffle: Auditing DP-SGD with Shufflingcited by 6
  32. 2025Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learningcited by 6
  33. 2022The Saddle-Point Accountant for Differential Privacycited by 5
  34. 2023Sparsity-Preserving Differentially Private Training of Large Embedding Modelscited by 5
  35. 2024Secure Aggregation is Not Private Against Membership Inference Attackscited by 5
  36. 2022Shuffle Gaussian Mechanism for Differential Privacycited by 4
  37. 2023Tractable MCMC for Private Learning with Pure and Gaussian Differential Privacycited by 4
  38. 2024The 2020 US Decennial Census is more private than you (might) thinkcited by 4

50 most cited of 83 All 83 (JSON)