Approximate Differential Privacy of the ℓ2 Mechanism

Matthew Joseph, Alex Kulesza, Alexander Yu
2/14/2026

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Abstract

We study the $\ell_2$ mechanism for computing a $d$-dimensional statistic with bounded $\ell_2$ sensitivity under approximate differential privacy. Across a range of privacy parameters, we find that the $\ell_2$ mechanism obtains lower error than the Laplace and Gaussian mechanisms, matching the former at $d=1$ and approaching the latter as $d \to \infty$.

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Cite this paper

@article{joseph2026approximate,
  title  = {Approximate Differential Privacy of the ℓ2 Mechanism},
  author = {Matthew Joseph and Alex Kulesza and Alexander Yu},
  year   = {2026},
  eprint = {2502.15929},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2502.15929},
  journal = {ICML 2025 2025}
}

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