Deep Learning under Fractional-Order Differential Privacy
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| Format: | Preprint |
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2026
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| _version_ | 1866918493899718656 |
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| author | Partohaghighi, Mohammad Marcia, Roummel |
| author_facet | Partohaghighi, Mohammad Marcia, Roummel |
| contents | Differentially private stochastic gradient descent (DP-SGD) is a standard approach to privacy-preserving learning based on per-example clipping, subsampling, Gaussian perturbation, and privacy accounting. Classical DP-SGD releases a noisy version of the current clipped subsampled gradient sum. We propose Fractional-Order Differentially Private Stochastic Gradient Descent (\textbf{FO-DP-SGD}), a mechanism-level extension that replaces this current-only query, before Gaussian noise is added, with a fractional recursive query combining the current clipped sum with a finite-window, power-law-weighted aggregation of previously released private sum-level outputs. This injects fractional memory into the release mechanism while preserving the standard \emph{sum-then-noise-then-divide} structure.
Under add/remove adjacency with Poisson subsampling, the current-step sensitivity analysis shows that the only newly data-dependent term is the scaled current clipped sum. Hence, conditioned on the private history, the effective \(\ell_2\)-sensitivity is at most \(βC\), where \(C\) is the clipping threshold and \(β\in(0,1]\) controls the current-step contribution. Thus, FO-DP-SGD admits standard per-step Rényi differential privacy accounting via a Poisson-subsampled Gaussian mechanism with effective noise-to-sensitivity ratio \(σ/β\), and composes to yield overall \((\varepsilon,δ)\)-differential privacy guarantees.
FO-DP-SGD provides a framework for studying long-memory effects in private optimization. The fractional order, memory window, and mixing coefficient govern the trade-off among current-step sensitivity, signal retention, and private-history influence. Experiments on SVHN, CIFAR-10, and CIFAR-100 show improved test accuracy and privacy--utility performance over DP-SGD and private baselines including DP-Adam, DP-IS, SA-DP-SGD, ADP-AdamW, DP-SAT, and DP-Adam-AC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09890 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deep Learning under Fractional-Order Differential Privacy Partohaghighi, Mohammad Marcia, Roummel Cryptography and Security Machine Learning Differentially private stochastic gradient descent (DP-SGD) is a standard approach to privacy-preserving learning based on per-example clipping, subsampling, Gaussian perturbation, and privacy accounting. Classical DP-SGD releases a noisy version of the current clipped subsampled gradient sum. We propose Fractional-Order Differentially Private Stochastic Gradient Descent (\textbf{FO-DP-SGD}), a mechanism-level extension that replaces this current-only query, before Gaussian noise is added, with a fractional recursive query combining the current clipped sum with a finite-window, power-law-weighted aggregation of previously released private sum-level outputs. This injects fractional memory into the release mechanism while preserving the standard \emph{sum-then-noise-then-divide} structure. Under add/remove adjacency with Poisson subsampling, the current-step sensitivity analysis shows that the only newly data-dependent term is the scaled current clipped sum. Hence, conditioned on the private history, the effective \(\ell_2\)-sensitivity is at most \(βC\), where \(C\) is the clipping threshold and \(β\in(0,1]\) controls the current-step contribution. Thus, FO-DP-SGD admits standard per-step Rényi differential privacy accounting via a Poisson-subsampled Gaussian mechanism with effective noise-to-sensitivity ratio \(σ/β\), and composes to yield overall \((\varepsilon,δ)\)-differential privacy guarantees. FO-DP-SGD provides a framework for studying long-memory effects in private optimization. The fractional order, memory window, and mixing coefficient govern the trade-off among current-step sensitivity, signal retention, and private-history influence. Experiments on SVHN, CIFAR-10, and CIFAR-100 show improved test accuracy and privacy--utility performance over DP-SGD and private baselines including DP-Adam, DP-IS, SA-DP-SGD, ADP-AdamW, DP-SAT, and DP-Adam-AC. |
| title | Deep Learning under Fractional-Order Differential Privacy |
| topic | Cryptography and Security Machine Learning |
| url | https://arxiv.org/abs/2605.09890 |