Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916948506312704 |
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| author | Shin, Hyeju Vincent-Daniel Jung, Kyudan Yun, Seongwon |
| author_facet | Shin, Hyeju Vincent-Daniel Jung, Kyudan Yun, Seongwon |
| contents | Differential Privacy (DP) has emerged as a key framework for protecting sensitive data in machine learning, but standard DP-SGD often suffers from significant accuracy loss due to injected noise. To address this limitation, we introduce the FFT-Enhanced Kalman Filter (FFTKF), a differentially private optimization method that improves gradient quality while preserving $(\varepsilon, δ)$-DP guarantees. FFTKF applies frequency-domain filtering to shift privacy noise into less informative high-frequency components, preserving the low-frequency gradient signals that carry most learning information. A scalar-gain Kalman filter with a finite-difference Hessian approximation further refines the denoised gradients. The method has per-iteration complexity $\mathcal{O}(d \log d)$ and achieves higher test accuracy than DP-SGD and DiSK on MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet with CNNs, Wide ResNets, and Vision Transformers. Theoretical analysis shows that FFTKF ensures equivalent privacy while delivering a stronger privacy--utility trade-off through reduced variance and controlled bias. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_04468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy Shin, Hyeju Vincent-Daniel Jung, Kyudan Yun, Seongwon Machine Learning Artificial Intelligence Information Theory Neural and Evolutionary Computing Differential Privacy (DP) has emerged as a key framework for protecting sensitive data in machine learning, but standard DP-SGD often suffers from significant accuracy loss due to injected noise. To address this limitation, we introduce the FFT-Enhanced Kalman Filter (FFTKF), a differentially private optimization method that improves gradient quality while preserving $(\varepsilon, δ)$-DP guarantees. FFTKF applies frequency-domain filtering to shift privacy noise into less informative high-frequency components, preserving the low-frequency gradient signals that carry most learning information. A scalar-gain Kalman filter with a finite-difference Hessian approximation further refines the denoised gradients. The method has per-iteration complexity $\mathcal{O}(d \log d)$ and achieves higher test accuracy than DP-SGD and DiSK on MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet with CNNs, Wide ResNets, and Vision Transformers. Theoretical analysis shows that FFTKF ensures equivalent privacy while delivering a stronger privacy--utility trade-off through reduced variance and controlled bias. |
| title | Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy |
| topic | Machine Learning Artificial Intelligence Information Theory Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2505.04468 |