Spectral and Temporal Denoising for Differentially Private Optimization

This paper introduces the FFT-Enhanced Kalman Filter (FFTKF), a differentially private optimization method that addresses the challenge of preserving performance in DP-SGD, where added noise typically degrades model utility. FFTKF integrates frequency-domain noise shaping with Kalman filtering to enhance gradient quality while preserving $(\varepsilon, \delta)$-DP guarantees. It employs a high-frequency shaping mask in the Fourier domain to concentrate differential privacy noise in less informative spectral components, preserving low-frequency gradient signals. A scalar-gain Kalman filter with finite-difference Hessian approximation further refines the denoised gradients. With a per-iteration complexity of $\mathcal{O}(d \log d)$, FFTKF demonstrates improved test accuracy over DP-SGD and DiSK across MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets using CNNs, Wide ResNets, and Vision Transformers. Theoretical analysis confirms that FFTKF maintains equivalent privacy guarantees while achieving a tighter privacy-utility trade-off through reduced noise and controlled bias.

@article{shin2025_2505.04468,
  title={ Spectral and Temporal Denoising for Differentially Private Optimization },
  author={ Hyeju Shin and Kyudan Jung and Seongwon Yun and Juyoung Yun },
  journal={arXiv preprint arXiv:2505.04468},
  year={ 2025 }
}