# Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy

arXiv: https://arxiv.org/abs/2505.04468 · HTML: https://mlsanity.com/paper/2505.04468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 14 of 14)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [AdaCliP: Adaptive Clipping for Private SGD](https://mlsanity.com/paper/1908.07643/) (2019)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [DP-AdamBC: Your DP-Adam Is Actually DP-SGD (Unless You Apply Bias Correction)](https://mlsanity.com/paper/2312.14334/) (2023)
- [DiSK: Differentially Private Optimizer with Simplified Kalman Filter for Noise Reduction](https://mlsanity.com/paper/2410.03883/) (2024)
- [On the utility and protection of optimization with differential privacy and classic regularization techniques](https://mlsanity.com/paper/2209.03175/) (2022)
- [DOPPLER: Differentially Private Optimizers with Low-pass Filter for Privacy Noise Reduction](https://mlsanity.com/paper/2408.13460/) (2024)
- [On the Convergence of DP-SGD with Adaptive Clipping](https://mlsanity.com/paper/2412.19916/) (2024)
- [An Adaptive Differential Privacy Method Based on Federated Learning](https://mlsanity.com/paper/2408.08909/) (2024)
- [Spectral diagonal ensemble Kalman filters](https://mlsanity.com/paper/1501.00219/) (2014)
- [Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes](https://mlsanity.com/paper/2111.03617/) (2021)

## Abstract (arXiv)

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 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.