SpecGradFilter: A Spectral Gradient Filtering Framework for Taming Federated Heterogeneity

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.

FedFFT: Taming Client Drift in Federated SAM via Spectral Perturbation Filtering

Federated Learning (FL) enables decentralized training without data sharing, but suffers from statistical heterogeneity across clients, leading to client drift, poor generalization, and sharp minima compared to centralized training. Sharpness-Aware Minimization (SAM) has emerged as a promising approach to improve generalization, yet its application in federated learning still suffers from divergence problems, since perturbations are computed locally and reflect client-specific loss geometries. To better understand this issue, we provide experimental evidence from a new perspective, the frequency domain, for SAM perturbations in federated settings, revealing that inter-client perturbation inconsistencies are predominantly concentrated in the low-frequency spectrum. Motivated by this insight, we propose Federated learning with Frequency-domain Filtering of SAM perturbations (FedFFT). It is a lightweight and plug-and-play method that filters out low-frequency components of SAM perturbations without requiring additional communication, thereby suppressing inconsistent components in client updates while preserving consistent learning signals. Extensive experiments across multiple benchmarks and diverse backbones demonstrate that FedFFT consistently outperforms SAM-based FL methods, particularly under severe non-IID distributions. These results highlight the effectiveness, scalability, and general applicability of our frequency-domain perspective for sharpness-aware federated optimization.