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 frequency-domain perspective and empirically observe a "Spectral Bias of Drift": in the evaluated training trajectories, a disproportionate fraction of inter-client gradient disagreement is concentrated in the lower-frequency bands of the adopted structured parameter layout. Motivated by this observation, we propose SpecGradFilter, which suppresses a small low-frequency portion of selected layer gradients and can be implemented using an FFT-based projection or spatial-domain detrending approximations. For the FFT-based realization, we establish a conditional convergence guarantee when the projection retains sufficient global descent signal and the post-filtering client heterogeneity is bounded. Extensive experiments on CIFAR-10/100, Tiny-ImageNet, and additional benchmarks show improved accuracy and time-to-target in the tested non-IID settings without increasing the per-round communication payload.