Interweaving Topology and Spectrum: Federated Spectral-Guided Riemannian Graph Learning

Federated Graph Learning (FGL) enables collaborative model training on distributed graph data while preserving privacy. However, structural and frequency heterogeneity across clients induces two critical challenges: local embedding distortion in flat Euclidean spaces, and global knowledge collapse caused by entangling disparate spatial topologies with spectral features. To address these challenges, we propose Federated Spectral-Guided Riemannian Graph Learning (FedSGR), a novel framework that systematically interweaves spatial topological structures with frequency domain signals. Specifically, FedSGR eliminates embedding distortion by establishing personalized product manifolds with mixed curvature tailored to local topologies. Concurrently, it circumvents knowledge collapse by distilling domain invariant frequency patterns globally, which are adaptively fused with local curvature features to steer personalized message passing directly on mixed manifolds. Extensive experiments on various graph benchmarks demonstrate that FedSGR consistently surpasses state-of-the-art FGL methods, exhibiting superior predictive accuracy and robust personalized adaptation.