Dual Manifold Calibration for Graph Federated Learning

Graph Federated Learning (GFL) enables collaborative representation learning across distributed graphs while preserving privacy. However, heterogeneity remains a critical challenge, as graphs across clients typically differ significantly in both semantics and structures. Existing methods address semantic heterogeneity and structural heterogeneity by enforcing the alignments of prototypes and spectral characteristics between clients and the server, respectively. However, these alignments implicitly enforce identical local representations across clients, which significantly compresses the personalized representation space of clients. To overcome these limitations, we propose $\underline{\text{Fed}}$erated $\underline{\text{G}}$raph $\underline{\text{M}}$anifold $\underline{\text{C}}$alibration (FedGMC), a novel paradigm that tackles semantic heterogeneity and structural heterogeneity from a unified manifold perspective. Instead of enforcing identical local representations, FedGMC introduces a dual manifold calibration mechanism that allows each client to establish client-specific correspondences with globally shared semantic and structural references. Specifically, for semantic heterogeneity, the server constructs a geometrically optimal semantic manifold via equidistant semantic anchors, so as to guide the calibration of local semantic manifolds. For structural heterogeneity, the server constructs a global structural manifold by building global structural templates, so as to guide the calibration of local structural manifolds. Finally, the server dynamically refines both global semantic manifolds and structural manifolds by aggregating local manifolds. Extensive experiments on eleven datasets demonstrate that FedGMC effectively balances global commonality and local personalization, thereby significantly outperforming eleven state-of-the-art methods. Our code is available at https://anonymous.4open.science/r/FedGMC.