Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration

Graph Federated Learning (GFL) enables collaborative representation learning across distributed subgraphs while preserving privacy. However, heterogeneity remains a critical challenge, as subgraphs across clients typically differ significantly in both semantics and structures. Existing methods address heterogeneity by enforcing the rigid alignment of model parameters or prototypes between clients and the server. However, these alignments implicitly rely on a restrictive global linearity assumption that summarizes local data distributions using a single and globally consistent representation space. This severely compresses the personalized representation space of clients and fails to preserve diverse local graph distributions. To overcome these limitations, we propose Federated Graph Manifold Calibration (FedGMC), a novel paradigm that tackles semantic heterogeneity and structural heterogeneity from a unified manifold perspective. Instead of enforcing rigid alignment, FedGMC introduces a dual manifold calibration mechanism that preserves global commonalities while maximizing the personalized representation space of local clients. 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 homophilic and heterophilic graphs demonstrate that FedGMC effectively balances global commonality and local personalization, thereby significantly outperforming state-of-the-art baseline methods.