Progressive Geometry Alignment for Heterogeneous Federated Learning

Statistical heterogeneity remains a fundamental challenge in federated learning, often leading to inconsistent representations across clients, thereby hindering global generalization. We identify an important optimization pathway behind this inconsistency: under conventional joint local optimization, classifiers co-adapt with heterogeneous client data, creating client-specific discriminative geometries that introduce an additional source of representation-gradient deviation. This motivates explicitly controlling the influence of client-specific decision structures on representation learning. Based on this principle, we propose FedVGA, which coordinates representation learning under a shared classifier-induced geometry and allows locally adapted decision structures to influence future representations only after server-side consolidation. FedVGA progressively refines this shared geometry, represented as a spherical Voronoi configuration, through a global–local–global loop consisting of Align-and-Adapt and Geometry-Confidence Aggregation. We theoretically characterize geometry-induced representation-gradient deviation and local-to-global geometry error propagation. Experiments under both label and feature heterogeneity demonstrate consistent performance gains, progressive geometric alignment, and pronounced improvements on boundary-sensitive samples.