Geometry-Regularized Collapse Resistance via Consensus Enhancement for Federated Learning

Knowledge distillation provides shared semantic supervision for local training in federated learning, reducing the tendency of client models to overfit their own data distributions. Existing methods construct a global knowledge repository from client-uploaded local information to establish consensus across clients. However, global knowledge that is fundamentally derived from client data inevitably contains local biases under heterogeneous settings. To address this issue, this study proposes a geometry-regularized cross-silo consensus enhancement method, termed RISE, which improves collapse resistance in federated learning by preserving pre-trained geometric consensus priors during local adaptation. Specifically, RISE introduces two complementary geometry regularizers. The Biased Low-dimensional Subspace Correction module preserves the spectral energy profile of pre-trained representations by constraining the energy distribution of adapted features within the principal representation subspace. Instead of enforcing direction-wise alignment, it discourages excessive energy concentration along a few dominant components, thereby mitigating biased low-dimensional feature collapse. The Manifold Relation Graph Alignment module regularizes the relational manifold geometry by constructing a transferable inter-class topology from pre-trained global class prototypes and aligning client-side class structures with this global relation, thereby mitigating class representation drift and stabilizing global aggregation. Extensive experiments on eight benchmark datasets across two tasks demonstrate that RISE improves cross-client consensus consistency and enhances the generalization ability of the global model, outperforming eight state-of-the-art methods.