FedC²: From Client Compatibility to Class Complementarity for Federated Learning from Label Proportions

Federated learning from label proportions (Fed-LLP) aims to learn instance-level predictors from distributed clients whose local bags are supervised only by class proportions. Existing LLP methods mainly focus on extracting supervision from aggregate proportions, while federated learning methods typically address client heterogeneity under standard instance-level supervision. However, in Fed-LLP, aggregate supervision is further complicated by substantial client heterogeneity, while the absence of instance-level labels makes such heterogeneity harder to characterize and exploit. Towards this end, we propose FedC², a hierarchical collaboration framework that organizes cross-client knowledge sharing from client compatibility to class-wise complementarity. FedC² first constructs a target-specific collaboration base from the geometry of clients’ observed bag-proportion sets, and then conservatively refines class-wise collaborator contributions according to target-relative coverage and local proportion consistency. We further provide a theoretical analysis characterizing when the resulting hierarchical reweighting tightens class-specific aggregation-error bounds. Extensive experiments across four benchmarks and three levels of client heterogeneity show that FedC² achieves the best accuracy in 10 of 12 settings against representative LLP-based, generic FL, and personalized FL methods. Further analyses support the effectiveness, generality, and transfer relevance of the proposed hierarchical collaboration strategy. A quick visual overview of this work is available at [https://fdletf7qxe.github.io](https://fdletf7qxe.github.io).