A unified basis decomposition framework for addressing the federated learning trilemma: Communication-efficiency,...

Federated learning (FL) is confronted with a fundamental trilemma: simultaneously achieving communication efficiency, personalized adaptation, and privacy protection. Current approaches typically optimize one objective at the expense of the others, failing to provide a unified solution. To address this challenge, we propose Federated Basis Decomposition (FedBD), a unified framework that leverages layer-wise basis decomposition to achieve balanced optimization across all three dimensions. The key innovation lies in reformulating the learning process as a subspace optimization problem: each network layer is represented as a linear combination of globally shared basis models, enabling clients to exchange only low-dimensional scalar weights rather than full model parameters. FedBD directly resolves the trilemma by drastically reducing communication overhead through compact parameter transmission, while simultaneously enabling effective personalization by decoupling globally shared scalar weights from private local parameters including Batch Normalization statistics. Furthermore, the framework strengthens privacy protection by projecting raw gradients into a random basis subspace. We validate our framework on three medical imaging datasets. The results demonstrate that FedBD achieves an accuracy density gain of up to 9.73 × , effectively maintaining competitive accuracy with an order-of-magnitude reduction in communication overhead compared to conventional FL methods. Ultimately, FedBD offers a unified solution to the FL trilemma, paving the way for practical deployment in complex real-world scenarios.