To improve the training efficiency of federated learning (FL), previous research has employed low-rank decomposition techniques to reduce communication overhead. In this paper, we seek to enhance the performance of these low-rank decomposition methods. Specifically, we focus on three key issues related to decomposition in FL: what to decompose, how to decompose, and how to aggregate. Subsequently, we introduce three novel techniques: Model Update Decomposition (MUD), Block-wise Kronecker Decomposition (BKD), and Aggregation-Aware Decomposition (AAD), each targeting a specific issue. These techniques are complementary and can be applied simultaneously to achieve optimal performance. Additionally, we provide a rigorous theoretical analysis to ensure the convergence of the proposed MUD. Extensive experimental results show that our approach achieves faster convergence and superior accuracy compared to relevant baseline methods. The code is available at https://github.com/Leopold1423/fedmud-icml25.

Federated Learning (FL) allows devices like smartphones to collaboratively train models without sharing their private data. However, frequent communication of model updates between devices and the central server creates a major bottleneck, especially with large models or slow networks. Researchers have tried compressing these updates using a technique called low-rank decomposition, but existing methods still suffer from inefficiencies and approximation errors.In our work, we identify three fundamental questions: what to compress, how to compress, and how to combine the compressed results. Further, we propose three new techniques, Model Update Decomposition (MUD), Block-wise Kronecker Decomposition (BKD), and Aggregation-Aware Decomposition (AAD), that target each of these challenges. Together, they reduce communication costs while preserving model accuracy.Our approach not only speeds up training but also achieves better results than current state-of-the-art methods. This has the potential to make privacy-preserving federated training more practical and efficient, especially in real-world settings with limited bandwidth or energy constraints.