Communication-Efficient Federated Learning Based on a Two-Stage Adaptive Basis Matrix for Gradient Compression

Abstract

Federated learning (FL) faces significant communication overhead due to the repeated exchange of large gradient tensors between clients and the server. While existing compression techniques, such as sparsification and quantization, help reduce this cost, they often result in information loss, which can negatively impact model accuracy. In this work, we propose TDGC-FL, a communication-efficient federated learning framework based on a two-stage adaptive basis matrix for gradient compression, which simultaneously minimizes transmission volume and preserves model accuracy. compression to simultaneously minimize transmission volume and maintain accuracy. TDGC-FL decomposes aggregated gradients on the server, extracts compact basis matrices, and transmits them to clients, which then approximate their gradients and return only low-dimensional coefficient matrices. An adaptive update mechanism, driven by a multi-factor mixed error metric, ensures that the basis matrices remain accurate throughout the training process. Extensive experiments on MNIST, FMNIST, CIFAR10, and SVHN show that TDGC-FL reduces communication overhead by up to 82.83% compared to FedAvg, and by 37.70%–73.53% relative to FedPAQ, QSGD, Topk, and Mask, while consistently achieving higher model accuracy, demonstrating that TDGC-FL effectively addresses the accuracy–efficiency trade-off, thus enabling federated learning to achieve scalability and high performance in bandwidth-constrained environments.