Low-Rank Gradient Compression with Error Feedback for MIMO Wireless Federated Learning

This paper presents a novel approach to enhance the communication efficiency of federated learning (FL) in multiple input and multiple output (MIMO) wireless systems. The proposed method centers on a low-rank matrix factorization strategy for local gradient compression based on alternating least squares, along with over-the-air computation and error feedback. The proposed protocol, termed over-the-air low-rank compression (Ota-LC), is demonstrated to have lower computation cost and lower communication overhead as compared to existing benchmarks while guaranteeing the same inference performance. As an example, when targeting a test accuracy of 80% on the Cifar-10 dataset, Ota-LC achieves a reduction in total communication costs of at least 30% when contrasted with benchmark schemes, while also reducing the computational complexity order by a factor equal to the sum of the dimension of the gradients.