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.

翻译：本文提出了一种新颖方法，用于提升多输入多输出（MIMO）无线系统中联邦学习（FL）的通信效率。该方法核心基于交替最小二乘法的低秩矩阵分解策略，用于局部梯度压缩，并结合了空中计算与误差反馈机制。所提出的协议，称为空中低秩压缩（Ota-LC），被证明相较于现有基准方法具有更低计算开销和通信开销，同时保证相同推理性能。以Cifar-10数据集上达到80%测试准确率目标为例，Ota-LC相较于基准方案实现了至少30%的总通信成本降低，同时计算复杂度阶数降低了梯度维度之和的倍数。