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.

本文提出了一种用于增强多输入多输出（MIMO）无线系统中联邦学习（FL）通信效率的新方法。该方法基于交替最小二乘算法，利用低秩矩阵分解策略对本地梯度压缩进行过空中计算和误差反馈。所提出的协议被称为空中低秩压缩（Ota-LC），在保证相同推理性能的同时，相比现有基准方案具有更低的计算成本和通信开销。以 Cifar-10 数据集为例，当目标测试准确度为 80% 时，Ota-LC 相比基准方案至少可以降低 30% 的总通信开销，并将计算复杂度的阶数降低到梯度维度之和的倍数。