Over-the-Air Split Machine Learning in Wireless MIMO Networks

In split machine learning (ML), different partitions of a neural network (NN) are executed by different computing nodes, requiring a large amount of communication cost. As over-the-air computation (OAC) can efficiently implement all or part of the computation at the same time of communication, thus by substituting the wireless transmission in the traditional split ML framework with OAC, the communication load can be eased. In this paper, we propose to deploy split ML in a wireless multiple-input multiple-output (MIMO) communication network utilizing the intricate interplay between MIMO-based OAC and NN. The basic procedure of the OAC split ML system is first provided, and we show that the inter-layer connection in a NN of any size can be mathematically decomposed into a set of linear precoding and combining transformations over a MIMO channel carrying out multi-stream analog communication. The precoding and combining matrices which are regarded as trainable parameters, and the MIMO channel matrix, which are regarded as unknown (implicit) parameters, jointly serve as a fully connected layer of the NN. Most interestingly, the channel estimation procedure can be eliminated by exploiting the MIMO channel reciprocity of the forward and backward propagation, thus greatly saving the system costs and/or further improving its overall efficiency. The generalization of the proposed scheme to the conventional NNs is also introduced, i.e., the widely used convolutional NNs. We demonstrate its effectiveness under both the static and quasi-static memory channel conditions with comprehensive simulations.