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In split machine learning (ML), different partitions of a neural network (NN)are executed by different computing nodes, requiring a large amount ofcommunication cost. To ease communication burden, over-the-air computation(OAC) can efficiently implement all or part of the computation at the same timeof communication. Based on the proposed system, the system implementation overwireless network is introduced and we provide the problem formulation. Inparticular, we show that the inter-layer connection in a NN of any size can bemathematically decomposed into a set of linear precoding and combiningtransformations over MIMO channels. Therefore, the precoding matrix at thetransmitter and the combining matrix at the receiver of each MIMO link, as wellas the channel matrix itself, can jointly serve as a fully connected layer ofthe NN. The generalization of the proposed scheme to the conventional NNs isalso introduced. Finally, we extend the proposed scheme to the widely usedconvolutional neural networks and demonstrate its effectiveness under both thestatic and quasi-static memory channel conditions with comprehensivesimulations. In such a split ML system, the precoding and combining matricesare regarded as trainable parameters, while MIMO channel matrix is regarded asunknown (implicit) parameters.

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