Implementing Graph Neural Networks Over Wireless Networks via Over-the-Air Computing: A Joint Communication and Computation Framework

A Graph Neural Network (GNN) conducts the graph convolution for structured data and obtains the weighted sum over the vertices according to its graph structure. However, in the context of a wireless network, the traditional separate implementation of a GNN usually requires the full channel state information, which is hard to obtain in practice, especially for the underlying interference channels. On the other hand, Over-the-Air Computing (OAC) is an efficient analog wireless technique in which the weighted sum can be simultaneously calculated over an equivalent wireless superposition channel. Since the main goal of a distributed learning-based system is the fulfillment of the overall learning task instead of its communication rate, OAC is of great potential for implementing such a system. In this article, we exploit some specific features of the wireless interference graphs and propose a novel task-ori-ented OAC-based framework to deploy GNNs more efficiently in wireless networks. In particu-lar, we take advantage of the structural similarity between OAC and the graph convolution oper-ation over an interference graph, and the chan-nel prediction procedure can be merged into the weight updating procedure. Moreover, the inher-ent noise tolerance of a neural network further ensures its convergence and performance. We also conduct case studies based on the proposed framework and discuss the comprehensive future research directions and open problems.