Multidimensional Graph Neural Networks for Wireless Communications

Graph neural networks (GNNs) can improve the efficiency of learning wireless policies by leveraging their permutation properties and topology prior. While mismatched permutation property to a policy may degrade the learning performance and overlooked permutations incurs low sample efficiency, there is still lacking a systematical approach for modeling graph and designing structure of GNNs to harness all permutation properties. Moreover, the information of input feature may lose during updating hidden representations with GNNs, which leads to poor learning performance. In this paper, we propose a unified framework to learn permutable wireless policies with multidimensional GNNs, which update the hidden representations of hyper-edges to avoid the information loss. We provide a method to construct graph for a policy, over which a GNN with proper parameter sharing can exploit all possible permutations of the policy. We also investigate the permutability of wireless channels that affects the sample efficiency, and show how to trade off the training, inference, and design complexities of GNNs. To showcase how to design the GNNs within the framework, we consider precoding optimization in different systems. Simulation results validate the gain of the proposed GNNs over existing counterparts from exploiting the permutation prior and avoiding the information loss.