  Deep learning-based approaches have been developed to solve challenging
problems in wireless communications, leading to promising results. Early
attempts adopted neural network architectures inherited from applications such
as computer vision. They often yield poor performance in large scale networks
(i.e., poor scalability) and unseen network settings (i.e., poor
generalization). To resolve these issues, graph neural networks (GNNs) have
been recently adopted, as they can effectively exploit the domain knowledge,
i.e., the graph topology in wireless communications problems. GNN-based methods
can achieve near-optimal performance in large-scale networks and generalize
well under different system settings, but the theoretical underpinnings and
design guidelines remain elusive, which may hinder their practical
implementations. This paper endeavors to fill both the theoretical and
practical gaps. For theoretical guarantees, we prove that GNNs achieve
near-optimal performance in wireless networks with much fewer training samples
than traditional neural architectures. Specifically, to solve an optimization
problem on an $n$-node graph (where the nodes may represent users, base
stations, or antennas), GNNs' generalization error and required number of
training samples are $\mathcal{O}(n)$ and $\mathcal{O}(n^2)$ times lower than
the unstructured multi-layer perceptrons. For design guidelines, we propose a
unified framework that is applicable to general design problems in wireless
networks, which includes graph modeling, neural architecture design, and
theory-guided performance enhancement. Extensive simulations, which cover a
variety of important problems and network settings, verify our theory and the
effectiveness of the proposed design framework.
