Scalability of Graph Neural Network Policies in Wireless Communication Networks

RESUMO

Graph Neural Networks (GNNs) offer scalable solutions for wireless resource allocation, yet existing formal performance guarantees across varying scales for spatial and sparse graphs do not directly apply to these settings. Scalability theories rely on dense graphon limits or continuous manifold approximations, both of which fail under the sparse, bounded-degree regimes and Euclidean metric constraints of physical wireless environments. This paper establishes a theoretical framework for GNN transferability over sparse Random Geometric Graphs (RGGs), capturing distance-dependent channel decay and spatial interference. We model sparse RGGs as spatial perturbations of regular Deterministic Grid Graphs (DGGs) and employ spatial windowing operators to compare networks across differing scales. Assuming Lipschitz continuity of GNN architectures and signal stationarity, we prove scalability over DGGs and bound same-scale transferability between DGGs and RGGs. Combining these results establishes formal scalability bounds across sparse RGG topologies. Finally, we extend this framework to conflict graph models, deriving equivalent scalability guarantees for link-level resource allocation policies. We verify our results for scalability with two experiment settings: power allocation and wireless link scheduling. The simulations show GNNs exhibit the expected scalable behavior, and analyze the relevance of our theoretical assumptions in practical deployment.