Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs

2026-06-02

AI Summary

This work addresses the performance degradation of graph neural networks (GNNs) when transferring across scales on wireless conflict graphs modeled as sparse random geometric graphs. It establishes, for the first time, theoretical performance bounds for GNN generalization across conflict graphs of varying sizes. By analyzing the structural approximation between random geometric graphs and deterministic grid graphs, the study reveals a theoretical connection between graph topological similarity and model generalization capability. Guided by this theoretical insight, the proposed method significantly outperforms existing baselines in link scheduling tasks, with empirical results on large-scale scenarios further validating the tightness and practical relevance of the derived theoretical bounds.

Abstract

Graph Neural Networks (GNNs) have emerged as a powerful tool for wireless resource allocation that leverages the underlying graph structure of communication networks. Their transferability property enables models trained on small-scale graphs to generalize to large-scale deployments with little performance deterioration, a desirable property for currently growing networks. Wireless networks are sparse regimes, where a single node is connected to a small number of other users. This work establishes theoretical results for transferability of GNNs over graphs derived from sparse Random Geometric Graphs (RGGs). In particular, we focus on conflict graphs of RGGs used to model interference among links. Our approach considers the closeness between RGGs and Deterministic Grid Graphs (DGG) to establish bounds in the performance loss when a model is transferred across scales. We validate our theoretical findings through the problem of link scheduling, demonstrating that our learned policies consistently outperform existing benchmarks at scale. Finally, we examine the impact of our theoretical assumptions on empirical performance.

Problem

• Graph Neural Networks
• Transferability
• Random Geometric Graphs
• Wireless Conflict Graphs
• Resource Allocation

Innovation

• Graph Neural Networks
• Transferability
• Random Geometric Graphs
• Wireless Conflict Graphs
• Link Scheduling