图神经网络策略在无线通信网络中的可扩展性

中文摘要 AI 辅助

图神经网络（GNNs）为无线资源分配提供了可扩展的解决方案，然而，现有针对空间图和稀疏图在不同规模下的形式化性能保证并不能直接适用于这些场景。可扩展性理论依赖于稠密图极限或连续流形近似，这两种方法在物理无线环境的稀疏、有界度机制和欧几里得度量约束下均失效。本文建立了一个针对稀疏随机几何图（RGGs）上GNN可转移性的理论框架，捕捉了距离相关的信道衰减和空间干扰。我们将稀疏RGGs建模为规则确定性网格图（DGGs）的空间扰动，并采用空间窗口算子来比较不同规模下的网络。假设GNN架构具有Lipschitz连续性且信号具有平稳性，我们证明了在DGGs上的可扩展性，并界定了DGGs与RGGs之间同规模的可转移性。结合这些结果，我们建立了跨越稀疏RGG拓扑的正式可扩展性界限。最后，我们将此框架扩展到冲突图模型，为链路级资源分配策略推导出等效的可扩展性保证。我们通过两个实验设置验证了我们的可扩展性结果：功率分配和无线链路调度。仿真表明GNNs表现出预期的可扩展行为，并分析了我们的理论假设在实际部署中的相关性。

英文摘要

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.

发表机构

• University of Pennsylvania（宾夕法尼亚大学）
• Washington University in St. Louis（华盛顿大学圣路易斯分校）

机构由 AI 辅助整理，请以论文原文为准。