理论证明GNN在无线冲突图上跨尺度迁移的性能稳定性
Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs
- 用随机几何图与确定性网格图的接近度分析GNN迁移边界
- 实测表明跨规模调度策略优于现有基准，性能损失可控
- 适合研究无线资源分配与图神经网络泛化性的研究人员
图神经网络（GNN）已成为利用通信网络底层图结构进行无线资源分配的强大工具。其可迁移性使在小规模图上训练的模型能在大规模部署中保持良好性能，这对快速扩展的网络极具价值。无线网络处于稀疏场景，单个节点仅与少数其他用户相连。本文针对由稀疏随机几何图（RGG）生成的冲突图，建立GNN可迁移性的理论结果。重点分析了RGG与确定性网格图（DGG）之间的相似性，以推导模型跨尺度迁移时的性能损失上限。通过链路调度任务验证理论结论，表明所学策略在大尺度下持续优于现有基准。最后，考察了理论假设对实际性能的影响。
原文摘要 · Abstract (English)
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.
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