可达性并不足够：诊断图神经网络中的长程行为
Reachability is not enough: Diagnosing long-range behavior in GNNs
- UiT The Arctic University of Norway（挪威北极大学）
- NORCE Norwegian Research Centre（NORCE挪威研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出诊断框架，揭示GNN长程能力不仅依赖架构可达性，更取决于学习并保持对远距离信息的有效利用。
AI中文摘要：
图神经网络（GNNs）常被称为长程模型，因为其架构能够连接远距离节点，但这并不能表明它们是否正确利用了远距离信息。我们引入了一个框架，用于衡量每个图距离上的输入对预测的影响强度，并区分了由架构、有限近似、训练和数值执行所带来的限制。我们的分析表明，局部消息传递可能缓慢地传播影响，因此即使理想计算使用整个图，有限实现也可能主要依赖附近输入。我们还解释了为什么数学上等价的滤波器在学习难易程度和运行可靠性上会有所不同。在受控任务中，具有相似架构可达性的模型在利用远距离信息方面差异显著，而低平均误差可能掩盖远距离交互上的失败。综合这些结果，长程能力取决于学习在任务所需距离上使用信息，并在计算过程中保持这种使用。
英文摘要：
Graph neural networks (GNNs) are often called long-range because their architecture can connect distant nodes, but this does not show whether they use distant information correctly. We introduce a framework that measures how strongly inputs at each graph distance affect predictions and separates limitations due to architecture, finite approximation, training, and numerical execution. Our analysis shows that local message-passing can spread influence slowly, so a finite implementation may rely mainly on nearby inputs even when the ideal computation uses the whole graph. We also explain why mathematically equivalent filters can differ in how easily they are learned and how reliably they run. Across controlled tasks, models with similar architectural reach use distant information very differently, while low average error can hide failures on distant interactions. Together, these results show that long-range capability depends on learning to use information at the distances required by the task and preserving that use during computation.
