探究图神经网络为何因输入图结构而受限
Are GNNs doomed by the topology of their input graph?
- 提出k跳相似性概念，分析局部结构如何影响消息传递
- 发现局部相似邻域可能导致节点表示趋同或学习失效
- 揭示图拓扑对模型性能的深层影响，适合图学习研究者
图神经网络（GNNs）在图结构数据上表现出色，但其输入图的拓扑特性对GNN行为的影响尚不明确。本文研究GNN是否因输入图结构而存在固有局限，聚焦局部拓扑特征与消息传递机制的交互，如何引发全局现象如过平滑或表达性表征。我们引入k-hop相似性概念，探究局部相似邻域是否导致一致的节点表示。这种交互可能促进有效学习，也可能导致不可避免的过平滑，具体取决于图的内在属性。实证实验验证了这些见解，凸显图拓扑对GNN性能的实际影响。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, the influence of the input graph's topology on GNN behavior remains poorly understood. In this work, we explore whether GNNs are inherently limited by the structure of their input graphs, focusing on how local topological features interact with the message-passing scheme to produce global phenomena such as oversmoothing or expressive representations. We introduce the concept of $k$-hop similarity and investigate whether locally similar neighborhoods lead to consistent node representations. This interaction can result in either effective learning or inevitable oversmoothing, depending on the inherent properties of the graph. Our empirical experiments validate these insights, highlighting the practical implications of graph topology on GNN performance.
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