通过图拓扑分析神经网络激活模式，发现其与曲率关系不如预期紧密。
Probing Graph Neural Network Activation Patterns Through Graph Topology
- 用极端边激活值探测图神经网络的注意力偏好
- 在分子数据集上，激活不集中在曲率极值区域
- 长程图基准中全局注意力加剧了拓扑瓶颈
图的曲率理论可描述图的拓扑结构，揭示信息流动的瓶颈和密集连接区。图神经网络中的消息传递范式导致的过平滑与过挤压现象，常被认为与这些区域有关。然而，图拓扑如何影响GNN的学习偏好尚不明确。本文通过大规模激活（Massive Activations，对应图变压器中的极端边激活值）来探查这种关联。在合成图和分子基准测试中，发现大规模激活并未集中于曲率极值处，尽管理论上二者与信息流相关。在长程图基准上，识别出系统性曲率偏移：全局注意力机制加剧了拓扑瓶颈，使负曲率出现频率显著上升。本研究将曲率重新定义为诊断图学习失败时机与原因的工具。
原文摘要 · Abstract (English)
Curvature notions on graphs provide a theoretical description of graph topology, highlighting bottlenecks and denser connected regions. Artifacts of the message passing paradigm in Graph Neural Networks, such as oversmoothing and oversquashing, have been attributed to these regions. However, it remains unclear how the topology of a graph interacts with the learned preferences of GNNs. Through Massive Activations, which correspond to extreme edge activation values in Graph Transformers, we probe this correspondence. Our findings on synthetic graphs and molecular benchmarks reveal that MAs do not preferentially concentrate on curvature extremes, despite their theoretical link to information flow. On the Long Range Graph Benchmark, we identify a systemic \textit{curvature shift}: global attention mechanisms exacerbate topological bottlenecks, drastically increasing the prevalence of negative curvature. Our work reframes curvature as a diagnostic probe for understanding when and why graph learning fails.
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