发表机构
Potsdam Institute for Climate Impact Research; Technical University of Berlin; University of Illinois at Chicago; Berlin Institute for the Foundations of Learning and Data (BIFOLD); Northwestern Polytechnical University; Fudan University; Humboldt University Berlin（波茨坦气候影响研究所; 柏林工业大学; 伊利诺伊大学芝加哥分校; 柏林学习与数据基础研究所; 西北工业大学; 复旦大学; 柏林洪堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对深度图神经网络过平滑问题，提出稳定性塑造的深度图学习（SDGL），利用主稳定性曲线刻画同步，通过图灵不稳定或近临界传播缓解过平滑，在多种基准上提升深度扩展和准确率。
AI 中文摘要
在深度图神经网络中，增加深度会扩大感受野，但往往导致过平滑，即节点表示趋于对齐。我们为深度GNN传播开发了一个统一的、模式化的稳定性框架，为过平滑提供了原则性的刻画。通过将层深度解释为时间、层更新解释为图耦合动力学，过平滑可以被理解为特征的一种不良动力学同步，主稳定性曲线为此提供了评估同步稳定性的理论工具。在该理论的指导下，我们进一步提出了稳定性塑造的深度图学习（SDGL）以缓解深度GNN中的过平滑问题。SDGL有两种互补的实例：一种诱导受控的图灵不稳定性，用空间模式形成取代同步；另一种维持稳定的近临界传播。在多种节点级和图级基准上的实验表明，与强基线相比，包括具有长程依赖的图，SDGL在深度扩展和一致的准确率提升上均有改进。
英文摘要
In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies.
