通过能量引导平滑性提升图神经网络抗噪声能力
Energy Guided smoothness to improve Robustness in Graph Classification
- 引入狄利克雷能量最小化作为新的归纳偏置，增强节点表示平滑性
- 在低阶图、标签覆盖率低等场景下，显著提升模型鲁棒性
- 方法不损害无噪声数据表现，适合实际中有标签噪声的图分类任务
图神经网络（GNN）在图分类任务中表现强大，但实际应用常面临标签噪声问题。本文研究了GNN对标签噪声的鲁棒性，发现模型在低阶图、标签覆盖不足或过参数化时易失效。我们建立了GNN鲁棒性与学习到的节点表示总狄利克雷能量降低之间的实证与理论关联，揭示了平滑性归纳偏置的作用。为此，提出两种训练策略：（1）通过移除权重矩阵中的负特征值引入新归纳偏置，与狄利克雷能量最小化相关；（2）扩展一种促进学习平滑性的损失惩罚项。两种方法在无噪声情况下均不损害性能，支持了GNN鲁棒性源于其平滑性归纳偏置的假设。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to generalise on low-order graphs, low label coverage, or when a model is over-parameterized. We establish both empirical and theoretical links between GNN robustness and the reduction of the total Dirichlet Energy of learned node representations, which encapsulates the hypothesized GNN smoothness inductive bias. Finally, we introduce two training strategies to enhance GNN robustness: (1) by incorporating a novel inductive bias in the weight matrices through the removal of negative eigenvalues, connected to Dirichlet Energy minimization; (2) by extending to GNNs a loss penalty that promotes learned smoothness. Importantly, neither approach negatively impacts performance in noise-free settings, supporting our hypothesis that the source of GNNs robustness is their smoothness inductive bias.
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