利用拉普拉斯特征值差距检测图数据中的异常样本，无需训练即可用。
SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps
- 通过特征值差距调整高阶特征，捕捉图结构异常
- 在多个基准数据集上达到当前最优性能
- 无需训练、可直接嵌入现有模型，适合部署场景
图级分布外（OOD）检测对图神经网络在真实场景中的应用至关重要。本文观察到，分布内（ID）与分布外（OOD）图样本在拉普拉斯矩阵最大与次大特征值之间的关系存在显著差异：OOD样本常表现出异常的谱间隙（即最大与次大特征值之差）。基于此，我们提出SpecGap，一种高效的后处理式图级OOD检测方法。SpecGap通过将与次大特征值相关的分量按谱间隙缩放后从高阶特征中减去（形式为：$/mathbf{X}-ig(λ_n-λ_{n-1}ig) /mathbf{u}_{n-1} /mathbf{v}_{n-1}^T$），实现对异常图的识别。该方法在多个基准数据集上表现优异，并通过大量消融实验与理论分析验证了其有效性。作为无参数的后处理方法，SpecGap无需额外训练或模型修改，可轻松集成至现有图神经网络模型中。
原文摘要 · Abstract (English)
The task of graph-level out-of-distribution (OOD) detection is crucial for deploying graph neural networks in real-world settings. In this paper, we observe a significant difference in the relationship between the largest and second-largest eigenvalues of the Laplacian matrix for in-distribution (ID) and OOD graph samples: \textit{OOD samples often exhibit anomalous spectral gaps (the difference between the largest and second-largest eigenvalues)}. This observation motivates us to propose SpecGap, an effective post-hoc approach for OOD detection on graphs. SpecGap adjusts features by subtracting the component associated with the second-largest eigenvalue, scaled by the spectral gap, from the high-level features (i.e., $\mathbf{X}-\left(λ_n-λ_{n-1}\right) \mathbf{u}_{n-1} \mathbf{v}_{n-1}^T$). SpecGap achieves state-of-the-art performance across multiple benchmark datasets. We present extensive ablation studies and comprehensive theoretical analyses to support our empirical results. As a parameter-free post-hoc method, SpecGap can be easily integrated into existing graph neural network models without requiring any additional training or model modification.
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