SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps
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| Format: | Preprint |
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2025
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| _version_ | 1866913854491983872 |
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| author | Gu, Jiawei Qiao, Ziyue Li, Zechao |
| author_facet | Gu, Jiawei Qiao, Ziyue Li, Zechao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps Gu, Jiawei Qiao, Ziyue Li, Zechao Machine Learning 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. |
| title | SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.15177 |