---
title: "SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps"
authors:
  - "Jiawei Gu"
  - "Ziyue Qiao"
  - "Zechao Li"
doi: "10.24963/ijcai.2025/584"
url: "https://ijcai.org/proceedings/2025/584"
pdf: "https://ijcai.org/proceedings/2025/0584.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "5244-5252"
track: "Main Track"
keywords:
  - "Machine Learning: ML: Open-World/Open-Set/OOD Learning"
---

# SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps

Jiawei Gu, Ziyue Qiao, Zechao Li

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 5244-5252. DOI: [10.24963/ijcai.2025/584](https://doi.org/10.24963/ijcai.2025/584)

## Abstract

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: 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., X - (λn - λn-1) u_n-1 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.