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

TL;DR

This paper introduces SpecGap, a spectral gap-based method for graph-level out-of-distribution detection that leverages Laplacian eigenvalue differences to identify anomalous graphs, achieving state-of-the-art results.

Contribution

The paper proposes a novel, parameter-free post-hoc spectral gap method for graph OOD detection, supported by theoretical analysis and extensive empirical validation.

Findings

SpecGap outperforms existing methods on benchmark datasets.

Spectral gaps effectively distinguish in-distribution and OOD graphs.

The method is easy to integrate without retraining models.

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: \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., $\mathbf{X}-\left(\lambda_n-\lambda_{n-1}\right) \mathbf{u}_{n-1} \mathbf{v}_{n-1}^T$). 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.