An Energy-centric Framework for Category-free Out-of-distribution Node Detection in Graphs

Graph neural networks have garnered notable attention for effectively processing graph-structured data. Prevalent models prioritize improving in-distribution (IND) data performance, frequently overlooking the risks from potential out-of-distribution (OOD) nodes during training and inference. In real-world graphs, the automated network construction can introduce noisy nodes from unknown distributions. Previous research into OOD node detection, typically referred to as entropy-based methods, calculates OOD measurements from the prediction entropy alongside category classification training. However, the nodes in the graph might not be pre-labeled with specific categories, rendering entropy-based OOD detectors inapplicable in such category-free situations. To tackle this issue, we propose an energy-centric density estimation framework for OOD node detection, referred to as EnergyDef. Within this framework, we introduce an energy-based GNN to compute node energies that act as indicators of node density and reveal the OOD uncertainty of nodes. Importantly, EnergyDef can efficiently identify OOD nodes with low-resource OOD node annotations, achieved by sampling hallucinated nodes via Langevin Dynamics and structure estimation, along with training through Contrastive Divergence. Our comprehensive experiments on real-world datasets substantiate that our framework markedly surpasses state-of-the-art methods in terms of detection quality, even under conditions of scarce or entirely absent OOD node annotations.