HADES: Self-Validated Energy Selection for Structural Out-of-Distribution Detection on Hypergraphs

Hypergraphs represent higher order interactions among groups of entities, and hypergraph neural networks (HNNs) exploit these relations for prediction. At deployment, hyperedge formation may change, placing nodes in relational contexts unseen during training. Structural out of distribution (OOD) detection flags when confident predictions rely on relational patterns no longer supported by training, making it essential for reliable deployment. Yet this task remains underexplored, and no fixed post hoc score is reliable across datasets and backbones. We introduce HADES (Hypergraph Adaptive Detection via Energy Selection), which pairs a new structural score with adaptive detector selection. The score measures disagreement between log partition confidence propagated over the current incidence and a soft incidence anchored by prototypes fitted to clean training embeddings. To handle detector heterogeneity, HADES turns score choice into a predeployment self validation problem. Matched perturbations of the clean hypergraph define a surrogate shift. Using this surrogate, HADES selects and freezes the single scoring rule best aligned with anticipated deployment changes. Across 12 hypergraphs and four backbones, HADES achieves the best average detector rank on every backbone. Its overall average rank is $2.16$, compared with $5.82$ for runner up KLM. These results show that reliable structural OOD detection depends on both a clean relational reference and score selection aligned with the anticipated shift.