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Graph Out-of-Distribution Detection Goes Neighborhood Shaping
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Proposes TopoOOD, a node-level OOD detector scoring each node by a generalized node-wise Dirichlet energy over its k-hop neighborhood, plus topology-based ID/OOD splits (triangleness, squareness, cliqueness) as new benchmarks.
Problem
Node-level out-of-distribution detection on graphs, where neighborhood interdependence makes existing image-style and GNNSafe-style energy scores unreliable, and existing evaluation splits are limited.
Approach
Replace per-node energy with a generalized node-wise Dirichlet energy that aggregates neighbor embedding disagreement over k hops with center-node-specific structural weights, avoiding energy convergence in large graphs; also split ID/OOD by topological properties of nodes.
Key results
- On Arxiv, TopoOOD reaches 87.11 AUROC and 32.10 FPR95 versus GNNSafe++'s 74.77 AUROC and 77.43 FPR95 (average over OOD splits).
- On Twitch, TopoOOD reaches 99.72 AUROC and 0.00 FPR95 versus GNNSafe++'s 95.36 AUROC and 33.57 FPR95.
- On Coauthor-CS triangleness split, TopoOOD reaches 95.73 AUROC versus 54.83 for GNNSafe++.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Twitch | AUROC: 95.36 -> 99.72 | Helped |
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Twitch | FPR95: 33.57 -> 0.00 | Helped |
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Arxiv | AUROC: 74.77 -> 87.11 | Helped |
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Arxiv | FPR95: 77.43 -> 32.10 | Helped |
| Use TopoOOD instead of the strongest baseline | Graph OOD detection · Amazon-Photo Squareness | AUROC: 91.58 -> 89.05 | Hurt |
| Use TopoOOD instead of the strongest baseline | Graph OOD detection · Amazon-Photo Cliqueness | AUROC: 95.87 -> 93.57 | Hurt |
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Coauthor-CS Cliqueness | AUROC: 93.36 -> 99.96 | Helped |
| Use TopoOOD instead of GNNSafe++ | Graph OOD detection · Coauthor-Physics Cliqueness | AUROC: 95.49 -> 100.0 | Helped |
| Add propagation to 1-hop GDE (ablation) | TopoOOD · Twitch and Coauthor-Triangleness | ID/OOD GDE distribution separation | Helped |
| Increase propagation steps beyond a threshold (ablation) | TopoOOD · Twitch and other settings | AUROC | No clear effect |
| Increase regularization weight within reasonable bounds (ablation) | TopoOOD · OOD detection and node classification | OOD awareness | Helped |
| Increase the gap between ein and eout (ablation) | TopoOOD · OOD detection | performance | Helped |
Surprising findings
- Standard GNNSafe++ energy fails on interdependent ID/OOD nodes intermixed in a neighborhood, as shown by a toy example.
- Raw k-hop Dirichlet energy converges to the energy of the whole connected subgraph as k grows, losing discriminative power.
Limitations
- Relies on a regularization loss with outlier exposure during training, requiring OOD training instances.
- Hyperparameters (k, alpha, e_in, e_out, lambda) selected by grid search and sensitive to propagation steps.
- Theoretical assumptions (density, subgraph size, logit scale) are simplifications that the implementation does not rely on.
Experimental setup
Datasets: Twitch-Explicit ogbn-Arxiv Amazon-Photo Coauthor-CS Coauthor-Physics Cora
Benchmarks: Twitch-Explicit ogbn-Arxiv Amazon-Photo Coauthor-CS Coauthor-Physics Cora
Metrics: AUROC AUPR FPR95 ID accuracy
Baselines: MSP Mahalanobis OE ODIN KNN GKDE GPN GNNSafe++
Builds on: GNNSafe Dirichlet energy outlier exposure KNN OOD detection Graph Posterior Network
Closest papers by meaning
- Revisiting Score Propagation in Graph Out-of-Distribution Detection (NeurIPS 2024 · similarity 0.92)
- Redundancy-Aware Test-Time Graph Out-of-Distribution Detection (NeurIPS 2025 · similarity 0.89)
- Bridging OOD Detection and Generalization: A Graph-Theoretic View (NeurIPS 2024 · similarity 0.89)
- Structural Entropy Guided Unsupervised Graph Out-Of-Distribution Detection (AAAI 2025 · similarity 0.89)
- GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation (ICLR 2025 · similarity 0.89)
- GOODAT: Towards Test-Time Graph Out-of-Distribution Detection (AAAI 2024 · similarity 0.88)
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