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Structural Entropy Guided Unsupervised Graph Out-Of-Distribution Detection
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Proposes SEGO, an unsupervised graph-level OOD detector that minimizes structural entropy to build a coding-tree anchor view and trains triplet-view (basic, tree, topological) contrastive learning at local, global, and tree levels.
Problem
Unsupervised graph-level out-of-distribution detection is hurt by redundant information in graph structures, which makes ID and OOD graphs hard to distinguish; existing augmentations can also perturb semantics.
Approach
Use a structural-entropy-minimizing coding tree as an essential anchor view, combined with a perturbation-free topological view (random-walk diffusion and Laplacian positional encoding), and contrast across local, global, and tree levels with triplet views, with adaptive weighting by prediction-error standard deviation.
Key results
- SEGO achieves best AUC on 9 of 10 OOD dataset pairs, average AUC 84.46 and average rank 1.1, about 3.7% above the second-best GOOD-D (80.73).
- On FreeSolv/ToxCast, SEGO reaches 90.95 AUC, surpassing the best competitor by 10.8%.
- On anomaly detection over 5 TUDataset benchmarks, SEGO achieves best results on ENZYMES, DHFR, BZR and IMDB-B and runner-up on NCI1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SEGO rather than GOOD-D | Graph OOD detection · BZR/COX2 | AUC: 94.99±2.25 -> 96.66±0.91 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · PTC-MR/MUTAG | AUC: 81.21±2.65 -> 85.02±0.94 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · AIDS/DHFR | AUC: 99.07±0.40 -> 99.48±0.11 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · ENZYMES/PROTEIN | AUC: 61.89±2.51 -> 64.42±4.95 | Helped |
| Use SEGO rather than InfoGraph-MD | Graph OOD detection · IMDB-M/IMDB-B | AUC: 81.38±1.14 -> 80.27±0.92 | Hurt |
| Use SEGO rather than GOOD-D | Graph OOD detection · Tox21/SIDER | AUC: 66.50±1.35 -> 66.67±0.82 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · FreeSolv/ToxCast | AUC: 80.13±3.43 -> 90.95±1.93 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · BBBP/BACE | AUC: 82.91±2.58 -> 87.55±0.13 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · ClinTox/LIPO | AUC: 69.18±3.61 -> 78.99±2.81 | Helped |
| Use SEGO rather than GOOD-D | Graph OOD detection · Esol/MUV | AUC: 91.52±0.70 -> 94.59±0.94 | Helped |
| Remove local-level contrastive loss (ablation) | SEGO · OOD dataset pairs (10 pairs) | AUC: 85.02±0.94 -> 87.71±1.35; 87.55±0.13 -> 88.34±1.64; 78.99±2.81 -> 79.21±4.55 | Mixed |
| Remove global-level contrastive loss (ablation) | SEGO · OOD dataset pairs (10 pairs) | AUC: 96.66±0.91 -> 79.36±8.69; 64.42±4.95 -> 63.38±4.18 | Mixed |
Surprising findings
- Removing the local-level contrast improves performance on some dataset pairs (e.g., PTC-MR/MUTAG, BBBP/BACE, ClinTox/LIPO), which the authors attribute to biomolecular data depending on global topology.
- SEGO nearly but not fully wins on IMDB-M/IMDB-B social network datasets, which the authors attribute to high connectivity and redundancy.
Limitations
- Coding tree only approximates the minimum structural entropy and does not fully remove redundancy, weakening performance on social network datasets.
- Results for baselines are taken from published works rather than re-run under identical settings.
Experimental setup
Datasets: TUDataset OGB BZR COX2 PTC-MR MUTAG AIDS DHFR ENZYMES PROTEIN IMDB-M IMDB-B
Benchmarks: BZR/COX2 PTC-MR/MUTAG AIDS/DHFR ENZYMES/PROTEIN IMDB-M/IMDB-B Tox21/SIDER FreeSolv/ToxCast BBBP/BACE ClinTox/LIPO Esol/MUV
Metrics: AUC average rank
Baselines: PK-LOF PK-OCSVM PK-iF WL-LOF WL-OCSVM WL-iF OCGIN GLocalKD InfoGraph-iF InfoGraph-MD GraphCL-iF GraphCL-MD
Builds on: GOOD-D graph information bottleneck InfoNCE GIN structural entropy minimization (SEP)
Closest papers by meaning
- Redundancy-Aware Test-Time Graph Out-of-Distribution Detection (NeurIPS 2025 · similarity 0.92)
- GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation (ICLR 2025 · similarity 0.89)
- Graph Out-of-Distribution Detection Goes Neighborhood Shaping (ICML 2024 · similarity 0.89)
- Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs (ICML 2024 · similarity 0.89)
- Revisiting Score Propagation in Graph Out-of-Distribution Detection (NeurIPS 2024 · similarity 0.88)
- Bridging OOD Detection and Generalization: A Graph-Theoretic View (NeurIPS 2024 · similarity 0.88)
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