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Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs
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Proposes NODESAFE, which adds bounded-norm and uniform-sum regularizers to logits so negative energy scores aggregated over graph neighbors have fewer extreme values, improving node-level OOD detection with GNNs.
Problem
Node-level out-of-distribution detection with GNNs via negative energy score aggregation (GNNSAFE) is hurt by extreme node scores caused by unbounded negative energy and logit shift.
Approach
Two added loss terms: L_bound reduces variance of logit 2-norms (making energy scores bounded, with bounds derived from the norm), and L_uniform reduces variance of logit sums (mitigating logit shift, computed separately for ID and OOD samples), added to the energy OOD loss to make aggregated scores more uniform.
Key results
- On Cora with Structure Manipulation OOD and no exposure, NODESAFE reduces FPR95 to 25.63 vs 73.15 for GNNSAFE; average FPR95 reduction over GNNSAFE is 28.4% without and 22.7% with OOD exposure.
- On Twitch, NODESAFE++ reaches AUROC 98.50 and FPR95 3.43 versus 95.36 and 33.57 for GNNSAFE++.
- On ogbn-Arxiv temporal OOD, gains are smaller (e.g., AUROC 72.44 vs 71.06 for GNNSAFE without exposure).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the bounded and uniform energy objectives (L_UB) to GNNSAFE | GNNSAFE · Structure Manipulation OOD detection | FPR95: 28.4% | Helped |
| Add the bounded and uniform energy objectives (L_UB) to GNNSAFE++ | GNNSAFE++ · Structure Manipulation OOD detection with OOD exposure | FPR95: 22.7% | Helped |
| Add L_uniform (ablation) | NODESAFE · Cora, average of three OOD types, no OOD exposure | FPR95: 26.04 -> 32.07 | Helped |
| Add L_bound (ablation) | NODESAFE · Cora, average of three OOD types, no OOD exposure | FPR95: 26.04 -> 77.55 | Helped |
| Add L_uniform (ablation) | NODESAFE++ · Cora, average of three OOD types, with OOD exposure | FPR95: 20.20 -> 26.43 | Helped |
| Add L_bound (ablation) | NODESAFE++ · Cora, average of three OOD types, with OOD exposure | FPR95: 20.20 -> 50.21 | Helped |
| Use L_uniform alone, without L_bound (ablation) | NODESAFE · OOD detection | AUROC | No clear effect |
| Use L_bound alone, without L_uniform (ablation) | NODESAFE · OOD detection | AUROC | Helped |
Surprising findings
- Using L_uniform alone does not significantly improve OOD detection, while L_bound alone gives most of the gain.
- LogitNorm yields much smaller improvements than the proposed bounded-norm objective despite a similar goal.
Limitations
- Improvement on temporal (ogbn-Arxiv) OOD split is limited, attributed to similar score means and poor ID classification.
- L_uniform alone is ineffective; benefit relies on combination with L_bound.
- Method only helps once the model is well-trained; applying it early in training hurts classification and detection.
Experimental setup
Datasets: Cora Citeseer PubMed ogbn-Arxiv Twitch-Explicit
Benchmarks: Cora Citeseer PubMed Twitch-Explicit ogbn-Arxiv
Metrics: AUROC AUPR FPR95 ID accuracy
Baselines: MSP ODIN Mahalanobis Energy Energy FT OE GKDE GPN GNNSAFE LogitNorm
Builds on: GNNSAFE energy-based OOD detection LogitNorm
Closest papers by meaning
- Revisiting Score Propagation in Graph Out-of-Distribution Detection (NeurIPS 2024 · similarity 0.90)
- Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs (ICLR 2025 · similarity 0.90)
- 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)
- Bridging OOD Detection and Generalization: A Graph-Theoretic View (NeurIPS 2024 · similarity 0.88)
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