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Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs
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Proposes DeGEM, which decouples a graph EBM into a DGI-trained multi-hop GNN encoder and an MLP energy head trained by MLE in latent space, avoiding adjacency sampling and energy propagation, for node OOD detection on homophilic and heterophilic graphs.
Problem
Node out-of-distribution detection on graphs is underexplored; existing energy-based graph methods (GNNSafe) derive energy from classification logits and rely on energy propagation, which degrades on heterophilic graphs.
Approach
Decouple the EBM into a graph encoder (trained with DGI contrastive learning plus classification) that captures topology, and a latent-space energy head trained by MLE with MCMC sampling only on node representations; add multi-hop encoding, conditional energy, energy readout, and recurrent updates between encoder and energy head.
Key results
- DeGEM averages 96.18/96.88 AUC on homophilic/heterophilic ablation settings, versus GNNSafe averaging 70.72 AUC in the ablation table.
- Reported average AUC improvement of 6.71% on homophilic and 20.29% on heterophilic graphs over prior SOTA (abstract); the main-text averages state 4.26% and 20.63%.
- Ablation shows DGI plus MLE energy head raises average AUC from 72.24 to 87.82 and full model reaches 96.88 average.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DeGEM instead of GNNSafe | Homophilic graphs · Homophilic graphs (average) | AUC: 88.73 -> 97.08 | Helped |
| Use DeGEM instead of GPN | Heterophilic graphs · Heterophilic graphs (average) | AUC: 76.92 -> 97.55 | Helped |
| Add energy propagation (ablation) | Energy on homophilic graphs · Homophilic graphs (average) | AUC: 77.22 -> 80.92 | Helped |
| Add energy propagation (ablation) | Energy on heterophilic graphs · Heterophilic graphs (average) | AUC: 76.51 -> 60.51 | Hurt |
| Add GCL to classification-logit energy (ablation) | Classify-Energy · Homophilic graphs (average) | AUC: 77.22 -> 65.37 | Hurt |
| Add GCL to classification-logit energy (ablation) | Classify-Energy · Heterophilic graphs (average) | AUC: +5.93% | Helped |
| Train the energy head with MLE instead of classification logits, without GCL (ablation) | Energy · Homophilic and heterophilic graphs (average) | AUC: 76.87 -> 72.24 | Hurt |
| Add GCL to MLE-trained energy (ablation) | MLE-Energy · Homophilic and heterophilic graphs (average) | AUC: 72.74% to 87.82% | Helped |
| Add Conditional Energy (ablation) | MLE-Energy + GCL + MH · Homophilic and heterophilic graphs (average) | AUC: 95.55 -> 96.18 | Helped |
| Add Energy Readout without Conditional Energy (ablation) | MLE-Energy + GCL · Homophilic and heterophilic graphs (average) | AUC: 87.82 -> 88.84 | Helped |
| Add Conditional Energy and Energy Readout together (ablation) | MLE-Energy + GCL · Homophilic and heterophilic graphs (average) | AUC: 87.82 -> 89.35 | Helped |
| Add the Multi-Hop encoder (ablation) | MLE-Energy + GCL · Homophilic and heterophilic graphs (average) | AUC: 87.82 -> 95.55 | Helped |
Surprising findings
- Adding energy propagation (GNNSafe) to the classify-energy baseline drops average AUC on heterophilic graphs from 76.51% to 60.51%.
- Combining DGI with classification-based energy hurts homophilic performance (77.22% to 65.37%).
Limitations
- Requires MCMC sampling during training, which adds cost.
- Results are near saturation on some datasets, limiting benchmark discrimination (as the authors note).
- Some OOD settings (e.g., Twitch) show weaker ID accuracy than baselines.
Experimental setup
Datasets: Cora Amazon-Photo Twitch ogbn-Arxiv Chameleon Actor Cornell
Benchmarks: Cora Amazon-Photo Twitch ogbn-Arxiv Chameleon Actor Cornell
Metrics: AUC AUPR FPR95 Acc
Baselines: MSP ODIN Mahalanobis Energy ResidualFlow GKDE GPN OODGAT GNNSafe OE Energy-FT GNNSafe++
Builds on: GNNSafe Deep Graph Infomax Energy-based OOD detection Langevin dynamics MCMC
Closest papers by meaning
- Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs (ICML 2024 · similarity 0.90)
- GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation (ICLR 2025 · similarity 0.88)
- Graph Out-of-Distribution Detection Goes Neighborhood Shaping (ICML 2024 · similarity 0.88)
- Harnessing Feature Resonance under Arbitrary Target Alignment for Out-of-Distribution Node Detection (NeurIPS 2025 · similarity 0.88)
- Structural Entropy Guided Unsupervised Graph Out-Of-Distribution Detection (AAAI 2025 · similarity 0.88)
- Bridging OOD Detection and Generalization: A Graph-Theoretic View (NeurIPS 2024 · similarity 0.87)
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