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EGonc : Energy-based Open-Set Node Classification with substitute Unknowns
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Proposes EGonc, an energy-based open-set node classifier that generates substitute unknown nodes via manifold mixup on graph boundaries and learns an energy-logit OOD class without real open-set data.
Problem
Open-set node classification on graphs: classify known classes and reject unknown-class nodes, where softmax confidence is overconfident on OOD nodes and thresholds are hard to tune.
Approach
Generate substitute unknown nodes by mixing up boundary nodes (inter-class pairs and peripheral nodes with inverted class centers) in GNN hidden space, propagate energy scores over the graph, and train an explicit (C+1)-th unknown logit with cross-entropy, a tailored complement entropy loss, and an energy regularization loss, avoiding threshold tuning.
Key results
- Near open-set (one unknown class, inductive): EGonc averages 76.5% accuracy and 69.1% macro-F1, versus 74.7%/67.6% for the second-best G2Pxy.
- Far open-set average accuracy 85.7% and macro-F1 76.3%, ahead of G2Pxy at 85.1%/75.7%, though GCN_soft_τ reaches 84.1% accuracy and the authors note thresholding is comparable.
- Ablation: removing substitute generation (using real far OOD samples or random mixup) yields lower accuracy than the full well-designed substitutes (e.g., 76.5 vs 71.2 average accuracy for the full model vs far-OOD-only variant).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add EGonc’s full method | GCN open-set node classifier · Near open-set (average of five datasets, u=1, inductive) | accuracy: 74.7 -> 76.5 | Helped |
| add energy regularization loss l3 (ablation) | EGonc with l1 and l2 · Near open-set (average of five datasets, u=1, inductive) | macro-F1: 67.6 -> 69.1 | Helped |
| add tailored complement entropy loss l2 (ablation) | EGonc with l1 · Near open-set (average of five datasets, u=1, inductive) | macro-F1: 62.6 -> 67.6 | Helped |
| use real far-OOD samples Xfar instead of designed substitutes (ablation) | EGonc · Near open-set (average of five datasets, u=1, inductive) | accuracy: 76.5 -> 71.2 | Hurt |
| generate substitutes with random parent-node mixup Xrand (ablation) | EGonc · Near open-set (average of five datasets, u=1, inductive) | accuracy: 76.5 -> 73.1 | Hurt |
| use inter-class substitutes only, omitting external substitutes (ablation) | EGonc · Near open-set (average of five datasets, u=1, inductive) | accuracy: 76.5 -> 74.1 | Hurt |
| use external substitutes only, omitting inter-class substitutes (ablation) | EGonc · Near open-set (average of five datasets, u=1, inductive) | accuracy: 76.5 -> 73.6 | Hurt |
| use EGonc instead of G2Pxy | GCN open-set node classifier · Near open-set (average of five datasets, u=1, inductive) | accuracy: 74.7 -> 76.5 | Helped |
| use EGonc instead of G2Pxy | GCN open-set node classifier · Far open-set (average: Co_Ci, Ci_DB, DB_Pub) | accuracy: 85.1 -> 85.7 | Helped |
Surprising findings
- Simple thresholding on GCN softmax (GCN_soft_τ) achieves far open-set performance comparable to EGonc.
- Known-class accuracy drops slightly (79.5% to 76.3% average) when adding unknown detection capability relative to closed-set GCN.
Limitations
- Far open-set performance is comparable to a simple threshold baseline, suggesting the generative approach's advantage is limited there.
- Relies on hyperparameters (lambda weights, substitute count, margins) tuned by grid search on validation data.
- Evaluated only on citation-style benchmarks with GCN, GAT and GraphSAGE backbones.
Experimental setup
Datasets: Cora Citeseer DBLP PubMed Ogbn_arxiv
Benchmarks: Cora Citeseer DBLP PubMed Ogbn_arxiv
Metrics: accuracy macro-F1
Baselines: GCN_soft GCN_sig GCN_soft_τ GCN_sig_τ Openmax DOC PROSER OpenWGL GNNSAFE G2Pxy
Builds on: GNNSAFE G2Pxy Manifold mixup Complement entropy GCN
Closest papers by meaning
- ROG_PL: Robust Open-Set Graph Learning via Region-Based Prototype Learning (AAAI 2024 · similarity 0.85)
- Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs (ICML 2024 · similarity 0.85)
- Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs (ICLR 2025 · similarity 0.85)
- Dual Energy-Based Model with Open-World Uncertainty Estimation for Out-of-distribution Detection (CVPR 2025 · similarity 0.85)
- GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights (NeurIPS 2025 · similarity 0.83)
- Open-Set Cross-Network Node Classification via Unknown-Excluded Adversarial Graph Domain Alignment (AAAI 2025 · similarity 0.83)
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