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Expand Horizon: Graph Out-of-Distribution Generalization via Multi-Level Environment Inference
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Proposes MLEI, which infers environments at global (linear graph transformer) and multi-hop local (ego-graph layer-wise) levels to learn invariant predictions for node-level graph OOD generalization.
Problem
Node classification under node-level distribution shifts, where GNNs learn environment-sensitive correlations; existing environment inference uses only low-hop ego-graphs and deeper GNNs over-smooth.
Approach
Combines a linear-complexity graph transformer that infers a global environment with layer-by-layer local environment inference on multi-hop ego-graphs, fusing both views in a causal backdoor-adjusted variational objective.
Key results
- On Pubmed with GCN, accuracy on OOD data is 91.84 vs CaNeT 88.05 (about 3.79 points higher).
- On Arxiv with GCN, OOD1 accuracy 60.03 vs CaNeT 59.01; Twitch GCN OOD1 ROC-AUC 68.59 vs CaNeT 67.47.
- Elliptic OOD results show highest improvement of 4.42% on OOD4 with GCN backbone over baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MLEI instead of CaNeT | GCN · Cora OOD | accuracy: 95.60 ± 0.93 -> 97.32 ± 0.29 | Helped |
| Use MLEI instead of CaNeT | GCN · Citeseer OOD | accuracy: 93.05 ± 0.91 -> 94.61 ± 0.74 | Helped |
| Use MLEI instead of CaNeT | GCN · Pubmed OOD | accuracy: 88.05 ± 1.09 -> 91.84 ± 0.59 | Helped |
| Use MLEI instead of CaNeT | GCN · Arxiv OOD 1, OOD 2, and OOD 3 | accuracy: 59.01 ± 0.30 -> 60.03 ± 0.48; 56.88 ± 0.70 -> 57.47 ± 0.51; 56.27 ± 1.21 -> 57.64 ± 0.87 | Helped |
| Use MLEI instead of CaNeT | GCN · Twitch OOD 1, OOD 2, and OOD 3 | ROC-AUC: 67.47 ± 0.32 -> 68.59 ± 0.46; 53.59 ± 0.19 -> 53.77 ± 0.18; 64.24 ± 0.18 -> 64.59 ± 0.26 | Helped |
| Use MLEI instead of CaNeT | GAT · Twitch OOD 1 | ROC-AUC: 68.08 ± 0.19 -> 67.93 ± 0.19 | Hurt |
| Use MLEI instead of CaNeT | GAT · Twitch OOD 2 and OOD 3 | ROC-AUC: 53.49 ± 0.14 -> 54.61 ± 0.15; 63.76 ± 0.17 -> 64.69 ± 0.08 | Helped |
| Add global relationship modeling (ablation) | MLEI · Arxiv and Twitch OOD subsets | accuracy / ROC-AUC | Helped |
| Add local relationship modeling (ablation) | MLEI · Arxiv and Twitch OOD subsets | accuracy / ROC-AUC | Helped |
| Use multi-hop local environment inference instead of one inference across all local layers (ablation) | MLEI · Arxiv and Twitch OOD subsets | accuracy / ROC-AUC | Helped |
| Add the regularization term (ablation) | MLEI · Arxiv and Twitch OOD subsets | accuracy / ROC-AUC | Mixed |
Surprising findings
- Deeper GNN layers on high-hop ego-graphs degrade OOD generalization due to over-smoothing (Arxiv and Citeseer experiments).
Limitations
- Reliance on heuristic synthetic OOD splits for citation datasets (spurious features from random GNNs)
- Hyperparameters (K, lambda, tau) are tuned per dataset with sensitivity to dataset size
Experimental setup
Datasets: Cora Citeseer Pubmed Twitch Arxiv Elliptic
Benchmarks: Cora Citeseer Pubmed Arxiv Twitch Elliptic
Metrics: accuracy ROC-AUC macro F1
Baselines: ERM IRM CORAL DANN GroupDRO Mixup SR-GNN EERM CaNeT
Builds on: CaNeT EERM IRM linear graph transformer
Closest papers by meaning
- Improving Generalization of Dynamic Graph Learning via Environment Prompt (NeurIPS 2024 · similarity 0.87)
- Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments (CVPR 2024 · similarity 0.87)
- Enhancing Graph Invariant Learning from a Negative Inference Perspective (ICML 2025 · similarity 0.87)
- Graph Invariant Learning with Subgraph Co-mixup for Out-of-Distribution Generalization (AAAI 2024 · similarity 0.86)
- Disentangled Graph Self-supervised Learning for Out-of-Distribution Generalization (ICML 2024 · similarity 0.85)
- TINED: GNNs-to-MLPs by Teacher Injection and Dirichlet Energy Distillation (ICML 2025 · similarity 0.85)
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