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Subgraph Aggregation for Out-of-Distribution Generalization on Graphs
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Proposes SuGAr, which learns multiple diverse invariant subgraphs with parallel CIGA-style invariant GNNs, a subgraph sampler and diversity regularizer, and aggregates them via subgraph ensembling or weight averaging for graph OOD generalization.
Problem
Graph OOD generalization methods extract only a single invariant subgraph, which is susceptible to spurious correlations and insufficient when multiple critical subgraphs determine the label (e.g., functional groups in molecules).
Approach
Train a set of invariant GNNs in parallel from identical initialization, using random subgraph sampling and a diversity regularizer on edge weights to make each extract different invariant subgraphs; then aggregate them by averaging/max of edge weights with soft-voting over classifiers (ENS) or by averaging weights (WA).
Key results
- On SUMotif (bias 0.9), SuGAr(ENS) reaches 77.71 accuracy vs 40.34 for ERM and 63.39 for the ensemble baseline; averages 84.30 on synthetic tables.
- On realistic datasets, SuGAr(ENS) averages 65.41 across nine datasets, above best baseline CIGA-based ENSEMBLE at 62.42.
- SuGAr(WA) averages 80.43 on SPMotif/SUMotif, outperforming DiWA (67.17) without extra inference cost.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SuGAr (ENS) instead of the strongest reported baseline | Graph OOD prediction · SPMotif and SUMotif, bias=0.33, 0.60, and 0.90 | accuracy | Helped |
| Use SuGAr (ENS) instead of the strongest reported baseline | Graph OOD prediction · EC-Assay, EC-Scaffold, EC-Size, SST5, Twitter, CMNIST, Ki-Assay, Ki-Scaffold, and Ki-Size | ROC-AUC or accuracy | Helped |
| Use SuGAr (ENS) rather than CIGA on SUMotif | CIGA · SUMotif bias=0.60 | accuracy: 30% | Helped |
| Use graph-tailored weight averaging rather than DiWA | DiWA · 15 graph datasets | classification accuracy or ROC-AUC | Helped |
| Add subgraph sampling while retaining the diversity regularizer (ablation) | SuGAr diversity injection · SPMotif-0.9, EC50-Scaffold, and EC50-Size | classification performance | Helped |
| Add the diversity regularizer while retaining the sampler (ablation) | SuGAr diversity injection · SPMotif-0.9, EC50-Scaffold, and EC50-Size | classification performance | Helped |
| Add the sampler while retaining the diversity regularizer (ablation) | SuGAr diversity injection · SPMotif-0.9, EC50-Scaffold, and EC50-Size | classification performance | Helped |
| Remove both sampler and diversity regularizer (ablation) | SuGAr · SPMotif-0.9, EC50-Scaffold, and EC50-Size | classification performance | Hurt |
| Aggregate base-model information using the proposed aggregation method (ablation) | SuGAr (ENS) · SPMotif-0.9, EC50-Scaffold, and EC50-Size | classification performance | Helped |
Surprising findings
- Existing ensemble methods (ENS(ERM), ENSEMBLE) often underperform their own base models on several datasets.
- Standard weight averaging (DiWA) can significantly underperform its base model on some datasets.
Limitations
- Ensemble variant requires running n base models at inference time.
- Diversity regularizer and sampling can disrupt invariance in worst cases, and greedy selection is needed to avoid spurious subgraphs.
Experimental setup
Datasets: SPMotif SUMotif DrugOOD (EC50/KI assay, scaffold, size) CMNIST-sp Graph-SST5 Twitter
Benchmarks: SPMotif SUMotif DrugOOD CMNIST-sp Graph-SST5 Twitter
Metrics: accuracy ROC-AUC
Baselines: ERM IRM V-REx IB-IRM EIIL GREA GSAT DISC CAL GIL DIR CIGA
Builds on: CIGA DiWA DIR GSAT
Closest papers by meaning
- Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization (NeurIPS 2025 · similarity 0.92)
- Disentangling Invariant Subgraph via Variance Contrastive Estimation under Distribution Shifts (ICML 2025 · similarity 0.90)
- A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening (NeurIPS 2024 · similarity 0.89)
- Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization (NeurIPS 2025 · similarity 0.89)
- Disentangled Graph Self-supervised Learning for Out-of-Distribution Generalization (ICML 2024 · similarity 0.89)
- Graph Invariant Learning with Subgraph Co-mixup for Out-of-Distribution Generalization (AAAI 2024 · similarity 0.89)
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