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Quantifying Distributional Invariance in Causal Subgraph for IRM-Free Graph Generalization
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Proposes IDG, an IRM-free graph OOD method that extracts causal subgraphs by maximizing representation norm of the extracted subgraph, motivated by an Invariant Distribution Criterion (causal subgraphs shift less across environments).
Problem
Out-of-distribution generalization for graph classification without IRM, which requires environment annotations or heuristically generated synthetic environments; the goal is to identify causal subgraphs without environment labels.
Approach
Proposes an Invariant Distribution Criterion (causal subgraphs shift less across environments) and links distribution shift to decaying representation norms, so maximizing the norm of the extracted subgraph serves as an IRM-free objective for causal subgraph discovery.
Key results
- IDG achieves best results on 15 of 17 dataset-domain settings in the GraphOOD/DrugOOD comparison, e.g., Motif-basis 82.53% vs. LIRS 75.51% and CMNIST 55.32% vs. LECI 51.80%.
- Ablation on Motif-basis: removing the norm loss drops accuracy from 77.83 to 76.12; ERM plus norm loss alone barely changes results (53.46 to 53.25).
- IDG shows lower training and inference time than GIL and DIR on Motif-basis, HIV-scaffold and SST2-length.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IDG instead of the strongest reported baseline | GIN for graph OOD generalization · GraphOOD and DrugOOD settings in the comparison table | accuracy or ROC-AUC | Helped |
| Add the norm-guided objective to the baseline (ablation) | Motif-basis and Motif-size ground-truth subgraph extraction · Motif-basis and Motif-size | accuracy, recall, precision, and F1: Motif-basis acc 0.6985 -> 0.7337; Motif-size acc 0.9064 -> 0.9373 | Helped |
| Add the norm objective to ERM (ablation) | GIN · Motif-basis, CMNIST, Twitter, and EC50-assay | accuracy or ROC-AUC: 53.46 -> 53.25; 27.82 -> 27.34; 57.04 -> 57.69; 67.39 -> 67.48 | Mixed |
| Remove cross-entropy loss from the extractor (ablation) | IDG · Motif-basis, CMNIST, Twitter, and EC50-assay | accuracy or ROC-AUC: 77.83 -> 66.58; 55.32 -> 48.32; 59.64 -> 57.47; 80.54 -> 69.02 | Hurt |
| Remove the compactness constraint (ablation) | IDG · Motif-basis, CMNIST, Twitter, and EC50-assay | accuracy or ROC-AUC: 77.83 -> 75.41; 55.32 -> 52.53; 59.64 -> 58.89; 80.54 -> 78.96 | Hurt |
| Remove the norm loss (ablation) | IDG · Motif-basis, CMNIST, Twitter, and EC50-assay | accuracy or ROC-AUC: 77.83 -> 76.12; 55.32 -> 49.64; 59.64 -> 58.43; 80.54 -> 76.64 | Hurt |
Surprising findings
- Simply adding the norm objective to ERM hardly improves generalization, so the norm term only helps when combined with the extractor objective.
Limitations
- Theoretical arguments rely on strong assumptions (causal mechanism invariance, sparse interventions on non-causal parts, support overlap) that may not hold in practice.
- The norm-distribution link is shown empirically on a few datasets with edge perturbation as the shift proxy.
Experimental setup
Datasets: Motif CMNIST HIV SST2 Twitter IC50 EC50
Benchmarks: GraphOOD DrugOOD
Metrics: accuracy ROC-AUC
Baselines: ERM IRM VREx Coral DIR GIL GSAT CIGA LECI iMoLD EQuAD LIRS
Builds on: Invariant Risk Minimization GSAT CIGA LECI
Closest papers by meaning
- Out-of-Distribution Generalization on Graphs via Progressive Inference (AAAI 2025 · similarity 0.93)
- Dissecting the Failure of Invariant Learning on Graphs (NeurIPS 2024 · similarity 0.90)
- Subgraph Aggregation for Out-of-Distribution Generalization on Graphs (AAAI 2025 · similarity 0.89)
- A Recipe for Causal Graph Regression: Confounding Effects Revisited (ICML 2025 · similarity 0.88)
- Graph Contrastive Invariant Learning from the Causal Perspective (AAAI 2024 · similarity 0.88)
- Disentangling Invariant Subgraph via Variance Contrastive Estimation under Distribution Shifts (ICML 2025 · similarity 0.88)
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