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Refining Latent Homophilic Structures over Heterophilic Graphs for Robust Graph Convolution Networks
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Proposes LHS, which learns latent homophilic structures over heterophilic graphs via a self-expressive generator and dual-view contrastive refinement, to make GCNs robust to structural OOD attacks.
Problem
GCNs are highly vulnerable to structural attacks on heterophilic graphs because adversarial or injected structure shifts the node-level heterophily distribution to the right (structural OOD), degrading node classification.
Approach
Induce a latent homophilic graph by expressing each node's features as a linear combination of other nodes (multi-node self-expression), refine it iteratively with a pairwise-constrained dual-view contrastive learner and structure bootstrapping, then run a truncated-threshold GCN encoder on it so aggregation is largely homophilic.
Key results
- Under OOD and Injected evasion attacks on five heterophilic benchmarks, LHS averages 62.41% accuracy versus 54.89% for the best baseline BM-GCN.
- Without attacks, LHS achieves the highest average accuracy of 76.34% across nine benchmarks, e.g., 60.27% on Squirrel versus 59.11% for GPNN.
- Under poisoning attacks, LHS outperforms baselines by up to about 20 points over ProGNN at 25% perturbation (as claimed in text).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LHS instead of the strongest listed baseline | Node classification models · Wisconsin | accuracy: 86.67 -> 88.32 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Texas | accuracy: 87.00 -> 86.32 | Hurt |
| Use LHS instead of the strongest listed baseline | Node classification models · Cornell | accuracy: 85.10 -> 85.96 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Chameleon | accuracy: 71.27 -> 72.31 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Squirrel | accuracy: 59.11 -> 60.27 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Actor | accuracy: 37.90 -> 38.87 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Cora | accuracy: 87.99 -> 88.71 | Helped |
| Use LHS instead of the strongest listed baseline | Node classification models · Citeseer | accuracy: 79.41 -> 78.53 | Hurt |
| Use LHS instead of the strongest listed baseline | Node classification models · Pubmed | accuracy: 90.49 -> 87.65 | Hurt |
| Add self-expressive generator (ablation) | LHS · Texas, OOD attack | accuracy: 62.17 -> 71.15 | Helped |
| Add self-expressive generator (ablation) | LHS · Texas, Injected attack | accuracy: 58.27 -> 73.34 | Helped |
| Add dual-view contrastive learner (ablation) | LHS · Texas, Injected attack | accuracy: 66.19 -> 73.34 | Helped |
Surprising findings
- Cora shows almost no right-shift of the heterophily distribution under attacks, suggesting homophily drives robustness.
Limitations
- Time complexity of the SVD-based structure generation is O(N^2) for small graphs, relying on randomized SVD for scale.
- Attacks are self-designed evasion attacks; robustness evaluated only against the authors' attack constructions.
- Many hyperparameters (threshold sigma, lambda1, lambda2, beta, tau) tuned per dataset.
Experimental setup
Datasets: Cornell Texas Wisconsin Chameleon Squirrel Actor Cora Citeseer PubMed
Benchmarks: Cornell Texas Wisconsin Chameleon Squirrel Actor Cora Citeseer PubMed
Metrics: classification accuracy
Baselines: MixHop H2GCN NLGNN GEOM-GCN Node2Seq GPNN ProGNN UGCN SimP-GCN BM-GCN GREET ALT-GCN
Builds on: ProGNN SimP-GCN GPNN BM-GCN
Closest papers by meaning
- Powerful Graph Convolutional Networks with Adaptive Propagation Mechanism for Homophily and Heterophily (AAAI 2022 · similarity 0.92)
- Is Homophily a Necessity for Graph Neural Networks? (ICLR 2022 · similarity 0.92)
- Understanding Heterophily for Graph Neural Networks (ICML 2024 · similarity 0.90)
- PC-Conv: Unifying Homophily and Heterophily with Two-Fold Filtering (AAAI 2024 · similarity 0.90)
- Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness–Generalization Perspective (NeurIPS 2025 · similarity 0.89)
- Integrating Co-Training with Edge Discrimination to Enhance Graph Neural Networks Under Heterophily (AAAI 2025 · similarity 0.89)
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