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Graph Structure Refinement with Energy-based Contrastive Learning
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Proposes ECL-GSR, an unsupervised energy-based contrastive learning framework that jointly trains a GNN encoder for graph structure refinement (edge add/remove via cosine similarity) and node classification.
Problem
Noisy or incomplete graph structures degrade GNN robustness and node classification, and existing generative graph models fit discriminative graph tasks poorly.
Approach
Combines energy-based models with contrastive learning so the contrastive (discriminative) loss is the special case of an ECL objective with the generative term disabled; the generative term is trained with SGLD sampling, and the refined adjacency is produced by thresholding cosine similarities between learned node representations.
Key results
- ECL-GSR achieves the best node classification accuracy on all eight benchmark datasets in the standard-split table, e.g., 84.06% on Cora and 71.27% on Cornell, with margins of 0.15% to 1.61% over the second-best method.
- With 1% training labels on Cora, ECL-GSR reaches 72.33% versus 70.83% for the next best (IDGL).
- ECL-GSR reports faster convergence and lower time and memory cost than GSR baselines, and it outperforms baselines on three graph classification datasets (e.g., 91.45% on MUTAG).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ECL-GSR instead of the strongest listed baseline | Node classification · Cora, Citeseer, Cornell, Texas, Wisconsin, Actor, Pubmed, and OGB-Arxiv | accuracy: 84.06 vs 83.88; 73.70 vs 73.55; 71.27 vs 70.29; 72.97 vs 70.21; 67.79 vs 66.73; 33.71 vs 32.95; 80.91 vs 79.30; 71.09 vs | Helped |
| Use ECL-GSR instead of the strongest listed baseline | Graph classification · COLLAB, MUTAG, and PROTEINS | accuracy: 83.00 vs 81.34; 91.45 vs 89.89; 78.77 vs 77.44 | Helped |
| Use ECL-GSR instead of the strongest listed baseline | Node classification with limited labels · Cora and Citeseer at train ratios 1%, 3%, 5%, and 10% | accuracy: 72.33 vs 70.83; 79.99 vs 78.60; 84.30 vs 83.82; 85.71 vs 85.56; 68.06 vs 67.03; 72.18 vs 71.61; 73.38 vs 72.88; 74.90 vs | Helped |
| Remove structural embeddings and use raw graph attributes (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Remove the generative term (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Remove the discriminative term (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Increase alpha to 1.0 or higher, strengthening the generative term relative to the discriminative term (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Decrease alpha below 0.1 (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Use lower output dimension (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | accuracy | Hurt |
| Use higher output dimension (ablation) | ECL-GSR · Cora, Citeseer, Actor, and Pubmed | model complexity | Hurt |
| Increase the number of SGLD iterations beyond a few steps (ablation) | ECL-GSR · Cora and Citeseer | accuracy | No clear effect |
Surprising findings
- The paper reports that a denser refined graph does not necessarily improve performance.
Limitations
- Several baselines OOM on larger datasets, so comparisons on Pubmed and OGB-Arxiv are incomplete.
- Evaluation is mainly on node classification; graph classification is only in the appendix.
Experimental setup
Datasets: Cora Citeseer Pubmed OGB-Arxiv Cornell Texas Wisconsin Actor COLLAB MUTAG PROTEINS
Benchmarks: Cora Citeseer Cornell Texas Wisconsin Actor Pubmed OGB-Arxiv COLLAB MUTAG PROTEINS
Metrics: accuracy t-test p-value training time memory
Baselines: GCN GAT LDS GEN GAuG-O SGSR GRCN IDGL SUBLIME ProGNN CoGSL STABLE
Builds on: SimCLR GSLB SGLD DeepWalk
Closest papers by meaning
- ReGCL: Rethinking Message Passing in Graph Contrastive Learning (AAAI 2024 · similarity 0.90)
- S3GCL: Spectral, Swift, Spatial Graph Contrastive Learning (ICML 2024 · similarity 0.90)
- TopoGCL: Topological Graph Contrastive Learning (AAAI 2024 · similarity 0.89)
- Does GCL Need a Large Number of Negative Samples? Enhancing Graph Contrastive Learning with Effective and Efficient Negative Sampling (AAAI 2025 · similarity 0.89)
- Leveraging Contrastive Learning for Enhanced Node Representations in Tokenized Graph Transformers (NeurIPS 2024 · similarity 0.89)
- Hierarchical Topology Isomorphism Expertise Embedded Graph Contrastive Learning (AAAI 2024 · similarity 0.89)
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