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Hierarchical Topology Isomorphism Expertise Embedded Graph Contrastive Learning
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Proposes HTML, a plug-and-play knowledge-distillation-style add-on for graph contrastive learning that trains the encoder to predict WL-based graph-tier isomorphism similarity and overlap-subgraph structural coefficients, improving GraphCL, RGCL, and BGRL on graph classification benchmarks.
Problem
Graph contrastive learning encoders (GNN-based) capture topology-level discriminative information poorly, so graphs with homogeneous node features are hard to distinguish.
Approach
Add two auxiliary self-supervised regression losses that distill topology isomorphism expertise into the GCL encoder: a graph-tier loss predicting 1-WL label-set Jaccard similarity between augmented views, and a subgraph-tier loss predicting overlap-subgraph structural coefficient matrices, with a theoretical Bayes error bound argument.
Key results
- GraphCL+HTML improves over GraphCL by 0.67% average accuracy on unsupervised TU benchmarks (76.38 vs 75.71), with paired t-test p=0.03.
- On transfer learning (ROC-AUC over 8 MoleculeNet datasets), GraphCL+HTML averages +2.82 over GraphCL and about 0.43 over RGCL.
- The abstract reports beating the SOTA by 0.23% in unsupervised representation learning and 0.43% in transfer learning.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add HTML to GraphCL | GraphCL · Unsupervised graph classification (average) | accuracy (%): +0.67 | Helped |
| Add HTML to GraphCL | GraphCL · Transfer learning (average across eight datasets) | ROC-AUC (%): +2.82 | Helped |
| Add HTML to RGCL | RGCL · Unsupervised graph classification (average; four datasets) | accuracy (%): +0.48 | Helped |
| Add graph-tier topology isomorphism expertise (ablation) | HTML · NCI1 and PROTEINS | accuracy | Helped |
| Add subgraph-tier topology isomorphism expertise (ablation) | HTML · NCI1 and PROTEINS | accuracy | Helped |
| Set graph-tier loss weight α to 10 (ablation) | HTML · PROTEINS | accuracy: α=10 | Helped |
| Set subgraph-tier loss weight β to 1000 (ablation) | HTML · PROTEINS | accuracy: β=1000 | Helped |
Surprising findings
- HTML does not improve over GraphCL on DD (-0.02) and RDT-M5K (-0.04), showing gains are not uniform across datasets.
Limitations
- Gains over strong baselines are small (e.g., 0.23% and 0.43%) and some datasets show no improvement.
- The theoretical bound relies on Gaussian assumptions, a 1-D/binary setting, and an empirically assumed bounded inherent-error condition.
- Graph-tier and subgraph-tier losses introduce extra hyperparameters alpha and beta that require tuning.
Experimental setup
Datasets: NCI1 PROTEINS DD MUTAG COLLAB RDT-B RDT-M5K IMDB-B ZINC-2M BBBP Tox21 ToxCast
Benchmarks: NCI1 PROTEINS DD MUTAG COLLAB RDT-B RDT-M5K IMDB-B BBBP Tox21 ToxCast SIDER
Metrics: classification accuracy ROC-AUC
Baselines: GL WL DGK InfoGraph GraphCL JOAO AD-GCL RGCL PGCL Infomax EdgePred AttrMasking
Builds on: GraphCL RGCL BGRL Weisfeiler-Lehman test
Closest papers by meaning
- TopoGCL: Topological Graph Contrastive Learning (AAAI 2024 · similarity 0.92)
- Does GCL Need a Large Number of Negative Samples? Enhancing Graph Contrastive Learning with Effective and Efficient Negative Sampling (AAAI 2025 · similarity 0.91)
- 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)
- Community-Invariant Graph Contrastive Learning (ICML 2024 · similarity 0.90)
- Graph Contrastive Invariant Learning from the Causal Perspective (AAAI 2024 · similarity 0.90)
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