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TopoGCL: Topological Graph Contrastive Learning
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Proposes TopoGCL, which adds a topo-topo contrastive loss over extended persistence representations (new extended persistence landscapes and images) to standard graph contrastive learning, reporting gains on 12 graph classification benchmarks.
Problem
Existing graph contrastive learning overlooks higher-order graph substructure and shape information, which persistent homology captures but has never been used in GCL for unsupervised graph classification.
Approach
Adds a topological contrastive mode that contrasts extended persistence representations (EPI or a new EPL summary with a stability proof) of two augmented views of the same graph, alongside the standard global-global graph contrastive loss, with a extended topological layer encoder.
Key results
- TopoGCL reports best results on 11 of 12 datasets, e.g., 90.09% on MUTAG and 82.12% on DHFR versus the best baseline.
- On REDDIT-B TopoGCL reaches 90.40% vs. 90.34% for RGCL, and on IMDB-B 74.67% vs. 73.65% for GCL-TAGS.
- Under 20% Gaussian node-feature noise, TopoGCL outperforms AD-GCL and RGCL on MUTAG, PTC_MR and IMDB-B (e.g., 89.47% vs. 88.20% on MUTAG).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace EPI with PI (ablation) | TopoGCL · MUTAG | accuracy: 89.78$\pm$1.33 -> 90.09$\pm$0.93 | Helped |
| replace EPL with PL (ablation) | TopoGCL · PTC_MR | accuracy: 62.78$\pm$0.87 -> 63.43$\pm$1.13 | Helped |
| replace EPI with PI (ablation) | TopoGCL · IMDB-B | accuracy: 70.55$\pm$0.19 -> 74.67$\pm$0.32 | Helped |
| add topo-topo contrastive learning (ablation) | TopoGCL · MUTAG | accuracy: 87.85$\pm$0.79 -> 90.09$\pm$0.93 | Helped |
| add topo-topo contrastive learning (ablation) | TopoGCL · PTC_MR | accuracy: 61.62$\pm$1.10 -> 63.43$\pm$1.13 | Helped |
| add topo-topo contrastive learning (ablation) | TopoGCL · IMDB-B | accuracy: 71.31$\pm$0.36 -> 74.67$\pm$0.32 | Helped |
Surprising findings
- Persistence landscapes (EPL) and extended persistence images (EPI) give comparable accuracy, with EPL somewhat faster to compute.
- Topological contrastive learning on PTC_MR performs better with EPL than EPI.
Limitations
- Stability guarantee is proven only for EPL; EPI stability is left open.
- Reported gains over runner-ups are small (average about 1.25%) and several differences are within standard deviation.
- Evaluated only on graph classification with SVM readout; node classification and link prediction left to future work.
Experimental setup
Datasets: NCI1 PROTEINS DD MUTAG DHFR BZR COX2 PTC_MR PTC_FM IMDB-BINARY IMDB-MULTI REDDIT-BINARY
Benchmarks: NCI1 PROTEINS DD MUTAG DHFR BZR COX2 PTC_MR PTC_FM IMDB-BINARY IMDB-MULTI REDDIT-BINARY
Metrics: 10-fold cross-validation accuracy with SVM standard deviation over 5 runs one-sided t-test
Baselines: Graphlet Kernel Weisfeiler-Lehman subtree kernel Deep Graph Kernels node2vec sub2vec graph2vec InfoGraph GraphCL AD-GCL AutoGCL RGCL GCL-TAGS
Builds on: GraphCL InfoGraph persistence images persistence landscapes GIN
Closest papers by meaning
- Hierarchical Topology Isomorphism Expertise Embedded Graph Contrastive Learning (AAAI 2024 · similarity 0.92)
- TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration (ICML 2025 · similarity 0.90)
- Does GCL Need a Large Number of Negative Samples? Enhancing Graph Contrastive Learning with Effective and Efficient Negative Sampling (AAAI 2025 · similarity 0.90)
- ReGCL: Rethinking Message Passing in Graph Contrastive Learning (AAAI 2024 · similarity 0.90)
- S3GCL: Spectral, Swift, Spatial Graph Contrastive Learning (ICML 2024 · similarity 0.89)
- Exploitation of a Latent Mechanism in Graph Contrastive Learning: Representation Scattering (NeurIPS 2024 · similarity 0.89)
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