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Towards Pre-trained Graph Condensation via Optimal Transport
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Proposes PreGC, a task- and architecture-agnostic pre-trained graph condensation method that uses hybrid-interval graph heat diffusion augmentation and optimal transport plan matching, with a traceable label harmonizer to transfer task labels to condensed nodes.
Problem
Existing graph condensation methods depend on a fixed GNN architecture and task-specific supervision, which limits reuse of condensed graphs across tasks and GNNs.
Approach
Derives a generalized GC objective (representation-level plus semantic-level discrepancy) and matches the optimal graph transport plan with the representation transport plan, so semantic correspondences are task-free; graph heat diffusion with randomly sampled step sizes augments representations to reduce architecture bias; the representation plan doubles as a traceable semantic harmonizer that ma
Key results
- On Pubmed at r=0.15%, PreGC reaches 79.8±1.3 average accuracy across nine GNNs, the highest among compared methods and above the whole-graph average of 78.1.
- On H&M (r=2.5%), PreGC improves category accuracy to 69.1 and price R^2 to 34.4 in ablation; PreGC_ft reaches 69.98 on C->C and 34.75 on P->P.
- On OGB-Arxiv Y->T, PreGC achieves 59.62 vs. 53.32 for the best baseline CGC (6.30 point gain).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| fine-tune the assignment matrix | PreGC · OGB-Arxiv T→T | accuracy: 60.55±0.43 -> 60.81±0.40 | Helped |
| fine-tune the assignment matrix | PreGC · OGB-Arxiv Y→T | accuracy: 59.62±0.47 -> 60.86±0.43 | Helped |
| fine-tune the assignment matrix | PreGC · OGB-Arxiv Y→Y | accuracy: 52.34±0.30 -> 52.47±0.20 | Helped |
| fine-tune the assignment matrix | PreGC · OGB-Arxiv T→Y | accuracy: 51.49±0.36 -> 52.41±0.25 | Helped |
| fine-tune the assignment matrix | PreGC · H&M C→C | accuracy: 69.06±0.25 -> 69.98±0.24 | Helped |
| fine-tune the assignment matrix | PreGC · H&M P→C | accuracy: 68.86±0.29 -> 69.98±0.28 | Helped |
| fine-tune the assignment matrix | PreGC · H&M P→P | R²: 34.39±0.93 -> 34.75±0.74 | Helped |
| fine-tune the assignment matrix | PreGC · H&M C→P | R²: 33.17±1.05 -> 34.63±0.69 | Helped |
| add graph diffusion augmentation (ablation) | PreGC · H&M category, r=2.5% | accuracy: 66.6±0.7 -> 69.1±0.3 | Helped |
| add graph diffusion augmentation (ablation) | PreGC · H&M price, r=2.5% | R²: 32.2±0.9 -> 34.4±0.9 | Helped |
| add graph diffusion augmentation (ablation) | PreGC · H&M category, r=5.0% | accuracy: 67.9±0.4 -> 71.1±0.3 | Helped |
| add graph diffusion augmentation (ablation) | PreGC · H&M price, r=5.0% | R²: 33.3±1.4 -> 36.9±1.1 | Helped |
Surprising findings
- Removing the cost loss on H&M drops price R^2 from 34.4 to 29.1, showing predefined labels hurt cross-task transfer.
- Only SFGC and PreGC exceed whole-graph average accuracy across GNNs on Pubmed, per the authors.
Limitations
- Some reported results are lower than baselines on certain tasks (e.g., Cora NC at 1.3% with CGC or SGDD ahead; PreGC 54.6 vs SGDD 59.0 on Citeseer-like NC row).
- Node significance and data valuation are shown mainly on Cora with limited quantitative analysis.
- Test-time fine-tuning adds a variant (PreGC_ft) whose gains are modest on some settings.
Experimental setup
Datasets: Cora Citeseer Pubmed OGB-Arxiv H&M
Benchmarks: Cora Citeseer Pubmed OGB-Arxiv H&M
Metrics: test accuracy NMI AUC R^2 average nearest neighbor distance labeled reconstruction error
Baselines: GCDM GCond SFGC SGDD GDEM CGC
Builds on: GCond SGC fused Gromov-Wasserstein graph heat equation
Closest papers by meaning
- Adapting Precomputed Features for Efficient Graph Condensation (ICML 2025 · similarity 0.92)
- Bonsai: Gradient-free Graph Condensation for Node Classification (ICLR 2025 · similarity 0.91)
- GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights (NeurIPS 2025 · similarity 0.90)
- Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching (ICML 2024 · similarity 0.89)
- Can Classic GNNs Be Strong Baselines for Graph-level Tasks? Simple Architectures Meet Excellence (ICML 2025 · similarity 0.88)
- Two Heads Are Better Than One: Boosting Graph Sparse Training via Semantic and Topological Awareness (ICML 2024 · similarity 0.88)
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