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Geometry-Aware Edge Pooling for Graph Neural Networks
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Proposes MagEdgePool and SpreadEdgePool, non-trainable edge-contraction graph pooling layers that greedily collapse edges with the smallest change in diffusion-distance magnitude (or spread), and evaluates them on graph classification, pooling ratios, and regression.
Problem
Existing graph pooling methods (node dropping, node clustering, EdgePool) often discard fundamental graph structure, giving unreliable performance across datasets, tasks and pooling ratios and poor preservation of geometry and spectral properties.
Approach
Treat graphs as metric spaces with diffusion distances and contract edges in order of the change in magnitude (an isometry-invariant diversity measure) they cause, using spread as a cheaper, closely related substitute.
Key results
- MagEdgePool and SpreadEdgePool achieve the best mean ranks in graph classification (2.4 and 3.0) across eight TU datasets, versus 3.6 for NDP and 7.6 for DiffPool.
- On DHFR, SpreadEdgePool reaches 90.7% accuracy, about 17 points above the no-pooling GNN (71.4%).
- The authors report that SpreadEdgePool and MagEdgePool keep low spectral distance and magnitude difference across pooling ratios, and stay stable at extreme ratios (e.g. 6.25%) where other non-trainable methods drop.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MagEdgePool instead of no pooling | Graph classification GNN · ENZYMES | accuracy: 87.3 ± 2.5 -> 91.5 ± 3.2 | Helped |
| Use SpreadEdgePool instead of no pooling | Graph classification GNN · DHFR | accuracy: 71.4 ± 1.9 -> 90.7 ± 3.8 | Helped |
| Use MagEdgePool instead of no pooling | Graph classification GNN · Mutagenicity | accuracy: 80.1 ± 1.3 -> 77.5 ± 2.7 | Hurt |
| Use MagEdgePool instead of no pooling | Graph classification GNN · PROTEINS | accuracy: 73.8 ± 0.8 -> 76.4 ± 3.9 | Helped |
| Use MagEdgePool instead of no pooling | Graph classification GNN · IMDB-B | accuracy: 69.7 ± 0.7 -> 72.4 ± 1.7 | Helped |
| Use MagEdgePool instead of no pooling | Graph classification GNN · IMDB-M | accuracy: 46.0 ± 0.7 -> 47.4 ± 1.7 | Helped |
| Use SpreadEdgePool instead of no pooling | Graph classification GNN · NCI1 | accuracy: 76.5 ± 1.8 -> 73.4 ± 2.5 | Hurt |
| Use MagEdgePool instead of no pooling | Graph classification GNN · NCI109 | accuracy: 74.3 ± 2.0 -> 73.0 ± 3.3 | Hurt |
| Replace MagEdgePool with SpreadEdgePool | Graph classification GNN · ENZYMES | accuracy: 91.5 ± 3.2 -> 92.8 ± 1.6 | No clear effect |
| Use MagEdgePool instead of no pooling | Graph regression GNN · MolEsol | RMSE: 1.44 ± 0.10 -> 1.47 ± 0.11 | Hurt |
| Use MagEdgePool instead of no pooling | Graph regression GNN · MolFreeSolv | RMSE: 2.98 ± 0.78 -> 2.81 ± 0.30 | Helped |
| Use SpreadEdgePool instead of no pooling | Graph regression GNN · MolLipo | RMSE: 0.98 ± 0.30 -> 0.91 ± 0.20 | Helped |
Surprising findings
- Non-trainable pooling outperformed trainable pooling layers on several datasets (ENZYMES, DHFR, IMDB-BINARY, IMDB-MULTI), suggesting trainable pooling is not necessary for strong benchmark performance.
- Spread and magnitude gave nearly identical structure-preservation scores on NCI1, with nigh-perfect correlation between them under diffusion distances.
Limitations
- Assumes redundancy and homophily in the graph so that geometry-guided contraction is beneficial; not useful when structure preservation is not task-relevant.
- Non-trainable design cannot adapt pooling to the learning objective.
- Relies on efficient distance computation; only one diffusion distance variant explored; magnitude cost is cubic in graph size.
Experimental setup
Datasets: ENZYMES PROTEINS Mutagenicity DHFR IMDB-BINARY IMDB-MULTI NCI1 NCI109 MolESOL MolFreeSolv MolLipo
Benchmarks: ENZYMES PROTEINS Mutagenicity DHFR IMDB-BINARY IMDB-MULTI NCI1 NCI109 MolESOL MolFreeSolv MolLipo
Metrics: accuracy mean rank RMSE spectral distance relative magnitude difference
Baselines: No Pooling NDP Graclus NMF TopK SAGPool DiffPool MinCut EdgePool
Builds on: EdgePool GIN Graph U-Nets (TopK) SAGPool DiffPool
Closest papers by meaning
- Enhancing Graph Classification Robustness with Singular Pooling (NeurIPS 2025 · similarity 0.90)
- SkipPool: Improved Sparse Hierarchical Graph Pooling with Differentiable Exploration (AAAI 2025 · similarity 0.90)
- MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks (ICLR 2025 · similarity 0.90)
- ENAHPool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks (ICML 2025 · similarity 0.89)
- Boosting Graph Pooling with Persistent Homology (NeurIPS 2024 · similarity 0.89)
- Fair Graph U-Net: A Fair Graph Learning Framework Integrating Group and Individual Awareness (AAAI 2025 · similarity 0.88)
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