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Graph Positional and Structural Encoder
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Trains a deep gated GCN with virtual node and random input features to reconstruct six graph positional/structural encodings on MolPCBA, then uses the frozen encoder's outputs as PSE features for downstream GNNs and graph Transformers.
Problem
Hand-crafted positional and structural encodings (PSEs) are task-dependent and costly to compute, and naively combining them does not help; there is no one-size-fits-all PSE for graph learning.
Approach
Pretrain an MPNN encoder (GatedGCN, 20 layers, virtual node, random node features) via self-supervised reconstruction of multiple PSEs (LapPE, LapEigVal, electrostatic PE, RWSE, heat kernel diagonal, cycle counts) from graph structure alone, then reuse its latent representations as transferable PSEs for any downstream GNN or GT.
Key results
- GPS+GPSE reaches 0.0648 MAE on ZINC (subset), versus 0.0700 for GPS+RWSE and 0.1182 for GPS with no PSE.
- GPSE attains average test R^2 of 0.9790 across six PSEs when trained on 5% of MolPCBA, rising to 0.9979 with 90% of the data.
- Across five GNNs on ZINC (12k), GPSE gives 56.24% average MAE reduction over no-PSE baselines, versus 50.85% for AllPSE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| augment GPS with GPSE instead of RWSE | GPS · ZINC (subset) | MAE: 0.0700 ± 0.0040 -> 0.0648 ± 0.0030 | Helped |
| augment GPS with GPSE instead of RWSE | GPS · PCQM4Mv2 (subset) | MAE: 0.1230 ± 0.0008 -> 0.1196 ± 0.0004 | Helped |
| augment GPS with GPSE instead of RWSE | GPS · MolHIV | AUROC: 0.7880 ± 0.0101 -> 0.7815 ± 0.0133 | Hurt |
| augment GPS with GPSE instead of LapPE | GPS · MolPCBA | AP: 0.2939 ± 0.0016 -> 0.2911 ± 0.0036 | Hurt |
| augment GNNs with GPSE instead of no PSE | GCN, GatedGCN, GIN, GINE, and Transformer · ZINC (12k subset) | MAE | Helped |
| augment GPS with GPSE instead of computed PSEs | GPS · Peptides-struct | MAE: 0.2500 ± 0.0005 -> 0.2464 ± 0.0025 | Helped |
| augment GINE with GPSE instead of no augmentation | GINE · MoleculeNet scaffold split | AUROC | Helped |
| exclude one PSE type from GPSE pre-training (ablation) | GPSE · PCQM4Mv2 and MolHIV | downstream performance | Hurt |
| increase the GPSE pre-training sample size (ablation) | GPSE · held-out PSE prediction | R²: 0.9790 -> 0.9979 | Helped |
| train GPSE on ChEMBL or MolPCBA rather than smaller datasets (ablation) | GPSE · ZINC | MAE | Helped |
| fine-tune GPSE on the downstream dataset (ablation) | GPSE · ZINC | MAE | Helped |
| fine-tune GPSE on the downstream dataset (ablation) | GPSE · PCQM4Mv2 | MAE | No clear effect |
Surprising findings
- Concatenating LapPE and RWSE gives no benefit over either alone, and AllPSE is often worse than individual PSEs.
- Random input features alone do not improve GIN on CSL/EXP, whereas GPSE does, yet GPSE still falls short of explicit LapPE/RWSE on those synthetic benchmarks.
Limitations
- The GPSE model is prohibitively large to train efficiently on datasets with over one million graphs.
- Expressivity gain from GPSE is partial; it does not fully resolve beyond-1-WL limitations compared with explicit LapPE/RWSE on CSL and EXP.
- Gains are inconsistent across datasets; on MolHIV and some MoleculeNet tasks GPSE only matches the best explicit PSE or underperforms.
Experimental setup
Datasets: MolPCBA ZINC PCQM4Mv2 MolHIV Peptides-struct Peptides-func CIFAR10 MNIST arXiv Proteins MoleculeNet (BBBP, BACE, Tox21, ToxCast, SIDER, ClinTox, MUV, HIV) CSL
Benchmarks: ZINC PCQM4Mv2 MolHIV MolPCBA Peptides-struct Peptides-func CIFAR10 MNIST MoleculeNet arXiv Proteins CSL
Metrics: MAE AUROC AP ACC R^2
Baselines: GCN GIN CIN CRaWI PR-MPNN SAT GPS+LapPE GPS+RWSE GraphLoG GraphMAE Graph MLP-Mixer DRew
Builds on: GraphGPS GatedGCN LapPE RWSE SignNet
Closest papers by meaning
- Learning Efficient Positional Encodings with Graph Neural Networks (ICLR 2025 · similarity 0.89)
- Positional Encoding meets Persistent Homology on Graphs (ICML 2025 · similarity 0.89)
- Learnable Spatial-Temporal Positional Encoding for Link Prediction (ICML 2025 · similarity 0.89)
- What Improves the Generalization of Graph Transformers? A Theoretical Dive into the Self-attention and Positional Encoding (ICML 2024 · similarity 0.89)
- On the Stability of Expressive Positional Encodings for Graphs (ICLR 2024 · similarity 0.89)
- GPEN: Global Position Encoding Network for Enhanced Subgraph Representation Learning (ICML 2025 · similarity 0.89)
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