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Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks
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Proposes ConAN, an E(3)-invariant message-passing network that fuses 2D graph features with 3D conformer ensembles via an entropic Fused Gromov-Wasserstein barycenter aggregation, evaluated on MoleculeNet regression and SARS-CoV-2 classification.
Problem
Molecular property prediction typically uses either 2D graphs or a single 3D conformer, ignoring the ensemble of low-energy conformers that governs many properties; existing conformer-ensemble methods are costly in conformer count and lack principled aggregation.
Approach
Aggregate 2D GAT features and SchNet features of K RDKit-generated conformers through a differentiable entropic FGW barycenter (solved with GPU Sinkhorn iterations), giving an order-invariant, E(3)-invariant conformer ensemble representation with a convergence rate of O(1/K).
Key results
- ConAN-FGW reaches RMSE 0.454 on Lipo, 0.514 on ESOL, 1.423 on FreeSolv and 0.654 on BACE, beating the listed baselines on all four regression datasets (UniMol 0.603 / 0.788 / 1.480).
- On CoV-2 3CL, ConAN-FGW with 10 conformers reaches ROC 0.924 versus 0.901 for CP3D-NDU with 200 conformers.
- Ablation shows K=10 best on Lipo and ESOL, and ConAN-FGW improves more consistently with larger K than ConAN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add FGW barycenter aggregation to ConAN (ablation) | ConAN · Lipo | RMSE: 0.531 \pm 0.013 -> 0.454 \pm 0.011 | Helped |
| add FGW barycenter aggregation to ConAN (ablation) | ConAN · ESOL | RMSE: 0.591 \pm 0.025 -> 0.514 \pm 0.019 | Helped |
| add FGW barycenter aggregation to ConAN (ablation) | ConAN · FreeSolv | RMSE: 1.548 \pm 0.281 -> 1.423 \pm 0.272 | Helped |
| add FGW barycenter aggregation to ConAN (ablation) | ConAN · BACE | RMSE: 0.816 \pm 0.032 -> 0.654 \pm 0.105 | Helped |
| add FGW barycenter aggregation (ablation) | ConAN · CoV-2 3CL | ROC: 0.881 $\pm$ 0.009 -> 0.924 $\pm$ 0.012 | Helped |
| add FGW barycenter aggregation (ablation) | ConAN · CoV-2 3CL | PRC: 0.317 $\pm$ 0.052 -> 0.442 $\pm$ 0.047 | Helped |
| add FGW barycenter aggregation (ablation) | ConAN · CoV-2 | ROC: 0.635 $\pm$ 0.061 -> 0.6875 $\pm$ 0.024 | Helped |
| add FGW barycenter aggregation (ablation) | ConAN · CoV-2 | PRC: 0.031 $\pm$ 0.023 -> 0.036 $\pm$ 0.014 | Mixed |
| use 3D conformers instead of only the 2D graph (ablation) | ConAN · Lipo | RMSE: 1.387 \pm 0.206 -> 0.619 \pm 0.045 | Helped |
| use 3D conformers instead of only the 2D graph (ablation) | ConAN · ESOL | RMSE: 2.288 \pm 0.017 -> 0.536 \pm 0.054 | Helped |
| use 3D conformers instead of only the 2D graph (ablation) | ConAN · FreeSolv | RMSE: 8.564 \pm 1.345 -> 2.306 \pm 0.807 | Helped |
| use 3D conformers instead of only the 2D graph (ablation) | ConAN · BACE | RMSE: 1.844 \pm 0.33 -> 0.705 \pm 0.064 | Helped |
Surprising findings
- ConAN-FGW with only 3 to 10 conformers outperforms the variant using 5 to 20 conformers without barycenter aggregation.
- On the CoV-2 datasets, the PRC of ConAN-FGW trails CP3D-NDU with average-neighbor conformers, which the authors note.
Limitations
- Gains in CoV-2 PRC and some datasets (FreeSolv, BACE for ConAN) are within large standard deviations; results not consistently best.
- Performance does not monotonically improve with the number of conformers K.
- Relies on RDKit conformer sampling without energy-based selection; future work proposed on better sampling.
Experimental setup
Datasets: Lipo ESOL FreeSolv BACE CoV-2 3CL Cov-2
Benchmarks: Lipo ESOL FreeSolv BACE CoV-2 3CL Cov-2
Metrics: RMSE ROC AUC PRC AUC
Baselines: 2D-GAT D-MPNN AttentiveFP GROVER ChemRL-GEM MolFormer UniMol SchNet ChemProp3D CP3D-NDU
Builds on: SchNet GAT Fused Gromov-Wasserstein distance RDKit distance geometry FGW-Mixup
Closest papers by meaning
- Learning Over Molecular Conformer Ensembles: Datasets and Benchmarks (ICLR 2024 · similarity 0.91)
- Swallowing the Bitter Pill: Simplified Scalable Conformer Generation (ICML 2024 · similarity 0.89)
- Empowering Active Learning for 3D Molecular Graphs with Geometric Graph Isomorphism (NeurIPS 2024 · similarity 0.87)
- 3D Denoisers Are Good 2D Teachers: Molecular Pretraining via Denoising and Cross-Modal Distillation (AAAI 2025 · similarity 0.86)
- Beyond Atoms: Enhancing Molecular Pretrained Representations with 3D Space Modeling (ICML 2025 · similarity 0.86)
- WGFormer: An SE(3)-Transformer Driven by Wasserstein Gradient Flows for Molecular Ground-State Conformation Prediction (ICML 2025 · similarity 0.86)
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