Research map / Probabilistic and scientific modeling / Molecules and proteins
Representing Molecules as Random Walks Over Interpretable Grammars
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Represents small, expert-motif-based polymer/molecule datasets as random walks over a learnable context-sensitive graph grammar (motif graph), enabling data-efficient property prediction and interpretable generation.
Problem
Property prediction and generation for complex, designer molecules (gas-separation polymers, photovoltaics, toxicity) with very few labeled examples (about 100-300) where existing molecular ML methods are data-hungry and lack interpretability.
Approach
Builds a hierarchical motif graph from expert-defined motifs and their attachment contexts, models molecules as random walks over this context-sensitive grammar, and parameterizes transition probabilities with a learnable graph heat diffusion whose Laplacian is adjusted by a set-based memory of visited motifs.
Key results
- On HOPV, the method achieves R^2 0.80 versus 0.74 for the second-best (Geo-DEG), and on Group Contribution R^2 0.80 vs 0.70.
- On PTC, accuracy 0.70 is the best reported, versus 0.69 for Geo-DEG.
- In generation, the method yields 100% unique and novel molecules, while JT-VAE and Hier-VAE achieve only 11% and 43% uniqueness on HOPV; synthesizability (Retro* score) on HOPV is 58% versus 19% for DEG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use heuristic motifs instead of expert motifs (ablation) | Ours · Group Contribution | R²: 0.80 ± 0.15 -> 0.74 ± 0.15 | Hurt |
| use heuristic motifs instead of expert motifs (ablation) | Ours · HOPV | MAE: 0.30 ± 0.05 -> 0.22 ± 0.15 | Helped |
| use heuristic motifs instead of expert motifs (ablation) | Ours · HOPV | R²: 0.80 ± 0.06 -> 0.77 ± 0.12 | Hurt |
| use heuristic motifs instead of expert motifs (ablation) | Ours · PTC | Accuracy: 0.70 ± 0.01 -> 0.67 ± 0.02 | Hurt |
| use heuristic motifs instead of expert motifs (ablation) | Ours · PTC | AUC: 0.69 ± 0.03 -> 0.66 ± 0.05 | Hurt |
| use expert motifs rather than heuristic motifs (ablation) | Ours · HOPV test | MAE: 0.288 ± 0.048 -> 0.295 ± 0.049 | Hurt |
| use expert motifs rather than heuristic motifs (ablation) | Ours · HOPV test | R²: 0.765 ± 0.146 -> 0.796 ± 0.105 | Helped |
| use expert motifs rather than heuristic motifs (ablation) | Ours · PTC test | Accuracy: 0.671 ± 0.020 -> 0.705 ± 0.007 | Helped |
| use expert motifs rather than heuristic motifs (ablation) | Ours · PTC test | AUC: 0.659 ± 0.047 -> 0.711 ± 0.018 | Helped |
| use expert motifs rather than heuristic motifs (ablation) | Ours · Group Contribution test | MAE: 0.268 ± 0.084 -> 0.222 ± 0.079 | Helped |
| apply main-chain reversal or side-chain permutation data augmentation (ablation) | Ours grammar training · Downstream tasks | performance | No clear effect |
| use the hierarchical grammar representation instead of bag-of-motifs features | Ours versus Bag-of-Motifs · HOPV test | R²: 0.489 ± 0.062 -> 0.796 ± 0.105 | Helped |
Surprising findings
- Bag-of-motifs with expert motifs was not better than heuristic motifs, suggesting motif quality matters only with a hierarchical representation.
- Heuristic motifs gave substantially lower MAE on HOPV (27% lower) than expert motifs, while expert motifs gave higher R^2.
Limitations
- Relies on expert annotation of motifs and red attachment groups, which takes about a day per dataset per expert.
- Evaluated only on three small datasets (100-350 molecules) and Membership metric is a sanity check; generation synthesizability is measured by a single retrosynthesis planner.
Experimental setup
Datasets: Group Contribution HOPV PTC
Benchmarks: Group Contribution HOPV PTC
Metrics: MAE R^2 accuracy AUC validity uniqueness novelty diversity Retro* score membership
Baselines: wD-MPNN ESAN HM-GNN PN Pre-trained GIN MolCLR UniMol Geo-DEG DEG JT-VAE Hier-VAE Bag-of-Motifs
Builds on: graph grammar ECFP Geo-DEG HM-GNN GIN
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