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Empowering Active Learning for 3D Molecular Graphs with Geometric Graph Isomorphism
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Proposes an active learning paradigm for 3D molecular graphs that combines a provably GWL-at-least-as-expressive geometric diversity measure (moments of reference distances, triangles, cross angles) with Bayesian (MC-dropout) SphereNet uncertainty, selecting batches via a QP.
Problem
Active learning for 3D molecular graph property prediction is lacking a principled diversity measure that can compare molecules with different planar graphs and capture 3D geometry, plus a geometry-aware uncertainty estimator to reduce expensive DFT annotation.
Approach
Define reference-distance, triangular, and cross-angle graph isometries whose geometric distributions (summarized by statistical moments around four reference points, USR-style) give a 48-dim model-agnostic descriptor for diversity; combine with MC-dropout SphereNet uncertainty and solve a QP for joint uncertainty-diversity batch selection.
Key results
- On QM9 with SphereNet, the proposed method attains lower test MAE than Random, Learning Loss, Coreset, and Evidential baselines at every AL iteration for mu, alpha, homo, and lumo, with paired t-test p-values below 0.05 for all comparisons.
- Diversity-only variant consistently beats Coreset on mu and lumo across AL iterations (ablation).
- Per-iteration wall-clock time is 64.9 min for the proposed method versus 53 min for Random and 127 min for Coreset.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed geometric diversity descriptor instead of SOAP (ablation) | Diversity-only active learning with SphereNet · QM9 mu | MAE: 1322 -> 1092 | Helped |
| Use the proposed geometric diversity descriptor instead of SOAP (ablation) | Diversity-only active learning with SphereNet · QM9 lumo | MAE: 667 -> 604 | Helped |
| Use proposed uncertainty and diversity instead of SOAP-based uncertainty and diversity | SphereNet active learning · QM9 mu | MAE: 1280 -> 1072 | Helped |
| Use proposed uncertainty and diversity instead of SOAP-based uncertainty and diversity | SphereNet active learning · QM9 lumo | MAE: 681 -> 594 | Helped |
| Add the proposed diversity component to uncertainty-only sampling (ablation) | Proposed SphereNet active learning · QM9 mu and lumo | MAE | Helped |
| Combine diversity and uncertainty instead of using either component alone (ablation) | Proposed SphereNet active learning · QM9 mu and lumo | MAE | Helped |
| Use the proposed diversity component instead of Coreset (ablation) | Diversity-only active learning with SphereNet · QM9 mu and lumo | MAE | Helped |
| Use the full proposed active-learning framework instead of classic AL baselines | SphereNet · QM9 mu, alpha, homo, and lumo | MAE | Helped |
| Use the full proposed active-learning framework instead of classic AL baselines | DimeNet++ · QM9 mu and lumo | MAE | Helped |
| Use the full proposed active-learning framework instead of classic AL baselines | SphereNet · MD17 Aspirin atomic forces | MAE | Helped |
Surprising findings
- Evidential uncertainty performs much worse than all other methods, with MAE far higher on all four QM9 properties.
- The diversity-only component alone performs strongly, only slightly below the full method.
Limitations
- Experiments are limited to small molecules on medium-scale QM9 and MD17 datasets.
- Diversity advantage has not been incorporated into 3D GNN architectures for diversity sampling.
- Batch selection relaxes the integer QP and uses greedy top-k rounding.
Experimental setup
Datasets: QM9 MD17
Benchmarks: QM9 MD17
Metrics: MAE paired t-test p-values computation time
Baselines: Random Sampling Coreset Learning Loss Evidential Uncertainty BatchBALD SOAP-based diversity
Builds on: USR GWL test SphereNet Coreset BatchBALD
Closest papers by meaning
- Enhancing Molecular Representation Learning Through the Combination of 3D and 2D Graph Machine Learning (Student Abstract) (AAAI 2025 · similarity 0.89)
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- 3D Denoisers Are Good 2D Teachers: Molecular Pretraining via Denoising and Cross-Modal Distillation (AAAI 2025 · similarity 0.88)
- HAGO-Net: Hierarchical Geometric Message Passing for Molecular Representation Learning (AAAI 2024 · similarity 0.88)
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