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A Plug-and-Play Quaternion Message-Passing Module for Molecular Conformation Representation
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Proposes a parameter-free quaternion message-passing (QMP) module that encodes bond rotations and dihedrals via a chained Hamilton product, plugged into invariant GNNs to improve molecular conformation representation.
Problem
Invariant GNNs for 3D molecules ignore opposite-side dihedrals and thus cannot distinguish conformations produced by bond torsions, while high-order equivariant or full dihedral models are computationally expensive.
Approach
Represent the 3D rotations from each bond's 1-hop neighboring bonds as unit quaternions, sort them by rotation angle, and merge them with an accelerated chained Hamilton product; the real part of the output is SE(3)-invariant yet encodes same-side and opposite-side dihedrals, and is concatenated into existing invariant GNNs with one line of code.
Key results
- Q-SchNet improves over SchNet on all eight MD17 molecules (e.g., Aspirin force MAE 1.339 to 1.289 and Ethanol 0.738 to 0.468).
- Q-DimeNet++ and Q-SphereNet improve over their backbones on most MD17 molecules (e.g., Aspirin 0.325 to 0.316 for Q-DimeNet++).
- On N-body prediction, Q-EGNN reduces MSE from 0.724 to 0.668 (×10^-2) relative to EGNN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add QMP to DimeNet++ | DimeNet++ · MD17 (Aspirin, Benzene, Ethanol, Malonaldehyde, Toluene, Uracil) | force MAE: 0.325 -> 0.316; 0.168 -> 0.151; 0.150 -> 0.148; 0.263 -> 0.241; 0.117 -> 0.107; 0.189 -> 0.178 | Helped |
| Add QMP to DimeNet++ | DimeNet++ · MD17 (Naphthalene, Salicylic acid) | force MAE: 0.100 -> 0.106; 0.231 -> 0.238 | Hurt |
| Add QMP to DimeNet++ | DimeNet++ · MD17@CCSD (Benzene, Ethanol) | force MAE: 0.049 -> 0.048; 0.129 -> 0.108 | Helped |
| Add QMP to DimeNet++ | DimeNet++ · MD17@CCSD (Aspirin, Malonaldehyde) | force MAE: 0.387 -> 0.365; 0.211 -> 0.231 | Mixed |
| Add QMP to DimeNet++ | DimeNet++ · OC20 IS2RE Average | energy MAE: 0.9015 -> 0.8950 | Helped |
| Add QMP to DimeNet++ | DimeNet++ · OC20 IS2RE Average | EwT (%): 1.77 -> 1.90 | Helped |
| Add QMP to EGNN | EGNN · N-body system future position estimation | MSE (×10−2): 0.724 -> 0.668 | Helped |
| Use j-side rotations only instead of rotations from both sides (ablation) | DimeNet++ with QMP · MD17 Aspirin and Benzene | force MAE: 0.316 -> 0.323; 0.151 -> 0.152 | Mixed |
| Use i-side rotations only instead of rotations from both sides (ablation) | DimeNet++ with QMP · MD17 Aspirin and Benzene | force MAE: 0.316 -> 0.360; 0.151 -> 0.166 | Hurt |
| Remove angle-based sorting (ablation) | DimeNet++ with QMP · MD17 Aspirin and Benzene | force MAE: 0.316 -> 0.390; 0.151 -> 0.173 | Hurt |
Surprising findings
- Using only j-side rotations or only i-side rotations gives little or no improvement, and removing angle-based sorting significantly degrades performance.
Limitations
- Only the real part is used, so the module is designed for invariant GNNs; equivariant use is only a preliminary N-body experiment.
- Gains on MD17@CCSD and OC20 are inconsistent across backbones (some Q-variants are not improved).
Experimental setup
Datasets: MD17 MD17@CCSD OC20 N-body particle system
Benchmarks: MD17 MD17@CCSD OC20 IS2RE N-body system
Metrics: force MAE energy MAE EwT MSE
Baselines: sGDML DimeNet SchNet DimeNet++ SphereNet CGCNN SE(3) Transformer TFN EGNN
Builds on: DimeNet DimeNet++ SphereNet SchNet quaternion product unit
Closest papers by meaning
- Learning 3D Representations of Molecular Chirality with Invariance to Bond Rotations (ICLR 2022 · similarity 0.89)
- LagNet: Deep Lagrangian Mechanics for Plug-and-Play Molecular Representation Learning (AAAI 2023 · similarity 0.87)
- Learning Over Molecular Conformer Ensembles: Datasets and Benchmarks (ICLR 2024 · similarity 0.87)
- HAGO-Net: Hierarchical Geometric Message Passing for Molecular Representation Learning (AAAI 2024 · similarity 0.86)
- Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks (ICML 2024 · similarity 0.85)
- Predicting directional flexibility in proteins (NeurIPS 2026 · similarity 0.85)
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