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Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learning
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Proposes physical consistency losses (optimality and score consistency) linking an energy model and a diffusion-based equilibrium structure model so that higher-accuracy energy data and force data improve structure prediction in molecular multi-task learning.
Problem
Molecular datasets have heterogeneous quality and coverage: equilibrium structures are often labeled at lower theory levels (PM6) than energies (B3LYP/6-31G*), and datasets for related tasks (forces, off-equilibrium structures) provide no direct supervision for structure prediction, so multi-task le
Approach
Enforce physical laws between energy and equilibrium structure as consistency losses: the equilibrium structure should minimize energy (optimality consistency, at large diffusion steps) and should match the Boltzmann score of the energy model (score consistency, at small steps); only the structure decoder is updated so the energy model is not contaminated by lower-accuracy structure data.
Key results
- Consistency training lowers structure RMSD vs multi-task on PCQ (denoising mean 1.189 -> 1.158 Å) and QM9 (denoising mean 0.928 -> 0.848 Å) without any more accurate structure data.
- Adding PM6-subset force labels with consistency training gives denoising mean RMSD 1.113 Å on PCQ vs 1.199 Å for multi-task with the same data.
- Consistency advantage persists after fine-tuning (e.g., QM9 denoising mean 0.889 -> 0.835 Å).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add optimality and score consistency losses to multi-task training | Molecular energy and structure prediction model trained on PM6 · PCQ and QM9, denoising and DDIM | Mean RMSD (Å): PCQ denoising: 1.189 -> 1.158; PCQ DDIM: 1.041 -> 1.007; QM9 denoising: 0.928 -> 0.848; QM9 DDIM: 0.669 -> 0.650 | Helped |
| Add optimality and score consistency losses to multi-task training | Molecular energy and structure prediction model trained on PM6 with SPICE force data · PCQ and QM9, denoising and DDIM | Mean RMSD (Å): PCQ denoising: 1.161 -> 1.147; PCQ DDIM: 1.047 -> 1.013; QM9 denoising: 0.876 -> 0.842; QM9 DDIM: 0.670 -> 0.644 | Helped |
| Add optimality and score consistency losses to multi-task training | Molecular energy and structure prediction model trained on PM6 with PM6 subset force data · PCQ and QM9, denoising and DDIM | Mean RMSD (Å): PCQ denoising: 1.199 -> 1.113; PCQ DDIM: 1.027 -> 1.019; QM9 denoising: 0.914 -> 0.836; QM9 DDIM: 0.648 -> 0.646 | Helped |
| Pre-train with optimality and score consistency losses, then fine-tune | Molecular structure prediction model trained on PM6 · PCQ and QM9, denoising and DDIM, fine-tuned | Mean RMSD (Å): PCQ denoising: 1.158 -> 1.152; PCQ DDIM: 0.921 -> 0.918; QM9 denoising: 0.889 -> 0.835; QM9 DDIM: 0.501 -> 0.493 | Helped |
| Add consistency losses | Molecular structure prediction model trained on PM6 · PCQ and QM9, test coverage | Coverage: Table 7 shows improvement in all reported PM6 settings after adding the consistency loss. | Helped |
| Add consistency losses | Molecular structure prediction model trained on PM6 · PM6 and PCQ structures in validation | Energy prediction MAE (eV): PM6 structures: 96.08 -> 88.58; 83.15 -> 78.56; 79.00 -> 72.61. PCQ structures: 136.66 -> 127.06; 135.93 -> 110.80; 117. | Helped |
| Add consistency losses | Molecular structure prediction model trained on PM6 · PM6 and PM6 with force data, PCQ test molecules | EGap: PM6: 0.1278 -> 0.1172; PM6 with SPICE force: 0.0546 -> 0.0306; PM6 with PM6 subset force: 0.1163 -> 0.1013 | Helped |
| Add force data to multi-task training without consistency losses | Molecular energy and structure prediction model · PCQ and QM9 structure prediction | Mean RMSD (Å): Compared with PM6 alone, SPICE force changes: 1.189 -> 1.161, 1.041 -> 1.047, 0.928 -> 0.876, 0.669 -> 0.670; PM6 subset | Mixed |
Surprising findings
- Adding force data does not uniformly improve multi-task learning; the gains are inconsistent, while consistency losses improve more consistently.
Limitations
- Improvements are bounded by the abundance of the involved data; gains are moderate (about 0.03 to 0.09 Å).
- Force data from SPICE use a different DFT setting (wB97M-D3(BJ)/def2-TZVPPD) than the PM6 energy labels, creating a level-of-theory mismatch.
- Evaluation is limited to energy and structure prediction; the consistency idea is shown for only one pair of physically related tasks.
Experimental setup
Datasets: PubChemQC B3LYP/6-31G*//PM6 SPICE (PubChem subset) PCQM4Mv2 QM9 PubChemQC
Benchmarks: PCQM4Mv2 (PCQ) test structures QM9 test structures
Metrics: RMSD mean RMSD min coverage energy gap (EGap) energy MAE (eV) t-test p-values
Baselines: Multi-task learning
Builds on: denoising diffusion probabilistic models Graphormer GeoMFormer Boltzmann generators
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