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Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modeling
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Proposes SPFrame, a local-global frame for crystal property prediction that uses invariant local frames (quaternion-based) plus a global QR/PCA-style frame to keep SO(3) invariance without breaking crystal symmetry, applied to eComFormer.
Problem
Equivariant local frames for crystal property prediction can break crystal symmetry, making symmetry-equivalent atoms indistinguishable, while global frames are too coarse to capture local heterogeneity.
Approach
Construct invariant local frames (predicted quaternions from SO(3)-invariant message passing, converted to rotation matrices) that assign identical frames to symmetry-equivalent atoms, combined with a shared equivariant global frame that enforces SO(3) invariance of the whole structure.
Key results
- On JARVIS-DFT, the quaternion-based SPFrame on eComFormer achieves formation energy MAE 0.0261 eV/atom vs 0.0284 for eComFormer and bandgap (MBJ) 0.239 vs 0.283.
- On Materials Project, quaternion-based SPFrame reaches formation energy MAE 0.0171 and bandgap 0.181, best on those two of four tasks.
- Visual example on PrBPt3 (JVASP-16632): equivariant local frame MAE 0.0551 vs SPFrame 0.0503.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add quaternion-based SPFrame to eComFormer | eComFormer · JARVIS-DFT formation energy | MAE (eV/atom): 0.0284 -> 0.0261 | Helped |
| Add quaternion-based SPFrame to eComFormer | eComFormer · JARVIS-DFT total energy | MAE (eV/atom): 0.0315 -> 0.0276 | Helped |
| Add quaternion-based SPFrame to eComFormer | eComFormer · JARVIS-DFT bandgap (OPT) | MAE (eV): 0.124 -> 0.107 | Helped |
| Add quaternion-based SPFrame to eComFormer | eComFormer · MP bandgap | MAE (eV): 0.202 -> 0.181 | Helped |
| Add quaternion-based SPFrame to eComFormer | eComFormer · MP bulk modulus | MAE (log(GPa)): 0.0417 -> 0.0371 | Hurt |
| Add quaternion-based SPFrame to eComFormer | eComFormer · MP shear modulus | MAE (log(GPa)): 0.0729 -> 0.0672 | Helped |
| Replace the SO(3)-equivariant Gram-Schmidt local frame with quaternion-based SPFrame (ablation) | eComFormer · JARVIS-DFT formation energy | MAE (eV/atom): 0.0285 -> 0.0261 | Helped |
| Replace the SO(3)-equivariant Gram-Schmidt local frame with quaternion-based SPFrame (ablation) | eComFormer · MP bandgap | MAE (eV): 0.187 -> 0.181 | Helped |
| Use quaternion-based rather than Gram-Schmidt-based SPFrame (ablation) | eComFormer · JARVIS-DFT formation energy | MAE (eV/atom): 0.0268 -> 0.0261 | Helped |
| Use quaternion-based rather than Gram-Schmidt-based SPFrame (ablation) | eComFormer · MP formation energy | MAE (eV/atom): 0.0174 -> 0.0171 | Helped |
| Use quaternion-based rather than Gram-Schmidt-based SPFrame (ablation) | eComFormer · MP bandgap | MAE (eV): 0.191 -> 0.181 | Helped |
Surprising findings
- On MP bulk and shear modulus, SPFrame does not clearly beat the baselines (e.g., shear modulus 0.0672 vs iComFormer 0.0637), which the authors acknowledge as weaker performance.
Limitations
- Gains on bulk and shear modulus on MP are weak or absent.
- Frame-based variants have more trainable components and are less efficient than the eComFormer backbone, though the quaternion version is cheaper than Gram-Schmidt variants.
- The theoretical superiority argument is a mutual-information sketch that relies on assumptions about distinguishability.
Experimental setup
Datasets: JARVIS-DFT Materials Project
Benchmarks: JARVIS-DFT Materials Project
Metrics: MAE
Baselines: CGCNN SchNet MEGNet GATGNN ALIGNN Matformer PotNet Crystalformer eComFormer iComFormer Crystalframer
Builds on: eComFormer Crystalframer frame averaging canonicalization
Closest papers by meaning
- Space Group Equivariant Crystal Diffusion (NeurIPS 2025 · similarity 0.88)
- Wyckoff Transformer: Generation of Symmetric Crystals (ICML 2025 · similarity 0.88)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.88)
- Conformal Crystal Graph Transformer with Robust Encoding of Periodic Invariance (AAAI 2024 · similarity 0.88)
- Complete and Efficient Graph Transformers for Crystal Material Property Prediction (ICLR 2024 · similarity 0.87)
- SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models (ICLR 2025 · similarity 0.87)
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