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Complete and Efficient Graph Transformers for Crystal Material Property Prediction
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Proposes ComFormer, an SE(3)-invariant (iComFormer) and SO(3)-equivariant (eComFormer) graph transformer built on geometrically complete, periodic-invariant lattice-based crystal graphs, achieving state-of-the-art crystal property prediction on JARVIS, Materials Project, and MatBench.
Problem
Crystal graph representations used for property prediction are not geometrically complete (they can map different crystals to the same graph), fail to respect periodic invariance, and cannot distinguish chiral crystals; prior complete matrix representations (AMD, PDD) are impractical for prediction.
Approach
Attach three periodic lattice vectors per atom (selected by smallest distances and right-hand rule) to build lattice-based crystal graphs that are SE(3)-invariant or SO(3)-equivariant, periodic-invariant and geometrically complete, then apply efficient O(nk) node-wise and edge-wise transformer layers (iComFormer) or tensor-product equivariant layers (eComFormer).
Key results
- On JARVIS, iComFormer reaches 27.2 meV/atom formation energy MAE vs 29.4 for PotNet (about 8% improvement) and 28.8 on E_total vs 32 for PotNet.
- On MatBench e_form (132752 crystals), both ComFormer variants reach MAE 16.5 vs 17.0 for coGN; iComFormer achieves best RMSE 43.8.
- Ablation removing bond angles/vectors degrades iComFormer MAE from 27.2 to 28.9 and eComFormer from 28.4 to 30.2 on JARVIS formation energy.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use iComFormer instead of PotNet | crystal property prediction · JARVIS | MAE | Helped |
| Use eComFormer instead of PotNet | crystal property prediction · Materials Project formation energy | MAE | Helped |
| Use iComFormer instead of PotNet | crystal property prediction · Materials Project | MAE | Helped |
| Use iComFormer instead of coGN | crystal property prediction · MatBench e_form-132752 | MAE: 17.0 ± 0.3 -> 16.5 ± 0.3 | Helped |
| Use iComFormer instead of MODNet | crystal property prediction · MatBench jdft2d-636 | MAE: 33.2 ± 7.3 -> 34.8 ± 9.9 | Mixed |
| Add bond vectors by retaining the equivariant updating layer (ablation) | eComFormer · JARVIS formation energy | Test MAE: 30.2 -> 28.4 | Helped |
| Add bond angles by retaining the edge-wise transformer layer (ablation) | iComFormer · JARVIS formation energy | Test MAE: 28.9 -> 27.2 | Helped |
Surprising findings
- Multi-edge crystal graphs (CGCNN-style) map distinct crystals to identical graphs, so widely used crystal GNNs are not geometrically complete.
- Using a fully-connected or radius molecular graph for crystals breaks periodic invariance.
Limitations
- Designed only for crystalline materials and not directly applicable to other domains.
- Cannot model complete geometric information of amorphous materials.
- Cannot currently predict higher-order crystal properties.
Experimental setup
Datasets: JARVIS Materials Project MatBench T2
Benchmarks: JARVIS Materials Project MatBench e_form MatBench jdft2d
Metrics: MAE RMSE structure RMSD
Baselines: CGCNN SchNet MEGNET GATGNN ALIGNN Matformer PotNet M3GNet MODNet coGN
Builds on: CGCNN ALIGNN Matformer PotNet SphereNet
Closest papers by meaning
- Conformal Crystal Graph Transformer with Robust Encoding of Periodic Invariance (AAAI 2024 · similarity 0.94)
- Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding (ICLR 2024 · similarity 0.90)
- Wyckoff Transformer: Generation of Symmetric Crystals (ICML 2025 · similarity 0.89)
- Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modeling (NeurIPS 2025 · similarity 0.87)
- Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation (NeurIPS 2024 · similarity 0.87)
- Learning the Electronic Hamiltonian of Large Atomic Structures (ICML 2025 · similarity 0.87)
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