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Conformal Crystal Graph Transformer with Robust Encoding of Periodic Invariance
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Proposes CrystalFormer, an E(3)- and periodic-invariant crystal graph transformer with a robust hierarchical-weight graph construction and a Dirichlet-energy-based angle-preserving attention, evaluated on five JARVIS property prediction tasks.
Problem
Predicting crystal material properties with graph neural networks requires representations that preserve E(3) and periodic invariance robustly under structural perturbations, and capturing angular information efficiently.
Approach
A hierarchical weighting graph construction (reciprocal distance, distance-penalizing, electronegativity weights with AUROC-based neighbor selection) that reduces neighbor-selection stochasticity, plus an angle-preserving graph transformer whose harmonic mapping is trained by minimizing a graph Dirichlet energy to approximate conformal mapping.
Key results
- CrystalFormer reaches MAE 0.13 eV on bandgap (MBJ), a 51.9% reduction vs. PotNet (0.27).
- Bandgap (OPT) MAE 0.101 eV (-20.5% vs. PotNet 0.127) and total energy 0.017 eV/atom (-46.9% vs. PotNet 0.032).
- Proposed graph construction costs 8.67 ms/structure vs 79.24 ms for Voronoi (about 8.1x faster); ablation without the angle-preserving block gives MAE 0.28 vs 0.13.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CrystalFormer instead of PotNet | CrystalFormer · JARVIS Bandgap (OPT) | MAE: 0.127 -> 0.101 | Helped |
| use CrystalFormer instead of PotNet | CrystalFormer · JARVIS Bandgap (MBJ) | MAE: 0.27 -> 0.13 | Helped |
| use CrystalFormer instead of PotNet | CrystalFormer · JARVIS Total Energy | MAE: 0.032 -> 0.017 | Helped |
| use CrystalFormer instead of PotNet | CrystalFormer · JARVIS Formation Energy | MAE: 0.029 -> 0.033 | Hurt |
| use CrystalFormer instead of PotNet | CrystalFormer · JARVIS Ehull | MAE: 0.055 -> 0.040 | Helped |
| add the proposed robust graph construction instead of multi-edge graph construction (ablation) | CrystalFormer · JARVIS Bandgap (MBJ) | MAE: 0.28 -> 0.13 | Helped |
| add the proposed robust graph construction instead of k-connected graph construction (ablation) | CrystalFormer · JARVIS Bandgap (MBJ) | MAE: 0.30 -> 0.13 | Helped |
| add the proposed robust graph construction instead of modified k-connected graph construction (ablation) | CrystalFormer · JARVIS Bandgap (MBJ) | MAE: 0.29 -> 0.13 | Helped |
| add the angle-preserving graph transformer blocks (ablation) | CrystalFormer · JARVIS Bandgap (MBJ) | MAE: 0.28 -> 0.13 | Helped |
Surprising findings
- Prior angle-aware graph transformer methods (SBF/RBF in Matformer) did not yield the expected performance gains, per the authors' framing.
- Formation energy is slightly worse than the state-of-the-art (0.033 vs 0.029 eV/atom for PotNet).
Limitations
- Formation energy result is slightly below state-of-the-art.
- Voronoi-based and matrix-form representations were discussed but only Voronoi was compared for efficiency; robustness is argued conceptually rather than tested on perturbed structures in the main text.
- Hyperparameters such as tolerance delta and lambda are described as set by default, with task-specific settings deferred to the appendix.
Experimental setup
Datasets: JARVIS-DFT 3D (DFT-2021.8.18)
Benchmarks: JARVIS bandgap (OPT) JARVIS bandgap (MBJ) JARVIS total energy JARVIS formation energy JARVIS Ehull
Metrics: MAE training time per epoch inference throughput
Baselines: CGCNN SchNet MEGNET GATGNN ALIGNN Matformer PotNet
Builds on: CGCNN Matformer PotNet ALIGNN Pan et al. 2021 weight-based neighbor selection
Closest papers by meaning
- Complete and Efficient Graph Transformers for Crystal Material Property Prediction (ICLR 2024 · similarity 0.94)
- Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding (ICLR 2024 · similarity 0.89)
- Wyckoff Transformer: Generation of Symmetric Crystals (ICML 2025 · similarity 0.89)
- Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modeling (NeurIPS 2025 · similarity 0.88)
- A Diffusion-Based Pre-training Framework for Crystal Property Prediction (AAAI 2024 · similarity 0.87)
- Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation (NeurIPS 2024 · similarity 0.87)
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