SYMMETRY-NATIVE CRYSTAL GENERATION
CrystalAR.
Autoregressive Modeling for
Symmetric Crystal Generation
From a symmetry template to a complete crystal.
One model. One autoregressive sequence.
* Equal contribution
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REAL STRUCTURE · INTERACTIVE BELOW
A unified sequence.
A crystallographic structure.
- 01Wyckoff template
- 02Lattice
- 03Free coordinates
- 04Full crystal
01 / THE METHOD
Symmetry sets the stage.
Autoregression fills it in.
CrystalAR generates a symmetry-constrained template, a lattice, and coordinates in sequence. Continuous geometry becomes a search through increasingly precise regions.
A structured template
Elements and Wyckoff positions describe the symmetry-inequivalent sites before geometry is generated.
Precision, level by level
Free Wyckoff parameters are refined from coarse to fine. Sites interact within each resolution level.
Symmetry by construction
Symmetry operations expand representative sites into the complete crystal, preserving their constraints.
02 / THE CRYSTALS
Generated.
Ready to explore.
Ten real outputs from CrystalAR, spanning different compositions and space groups. Rotate a crystal, inspect its symmetry, or download its structure.
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About these structures
These are saved generated structures, not an online model run. Periodic copies make the crystal boundaries easier to read; they are not additional atoms in the source cell. Any connecting segments show geometric near neighbors, not a confirmed chemical-bond assignment. The two-dimensional method illustration above is separate from these three-dimensional examples.
03 / THE RESULTS
Explore new templates.
Keep the structure.
Evaluate the model from three complementary perspectives: symmetry-aware exploration, material quality, and recovery of known structures.
Template exploration × material discovery
MP-20 · 2,500 SAMPLES / METHODA balance between
exploration and stability.
Symmetric, stable, unique & novel
The default model discovers 161 novel unique templates. The flexible-size variant explores 268, with a lower S.S.U.N. rate of 0.19%.
S.S.U.N. adds a non-P1 requirement to S.U.N.; it does not by itself mean the Wyckoff template is novel. Template novelty ignores element identity.
View exact numbers and definitions
Table 2, manuscript p. 7. Template counts and S.S.U.N. measure different properties; neither is a universal score.
Stability and S.U.N.
LeMat-GenBenchExplicit symmetry.
Competitive stability.
Stable · without pre-relaxation
CrystalAR improves from 6.0% to 13.7% stable structures with pre-relaxation. The corresponding S.U.N. rates are 0.3% and 0.9%.
The two settings are separate evaluations. The chart shows selected baselines from Table 1, not every model in the benchmark.
View exact numbers and evaluation notes
Table 1, manuscript p. 7. † CrystalFormer uses 1,000 publicly available samples; other methods use the standard evaluation set. PLaID++ includes post-training. S.U.N. means stable, unique and novel.
Recovering known crystal structures
MATCH RATE (%) ↑Composition + space group.
No retrieved template.
MPTS-52 match rate · one candidate
Given chemical composition and a space group, CrystalAR predicts the Wyckoff template and geometry. Multiple candidates explore alternative symmetry-compatible structures.
“Template-free” means no retrieved Wyckoff template is supplied. Composition and space group are still inputs.
View match rates and RMSE
Table 3, manuscript p. 9. “—” means not reported. The chart shows selected baselines; results with one and 20 candidates are separate settings.
READ, BUILD, CITE
Continue the exploration.
The paper describes the representation, architecture,
evaluation protocols, and limitations in detail.