CrystalAR: Autoregressive Modeling for Symmetric Crystal Generation
Abstract
Deep generative modeling has achieved remarkable progress in crystal generation. Given the rich symmetries inherent in crystalline structures, recent work has sought to explicitly incorporate space-group symmetry into generative models, enabling more effective exploration of novel symmetry templates. Yet introducing symmetry templates increases the combinatorial complexity of stoichiometric relationships between atomic species and crystallographic sites, while creating a fundamental tension between flexible exploration of discrete crystallographic templates and faithful realization of these templates as continuous three-dimensional structures. To address these challenges, we propose CrystalAR, a unified autoregressive framework that models Wyckoff symmetry templates and complete crystal structures within a single generative sequence. Specifically, CrystalAR reformulates continuous coordinate generation as a symmetry-conditioned hierarchy of discrete spatial localization decisions, autoregressively refining the positions of all symmetry-inequivalent sites across resolution levels while jointly modeling their spatial configuration within each level. This discrete hierarchical formulation further enables constraint-aware search over both crystallographic templates and geometric realizations. As a result, CrystalAR retains strong symmetry-template generation capability while achieving competitive de novo generation performance and template-free crystal structure prediction (CSP) accuracy. These results suggest that symmetry-template generation can be retained alongside broadly competitive de novo generation performance and competitive CSP without reliance on symmetry templates retrieved from prior data, providing a promising alternative paradigm for symmetry-preserving crystal generation.
Related
- Near-unit-root persistence of symmetric and asymmetric stable autoregressive sequences
- Automated mode-aware design of nonlinear photonic crystal cavities for intrinsic second harmonic generation
- 266 nm generation performance of NSBBF crystal improved by elevating the operating temperature
- OxiGen: Oxidation-State-Aware Crystal Generation
- SymADiT: Symmetry-Aware Crystal Generation with Latent Flow Matching
BibTeX
@misc{meng2026crystalar,
title = {{CrystalAR: Autoregressive Modeling for Symmetric Crystal Generation}},
author = {Ziqiao Meng and Rongsheng Chen and Zhi Zheng and Nikita Kazeev and Zhenkun Wang and Andrey Ustyuzhanin and Wee Sun Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27762},
eprint = {2610.27762},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27762},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CrystalAR: Autoregressive Modeling for Symmetric Crystal Generation
AU - Ziqiao Meng
AU - Rongsheng Chen
AU - Zhi Zheng
AU - Nikita Kazeev
AU - Zhenkun Wang
AU - Andrey Ustyuzhanin
AU - Wee Sun Lee
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.27762
UR - https://arxiv.org/abs/2610.27762
AB - Deep generative modeling has achieved remarkable progress in crystal generation. Given the rich symmetries inherent in crystalline structures, recent work has sought to explicitly incorporate space-group symmetry into generative models, enabling more effective exploration of novel symmetry templates. Yet introducing symmetry templates increases the combinatorial complexity of stoichiometric relationships between atomic species and crystallographic sites, while creating a fundamental tension between flexible exploration of discrete crystallographic templates and faithful realization of these templates as continuous three-dimensional structures. To address these challenges, we propose CrystalAR, a unified autoregressive framework that models Wyckoff symmetry templates and complete crystal structures within a single generative sequence. Specifically, CrystalAR reformulates continuous coordinate generation as a symmetry-conditioned hierarchy of discrete spatial localization decisions, autoregressively refining the positions of all symmetry-inequivalent sites across resolution levels while jointly modeling their spatial configuration within each level. This discrete hierarchical formulation further enables constraint-aware search over both crystallographic templates and geometric realizations. As a result, CrystalAR retains strong symmetry-template generation capability while achieving competitive de novo generation performance and template-free crystal structure prediction (CSP) accuracy. These results suggest that symmetry-template generation can be retained alongside broadly competitive de novo generation performance and competitive CSP without reliance on symmetry templates retrieved from prior data, providing a promising alternative paradigm for symmetry-preserving crystal generation.
ER -