# Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation

arXiv: https://arxiv.org/abs/2503.00152 · HTML: https://mlsanity.com/paper/2503.00152/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [Language models can generate molecules, materials, and protein binding sites directly in three dimensions as XYZ, CIF, and PDB files](https://mlsanity.com/paper/2305.05708/) (2023)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)

## Built on by (most cited first, 12 of 12)

- [Token Reduction Should Go Beyond Efficiency in Generative Models -- From Vision, Language to Multimodality](https://mlsanity.com/paper/2505.18227/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Toward Greater Autonomy in Materials Discovery Agents: Unifying Planning, Physics, and Scientists](https://mlsanity.com/paper/2506.05616/) (2025)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [InertialAR: Autoregressive 3D Molecule Generation with Inertial Frames](https://mlsanity.com/paper/2510.27497/) (2025)
- [L^2M^3OF: A Large Language Multimodal Model for Metal-Organic Frameworks](https://mlsanity.com/paper/2510.20976/) (2025)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [Preference Learning from Physics-Based Feedback: Tuning Language Models to Design BCC/B2 Superalloys](https://mlsanity.com/paper/2511.12036/) (2025)
- [Challenges in Non-Polymeric Crystal Structure Prediction: Why a Geometric, Permutation-Invariant Loss is Needed](https://mlsanity.com/paper/2509.00832/) (2025)

## Abstract (arXiv)

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods.