# Using large language models to probe the limits of atom-centered structural descriptors

arXiv: https://arxiv.org/abs/2607.26984 · HTML: https://mlsanity.com/paper/2607.26984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 29 Jul 2026.

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

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domains](https://mlsanity.com/paper/2410.24169/) (2024)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [Incompleteness of graph neural networks for points clouds in three dimensions](https://mlsanity.com/paper/2201.07136/) (2022)
- [Complete Neural Networks for Complete Euclidean Graphs](https://mlsanity.com/paper/2301.13821/) (2023)
- [Polynomial-time algorithms for continuous metrics on atomic clouds of unordered points](https://mlsanity.com/paper/2207.08502/) (2022)
- [Bolzano: Case Studies in LLM-Assisted Mathematical Research](https://mlsanity.com/paper/2604.16989/) (2026)
- [Complete invariants of atomic clouds under rigid motion with Lipschitz continuous metrics in a polynomial time](https://mlsanity.com/paper/2303.13486/) (2023)

## Abstract (arXiv)

Mapping an atomic structure to a compact set of geometric descriptors is an essential step in any machine-learning application to atomic-scale modeling. A powerful and widely-used approach can be understood as a discretization of the histogram of pair distances, triangles, etc., that results in a hierarchy of symmetry-invariant atom-centered descriptors. Unfortunately, the lower rungs on this hierarchy (two, three, four-neighbor clusters) were found to be incomplete, with symmetry-unrelated pairs of structures having exactly the same descriptors. However, all the ``degeneracies'' reported so far are resolved by considering larger clusters of neighbors to build the descriptors. We report examples of 3D structures that are indistinguishable even if one considers clusters of up to seven neighbors, and to arbitrary order when considering a practical level of discretization of the descriptors, discovered with the assistance of large language models. The key ingredients in their construction can be traced to results that have been known for decades in different communities: the model was able to find the references and recognize their significance for the problem at hand. We believe this experiment exposes an extremely fruitful usage pattern for AI in science: translating results between different communities and application domains, accelerating the process by which serendipitous discoveries in a field become breakthroughs in another.