HATSolver: Learning Gröbner Bases with Hierarchical Attention Transformers
Abstract
At NeurIPS 2024, Kera (2311.12904) introduced the use of transformers for computing Groebner bases, a central object in computer algebra with numerous practical applications. In this paper, we improve this approach by applying Hierarchical Attention Transformers (HATs) to solve systems of multivariate polynomial equations via Groebner bases computation. The HAT architecture incorporates a tree-structured inductive bias that enables the modeling of hierarchical relationships present in the data and thus achieves significant computational savings compared to conventional flat attention models. We generalize to arbitrary depths and include a detailed computational cost analysis. Combined with curriculum learning, our method solves instances that are much larger than those in Kera (2311.12904).
Cite
Text
Malhou et al. "HATSolver: Learning Gröbner Bases with Hierarchical Attention Transformers." International Conference on Learning Representations, 2026.Markdown
[Malhou et al. "HATSolver: Learning Gröbner Bases with Hierarchical Attention Transformers." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/malhou2026iclr-hatsolver/)BibTeX
@inproceedings{malhou2026iclr-hatsolver,
title = {{HATSolver: Learning Gröbner Bases with Hierarchical Attention Transformers}},
author = {Malhou, Mohamed and Perret, Ludovic and Lauter, Kristin E.},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/malhou2026iclr-hatsolver/}
}