HATSolver: Learning Gröbner Bases with Hierarchical Attention Transformers

ICLR 2026 Conference Submission18803 Authors

Keywords: Hierarchical Attention Transformer, Groebner Basis, Symbolic Computation, Multivariate Polynomial Equations

TL;DR: Efficient hierarchical attention transformers for learning to solve non-linear equations through by computing groebner bases.

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).

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 18803