# Predicting the cardinality and maximum degree of a reduced Gr"obner basis

arXiv: https://arxiv.org/abs/2302.05364 · HTML: https://mlsanity.com/paper/2302.05364/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 10 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Learning selection strategies in Buchberger's algorithm](https://mlsanity.com/paper/2005.01917/) (2020)
- [Learning a performance metric of Buchberger's algorithm](https://mlsanity.com/paper/2106.03676/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Fast Monomial Orders for Gr"obner Basis Computations](https://mlsanity.com/paper/2602.02972/) (2026)

## Abstract (arXiv)

We construct neural network regression models to predict key metrics of complexity for Gr"obner bases of binomial ideals. This work illustrates why predictions with neural networks from Gr"obner computations are not a straightforward process. Using two probabilistic models for random binomial ideals, we generate and make available a large data set that is able to capture sufficient variability in Gr"obner complexity. We use this data to train neural networks and predict the cardinality of a reduced Gr"obner basis and the maximum total degree of its elements. While the cardinality prediction problem is unlike classical problems tackled by machine learning, our simulations show that neural networks, providing performance statistics such as r2 = 0.401, outperform naive guess or multiple regression models with r2 = 0.180.