# Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems

arXiv: https://arxiv.org/abs/2404.17508 · HTML: https://mlsanity.com/paper/2404.17508/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 26 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Stop ordering machine learning algorithms by their explainability! A user-centered investigation of performance and explainability](https://mlsanity.com/paper/2206.10610/) (2022)
- [Learning selection strategies in Buchberger's algorithm](https://mlsanity.com/paper/2005.01917/) (2020)
- [Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/1404.6369/) (2014)
- [Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/1904.11061/) (2019)
- [Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/2304.12154/) (2023)
- [Algorithmically generating new algebraic features of polynomial systems for machine learning](https://mlsanity.com/paper/1906.01455/) (2019)
- [Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness](https://mlsanity.com/paper/1911.12672/) (2019)
- [Machine learning the real discriminant locus](https://mlsanity.com/paper/2006.14078/) (2020)
- [Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases](https://mlsanity.com/paper/1608.04219/) (2016)
- [A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputs](https://mlsanity.com/paper/2005.11251/) (2020)
- [TheoryGuru: A Mathematica Package to apply Quantifier Elimination](https://mlsanity.com/paper/1806.10925/) (2018)
- [Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD](https://mlsanity.com/paper/2401.13343/) (2024)

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

- [Algebraic Representations for Faster Predictions in Convolutional Neural Networks](https://mlsanity.com/paper/2408.07815/) (2024)

## Abstract (arXiv)

We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development.