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

TL;DR

This paper introduces a method that uses constrained neural networks to optimize heuristics in symbolic computation, specifically for variable ordering in cylindrical algebraic decomposition, enhancing explainability and performance.

Contribution

The authors demonstrate how to encode a traditional heuristic as a constrained neural network, enabling machine learning-based optimization of heuristics in computer algebra systems.

Findings

Neural networks can represent human-designed heuristics.

Optimized heuristics perform similarly to original ones but are improved through learning.

Provides a framework for explainable AI in symbolic computation.

Abstract

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.