Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition

In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using explainable AI (XAI) techniques on such ML models can offer new insight for symbolic computation, inspiring new implementations within computer algebra systems that do not directly call upon AI tools. We present a case study on the use of ML to select the variable ordering for cylindrical algebraic decomposition. It has already been demon-strated that ML can make the choice well, but here we show how the SHAP tool for explainability can be used to inform new heuris-tics of a size and complexity similar to those human-designed heuristics currently commonly used in symbolic computation. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

Automated summary

In recent years, there has been an increase in the use of machine learning techniques in mathematics, specifically in symbolic computation for optimizing and selecting algorithms. This paper explores the potential of using explainable AI techniques on these ML models to provide new insights for symbolic computation and inspire new implementations within computer algebra systems.