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 demonstrated that ML can make the choice well, but here we show how the SHAP tool for explainability can be used to inform new heuristics of a size and complexity similar to those human-designed heuristics currently commonly used in symbolic computation.

翻译：近年来，机器学习技术在数学领域中的应用日益增多，包括可安全地用于优化或选择算法的符号计算。本文探讨了对此类机器学习模型应用可解释人工智能技术是否能为符号计算提供新见解，并启发计算机代数系统中不直接调用人工智能工具的新实现。我们以机器学习选择柱形代数分解变量序为例进行案例研究。已有研究证明机器学习能良好完成此选择，但本文进一步展示了可解释性工具SHAP如何能够启发设计出与当前符号计算中常用的人工启发式算法规模及复杂度相当的新启发式方法。