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的应用日益增多，包括可安全用于优化或算法选择的符号计算领域。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洞见，并激发计算机代数系统中不直接调用人工智能工具的新实现。我们以机器学习在柱形代数分解中选择变量排序的案例研究展开分析。已有研究表明机器学习能有效完成最优选择，但本文进一步揭示：如何利用可解释性工具SHAP，推导出与当前符号计算领域常用的人工设计启发式方法在规模与复杂度上相当的新启发式策略。