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.

本研究探讨机器学习在符号计算中的应用，特别是如何使用可解释的AI技术为该领域提供新的视角和信息。在基于机器学习模型选择代数计算变量排序的案例研究中，我们采用了SHAP解释性工具，在不调用AI工具的计算机代数系统中启发了新的启发式方法。研究结果表明，机器学习和可解释的AI技术的结合对于符号计算可以带来很大的帮助。

对符号计算的可解释AI洞见：圆柱代数分解中选择变量排序的案例研究