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

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2023-11-15 DOI:10.1016/j.jsc.2023.102276

Lynn Pickering , Tereso del Río Almajano , Matthew England , Kelly Cohen

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引用次数: 0

Abstract

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.

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符号计算中可解释的人工智能洞察:圆柱代数分解中变量排序选择的案例研究

近年来，机器学习(ML)技术在数学中的应用越来越多，包括符号计算，它可以安全地应用于优化或选择算法。本文探讨了在这种机器学习模型上使用可解释的人工智能(XAI)技术是否可以为符号计算提供新的见解，从而在不直接调用人工智能工具的计算机代数系统中激发新的实现。我们提出了一个使用ML来选择圆柱代数分解的变量排序的案例研究。已经证明ML可以很好地做出选择，但这里我们展示如何使用SHAP可解释性工具来通知新的启发式，其大小和复杂性类似于目前在符号计算中常用的人类设计的启发式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.