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Computer Science > Symbolic Computation

arXiv:2304.12154 (cs)
[Submitted on 24 Apr 2023 (v1), last revised 29 Aug 2023 (this version, v2)]

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

Authors:Lynn Pickering, Tereso Del Rio Almajano, Matthew England, Kelly Cohen
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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.
Comments: 40 pages
Subjects: Symbolic Computation (cs.SC); Machine Learning (cs.LG)
MSC classes: 68W30, 68T05, 03C10
ACM classes: I.2.6; I.1.0
Cite as: arXiv:2304.12154 [cs.SC]
  (or arXiv:2304.12154v2 [cs.SC] for this version)
  https://doi.org/10.48550/arXiv.2304.12154
Journal reference: Journal of Symbolic Computation, Volume 123, Article Number 102276. Elsevier, 2024
Related DOI: https://doi.org/10.1016/j.jsc.2023.102276

Submission history

From: Matthew England Dr [view email]
[v1] Mon, 24 Apr 2023 15:05:04 UTC (1,673 KB)
[v2] Tue, 29 Aug 2023 11:19:40 UTC (2,004 KB)
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