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

Fuente: arXiv
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Main Authors: Pickering, Lynn, Almajano, Tereso Del Rio, England, Matthew, Cohen, Kelly
Format: Preprint
Published: 2023
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author Pickering, Lynn
Almajano, Tereso Del Rio
England, Matthew
Cohen, Kelly
author_facet Pickering, Lynn
Almajano, Tereso Del Rio
England, Matthew
Cohen, Kelly
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_12154
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition
Pickering, Lynn
Almajano, Tereso Del Rio
England, Matthew
Cohen, Kelly
Symbolic Computation
Machine Learning
68W30, 68T05, 03C10
I.2.6; I.1.0
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.
title Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition
topic Symbolic Computation
Machine Learning
68W30, 68T05, 03C10
I.2.6; I.1.0
url https://arxiv.org/abs/2304.12154