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

• URL: http://arxiv.org/abs/2304.12154v2
• Date: Tue, 29 Aug 2023 11:19:40 GMT
• 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 and Kelly Cohen
• Abstract summary: This paper explores whether using explainable AI (XAI) techniques on such machine learning models can offer new insight for symbolic computation. We present a case study on the use of ML to select the variable ordering for cylindrical algebraic decomposition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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