mlsanityData to 7 Oct 2026

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

arXiv 2304.12154 ↗First posted 24 Apr 2023cs.SC cs.LGcited by 7

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 15 of its 60 references that are in the map. First posted on arXiv 24 Apr 2023.

Builds on

15 of 60 references.

References · 15

  1. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  2. 2019Deep Learning for Symbolic Mathematicscited by 266
  3. 2018Techniques for Interpretable Machine Learningcited by 237
  4. 2021Machine-Learning Mathematical Structurescited by 25
  5. 2022Stop ordering machine learning algorithms by their explainability! A user-centered investigation of performance and explainabilitycited by 21
  6. 2020Learning selection strategies in Buchberger's algorithmcited by 20
  7. 2014Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decompositioncited by 10
  8. 2019Comparing machine learning models to choose the variable ordering for cylindrical algebraic decompositioncited by 7
  9. 2018Using Machine Learning to Improve Cylindrical Algebraic Decompositioncited by 6
  10. 2019Algorithmically generating new algebraic features of polynomial systems for machine learningcited by 6
  11. 2019Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctnesscited by 5
  12. 2020Machine learning the real discriminant locuscited by 5
3 more
  1. 2016Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Basescited by 4
  2. 2020A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputscited by 4
  3. 2018TheoryGuru: A Mathematica Package to apply Quantifier Eliminationcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 1; 2026: 1.

7 papers.

  1. 2024Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMscited by 3
  2. 2024Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CADcited by 2
  3. 2024Transformers to Predict the Applicability of Symbolic Integration Routinescited by 2
  4. 2024Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systemscited by 1
  5. 2024Algebraic Representations for Faster Predictions in Convolutional Neural Networkscited by 1
  6. 2025Tree-Based Deep Learning for Ranking Symbolic Integration Algorithmscited by 1
  7. 2026Breaking the Data Barrier in Learning Symbolic Computation: A Case Study on Variable Ordering Suggestion for Cylindrical Algebraic Decompositioncited by 0