Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation - A Case Study on CAD

Aug 2, 2026

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Symbolic computation algorithms used in computer algebra systems include implementation choices that do not change correctness but can substantially affect runtime and output structure. The study distills lessons from applying machine learning to symbolic computation, emphasizing dataset analysis before training and comparing available learning paradigms. A detailed case study focuses on selecting variable ordering for cylindrical algebraic decomposition, where an existing example dataset is imbalanced. Polynomial-system augmentation balances and expands the dataset, yielding average improvements of 28% for classification and 38% for related results, and reformulates the approach from classification to regression to broaden applicable decision-making.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages28

Reading Time1 h 11 min

AccessFree to download

Introduction

Background and motivation

Machine learning for symbolic computation choices

Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD del Río, T. & England, M Published PDF deposited in Coventry University’s Repository Original citation: del Río, T & England, M 2024, 'Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD', Mathematics in Computer Science, vol. 18, 17. [https://doi.org](https://doi.org) del Río, T & England, M 2024, 'Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD', Mathematics in Computer Science, vol. 18, 17. [https://doi.org/10.1007/s11786-024-](https://doi.org/10.1007/s11786-024-)[ ](https://doi.org/10.1007/s11786-024-)[00591-0](00591-0) DOI 10. 1007/s11786-024-00591-0 ISSN 1661-8270 ESSN 1661-8289 Publisher: Springer This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit [http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/). Math.Comput.Sci. (2024) 18:17 [https://doi.org/10.1007/s11786-024-00591-0](https://doi.org/10.1007/s11786-024-00591-0) Mathematics in Computer Science Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD Tereso del Río · Matthew England Received: 20 February 2024 / Accepted: 19 June 2024 © The Author(s) 2024 Abstract Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can signiﬁcantly impact the resources required: such choices can beneﬁt from having them made separately for each problem via a machine learning model. This study reports lessons on such use of machine learning in symbolic computation, in particular on the importance of analysing datasets prior to machine learning and on the different machine learning paradigms that may be utilised. We present results for a particular case study, the selection of variable ordering for cylindrical algebraic decomposition, but expect that the lessons learned are applicable to other decisions in symbolic computation. We utilise an existing dataset of examples derived from applications which was found tobe imbalanced with respect to the variable ordering decision. We introduce an augmentation technique for polynomial systems problems that allows us to balance and further augment the dataset, improving the machine learning results by 28% and 38% on average, respectively. We then demonstrate how the existing machine learning methodology used for the problem—classiﬁcation—might be recast into the regression paradigm. While this does not have a radical change on the performance, it does widen the scope in which the methodology can be applied to make choices. Keywords Symbolic computation · Machine learning · Data augmentation · Classiﬁcation · Regression · Cylindrical algebraic decomposition Mathematics Subject Classiﬁcation 68W30 · 68T05 1 Introduction Symbolic computation algorithms, including those commonly used within theory solvers for SMT, often have within them a variety of choices to be made: choices that do not affect the correctness of the outputs, but can still have asigniﬁcant effect upon theresources needed for such algor

FAQs

What role do datasets play in machine learning for symbolic computation decisions?

The work stresses analyzing datasets before training because implementation choices can be learned effectively only when the data distribution matches the decision being predicted.

What is the main case study examined in the paper?

The case study targets variable ordering selection for cylindrical algebraic decomposition within polynomial system problems.

How does the paper improve the dataset and what impact does it have?

It introduces a polynomial-system augmentation technique to balance and further augment an initially imbalanced dataset, improving machine learning results by 28% and 38% on average.

Aug 2, 2026

Upload by Noah