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

TL;DR

This paper explores how machine learning can optimize symbolic computation tasks, emphasizing dataset analysis and different paradigms, demonstrated through variable ordering in cylindrical algebraic decomposition, with improved dataset handling and methodological insights.

Contribution

It highlights the importance of dataset analysis and augmentation in applying machine learning to symbolic computation, and shows how classification can be reframed as regression for broader applicability.

Findings

Dataset imbalance affects machine learning performance in symbolic computation.

Augmentation techniques improve model accuracy by up to 38%.

Recasting classification as regression broadens methodological scope.

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 to be 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.