Data Augmentation for Mathematical Objects

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This paper discusses and evaluates ideas of data balancing and data augmentation in the context of mathematical objects: an important topic for both the symbolic computation and satisfiability checking communities, when they are making use of machine learning techniques to optimise their tools. We consider a dataset of non-linear polynomial problems and the problem of selecting a variable ordering for cylindrical algebraic decomposition to tackle these with. By swapping the variable names in already labelled problems, we generate new problem instances that do not require any further labelling when viewing the selection as a classification problem. We find this augmentation increases the accuracy of ML models by 63% on average. We study what part of this improvement is due to the balancing of the dataset and what is achieved thanks to further increasing the size of the dataset, concluding that both have a very significant effect. We finish the paper by reflecting on how this idea could be applied in other uses of machine learning in mathematics.
Original languageEnglish
Title of host publicationProceedings of the 8th SC-Square Workshop co-located with the 48th International Symposium on Symbolic and Algebraic Computation (ISSAC 2023)
EditorsErika Abraham, Thomas Sturm
PublisherCEUR Workshop Proceedings
Number of pages10
Publication statusPublished - 15 Aug 2023
Event8th International Workshop on Satisfiability Checking and Symbolic Computation - The Arctic University of Norway (UiT), Tromso, Norway
Duration: 28 Jul 202328 Jul 2023

Publication series

NameCEUR Workshop Proceedings
ISSN (Electronic)1613-0073


Conference8th International Workshop on Satisfiability Checking and Symbolic Computation
Abbreviated title ISSAC 2023
Internet address


  • Machine Learning
  • Data Balancing
  • Data Augmentation
  • Cylindrical Algebraic Decomposition


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