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.Comment: 10 pages. To be presented at the 2023 SC-Square Worksho