Why are numeral systems regular? The role of learnability and generalisability

Human recursive numeral systems (e.g. counting systems such as Mandarin or English base-10 numerals) are, like many other linguistic systems, highly regular, i.e. they can be represented by a simple grammar. We are interested in modelling what pressures select for such representations over the course of linguistic evolution. Following prior work that relates cross-linguistic tendencies to biases in learning, we hypothesise that regular systems are common because regularity allows the extraction of highly-learnable, highly-compressible representations. We compile a dataset of 20,732 unique numeral systems (both human and artificial) and experiment with both reinforcement and supervised learning as high-level analogues for human learning. Experiments confirm that highly regular human(-like) systems are indeed more learnable than unattested irregular systems, but only when learnability is taken as the capacity to derive a generalisable representation of the whole numeral system from skewed, limited data. Intriguingly, our results indicate that the advantage of regularity is more significant for reinforcement learning. We also conduct exploratory analyses which show that a multitude of factors affect numeral systems' learnability, but crucially, regularity robustly remains one of the key predictors. Our results contribute to the body of work linking learnability to cross-linguistic prevalence.