Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (*regularity*), a key property of natural language. Here, we demonstrate the importance of regularity in explaining the shape of linguistic systems by looking at recursive numeral systems. Previous work has argued that these systems optimise the trade-off between lexicon size and average morphosyntatic complexity (Denić and Szymanik, 2024). However, showing that *only* natural-language-like systems optimise this trade-off has proven elusive, and existing solutions rely on ad-hoc constraints to rule out unnatural systems (Yang and Regier, 2025). Drawing on the Minimum Description Length (MDL) approach, we argue that recursive numeral systems are better viewed as efficient with regard to their regularity and processing complexity. We show that our MDL-based measures of regularity and processing complexity better capture the key differences between attested, natural systems and theoretically possible ones, including “optimal” recursive numeral systems from previous work, and that the ad-hoc constraintsnaturally follow from regularity. Our approach highlights the need to incorporate regularity across sets of forms in studies attempting tomeasure efficiency in language.

Natural language is compositional; the meaning of a sentence is a function of the meaning of its parts. This property allows humans to create and interpret novel sentences, generalizing robustly outside their prior experience. Neural networks have been shown to struggle with this kind of generalization, in particular performing poorly on tasks designed to assess compositional generalization (i.e. where training and testing distributions differ in ways that would be trivial for a compositional strategy to resolve). Their poor performance on these tasks may in part be due to the nature of supervised learning which assumes training and testing data to be drawn from the same distribution. We implement a meta-learning augmented version of supervised learning whose objective directly optimizes for out-of-distribution generalization. We construct pairs of tasks for meta-learning by sub-sampling existing training data. Each pair of tasks is constructed to contain relevant examples, as determined by a similarity metric, in an effort to inhibit models from memorizing their input. Experimental results on the COGS and SCAN datasets show that our similarity-driven meta-learning can improve generalization performance.