Recursive numeral systems are highly regular and easy to process

Generative AI & LLMs
Published: arXiv: 2510.27049v1
Authors

Ponrawee Prasertsom Andrea Silvi Jennifer Culbertson Moa Johansson Devdatt Dubhashi Kenny Smith

Abstract

Previous work has argued that recursive numeral systems optimise the trade-off between lexicon size and average morphosyntatic complexity (Deni\'c and Szymanik, 2024). However, showing that only natural-language-like systems optimise this tradeoff has proven elusive, and the existing solution has relied on ad-hoc constraints to rule out unnatural systems (Yang and Regier, 2025). Here, we argue that this issue arises because the proposed trade-off has neglected regularity, a crucial aspect of complexity central to human grammars in general. Drawing on the Minimum Description Length (MDL) approach, we propose 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 unattested but possible ones, including "optimal" recursive numeral systems from previous work, and that the ad-hoc constraints from previous literature naturally follow from regularity. Our approach highlights the need to incorporate regularity across sets of forms in studies that attempt to measure and explain optimality in language.

Paper Summary

Problem
The main problem addressed in this research paper is that previous studies on recursive numeral systems, which are like the English decimal system, have found it difficult to explain why natural languages are the way they are. These studies have suggested that natural languages optimize a trade-off between simplicity and informativeness, but have struggled to show that only natural languages follow this trade-off.
Key Innovation
The innovation of this paper is that it proposes a new way of thinking about recursive numeral systems, focusing on their regularity and processing complexity rather than just simplicity and informativeness. The researchers use the Minimum Description Length (MDL) approach to measure the regularity and processing complexity of numeral systems, and show that human-like systems are significantly more regular and easier to process than other theoretically possible systems.
Practical Impact
The practical impact of this research is that it provides a new framework for understanding how natural languages are shaped by cognitive and communicative constraints. This could have implications for fields such as linguistics, cognitive science, and computer science, where understanding the structure and processing of language is crucial. For example, this research could inform the development of more efficient and effective language processing algorithms.
Analogy / Intuitive Explanation
Think of a language like a recipe book. Just as a good recipe book has a clear and consistent structure, making it easy to follow and use, a natural language has a regular and efficient structure, making it easy for humans to process and understand. The researchers in this paper are saying that this regularity is a key feature of natural languages, and that it's what makes them so effective and efficient.
Paper Information
Categories:
cs.CL cs.FL
Published Date:

arXiv ID:

2510.27049v1

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