Evaluating the relationship between regularity and learnability in recursive numeral systems using Reinforcement Learning

2026-02-25

AI Summary

This study investigates whether regularity in recursive numeral systems enhances learnability, offering a potential explanation for the widespread adoption of rule-based systems in human languages. For the first time, reinforcement learning is applied to this question by constructing both regular and irregular—but grammatically valid—recursive numeral systems and simulating how learners generalize from limited data to represent all integers. The results demonstrate that the highly regular systems commonly found in natural languages are significantly more learnable. In contrast, within unnatural, highly irregular systems, the advantage of regularity vanishes, and signal length becomes the dominant factor governing learnability. This work reveals the cognitive advantage of regularity in language evolution and provides computational evidence for its role in shaping the learnable structure of linguistic systems.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Structured Learning
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Human recursive numeral systems (i.e., counting systems such as English base-10 numerals), like many other grammatical systems, are highly regular. Following prior work that relates cross-linguistic tendencies to biases in learning, we ask whether regular systems are common because regularity facilitates learning. Adopting methods from the Reinforcement Learning literature, we confirm that highly regular human(-like) systems are easier to learn than unattested but possible irregular systems. This asymmetry emerges under the natural assumption that recursive numeral systems are designed for generalisation from limited data to represent all integers exactly. We also find that the influence of regularity on learnability is absent for unnatural, highly irregular systems, whose learnability is influenced instead by signal length, suggesting that different pressures may influence learnability differently in different parts of the space of possible numeral systems. Our results contribute to the body of work linking learnability to cross-linguistic prevalence.

Problem

• regularity
• learnability
• recursive numeral systems
• Reinforcement Learning
• cross-linguistic prevalence

Innovation

• Reinforcement Learning
• regularity
• learnability
• recursive numeral systems
• cross-linguistic prevalence