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

arXiv: https://arxiv.org/abs/2602.21720 · HTML: https://mlsanity.com/paper/2602.21720/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 12 of 12)

- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Emergence of Grounded Compositional Language in Multi-Agent Populations](https://mlsanity.com/paper/1703.04908/) (2017)
- [Multi-Agent Cooperation and the Emergence of (Natural) Language](https://mlsanity.com/paper/1612.07182/) (2016)
- [The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents](https://mlsanity.com/paper/1910.05291/) (2019)
- [What makes a language easy to deep-learn? Deep neural networks and humans similarly benefit from compositional structure](https://mlsanity.com/paper/2302.12239/) (2023)
- [Cultural evolution via iterated learning and communication explains efficient color naming systems](https://mlsanity.com/paper/2305.10154/) (2023)
- [Quantifying the dynamics of topical fluctuations in language](https://mlsanity.com/paper/1806.00699/) (2018)
- [Learning Approximate and Exact Numeral Systems via Reinforcement Learning](https://mlsanity.com/paper/2105.13857/) (2021)
- [Recursive numeral systems are highly regular and easy to process](https://mlsanity.com/paper/2510.27049/) (2025)
- [Learning Efficient Recursive Numeral Systems via Reinforcement Learning](https://mlsanity.com/paper/2409.07170/) (2024)
- [Systematicity between Forms and Meanings across Languages Supports Efficient Communication](https://mlsanity.com/paper/2601.17181/) (2026)

## Abstract (arXiv)

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.