# Learning Efficient Recursive Numeral Systems via Reinforcement Learning

arXiv: https://arxiv.org/abs/2409.07170 · HTML: https://mlsanity.com/paper/2409.07170/

## Key facts

- Cited by 1 papers in the map (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 4 of its 35 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## 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, 4 of 4)

- [The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents](https://mlsanity.com/paper/1910.05291/) (2019)
- [Color naming reflects both perceptual structure and communicative need](https://mlsanity.com/paper/1805.06165/) (2018)
- [Cultural evolution via iterated learning and communication explains efficient color naming systems](https://mlsanity.com/paper/2305.10154/) (2023)
- [Learning Approximate and Exact Numeral Systems via Reinforcement Learning](https://mlsanity.com/paper/2105.13857/) (2021)

## Built on by (most cited first, 1 of 1)

- [Evaluating the relationship between regularity and learnability in recursive numeral systems using Reinforcement Learning](https://mlsanity.com/paper/2602.21720/) (2026)

## Abstract (arXiv)

It has previously been shown that by using reinforcement learning (RL), agents can derive simple approximate and exact-restricted numeral systems that are similar to human ones (Carlsson, 2021). However, it is a major challenge to show how more complex recursive numeral systems, similar to for example English, could arise via a simple learning mechanism such as RL. Here, we introduce an approach towards deriving a mechanistic explanation of the emergence of efficient recursive number systems. We consider pairs of agents learning how to communicate about numerical quantities through a meta-grammar that can be gradually modified throughout the interactions. Utilising a slightly modified version of the meta-grammar of Hurford (1975), we demonstrate that our RL agents, shaped by the pressures for efficient communication, can effectively modify their lexicon towards Pareto-optimal configurations which are comparable to those observed within human numeral systems in terms of their efficiency.