Learning Efficient Recursive Numeral Systems via Reinforcement Learning

TL;DR

This paper demonstrates that reinforcement learning agents can develop efficient, human-like recursive numeral systems through communication and meta-grammar modifications, providing insights into the emergence of complex number systems.

Contribution

It introduces a novel RL-based approach with a meta-grammar framework to explain how recursive numeral systems similar to English can emerge through communication pressures.

Findings

Agents develop Pareto-optimal numeral systems.

Modified meta-grammar guides efficient communication.

Emergence of human-like recursive number systems.

Abstract

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.