Learning Efficient Recursive Numeral Systems via Reinforcement Learning
This work addresses a fundamental problem in cognitive science and AI by providing a mechanistic explanation for the emergence of efficient numeral systems, which is incremental as it builds on prior RL approaches to simpler numeral systems.
The paper tackles the challenge of explaining how complex recursive numeral systems, like English, can emerge through simple learning mechanisms such as reinforcement learning. It demonstrates that RL agents, using a modified meta-grammar and shaped by efficiency pressures, can develop lexicons comparable to human numeral systems in efficiency, achieving Pareto-optimal configurations.
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.