Invited Talk - Learning Efficient Recursive Numeral Systems via Reinforcement Learning

While there is evidence to suggest that animals, young infants and adult humans possess a biologically determined, domain-specific representation of numbers and elementary arithmetic operations, only humans have a capacity for generating an infinite set of natural numbers. This unique capacity is central to many aspects of human cognition, including, of course, the development of sophisticated mathematics.

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 et al. (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. We introduce an approach towards deriving a mechanistic explanation of the emergence of such 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.