Learning Approximate and Exact Numeral Systems via Reinforcement Learning
This provides a mechanistic explanation for numeral system efficiency, potentially generalizable to other semantic domains, but is incremental as it builds on prior information-theoretic work.
The study tackled the problem of how numeral systems emerge for efficient communication by using reinforcement learning in a signaling game between two agents, resulting in numeral systems that are information-theoretically efficient and similar to human systems.
Recent work (Xu et al., 2020) has suggested that numeral systems in different languages are shaped by a functional need for efficient communication in an information-theoretic sense. Here we take a learning-theoretic approach and show how efficient communication emerges via reinforcement learning. In our framework, two artificial agents play a Lewis signaling game where the goal is to convey a numeral concept. The agents gradually learn to communicate using reinforcement learning and the resulting numeral systems are shown to be efficient in the information-theoretic framework of Regier et al. (2015); Gibson et al. (2017). They are also shown to be similar to human numeral systems of same type. Our results thus provide a mechanistic explanation via reinforcement learning of the recent results in Xu et al. (2020) and can potentially be generalized to other semantic domains.