Learning Approximate and Exact Numeral Systems via Reinforcement Learning
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.
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