Discretisation and continuity: The emergence of symbols in communication

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and prosodic features to convey the emotions of the speaker. However, continuous aspects are not always expressed with the continuous properties of an utterance but are frequently categorised into discrete symbols. While the existence of symbols in communication is self-evident, the emergence of discretisation from a continuous space is not well understood. In this paper, we investigate the emergence of discrete symbols in regions with a continuous semantics by simulating the learning process of two agents that acquire a shared signalling system. The task is formalised as a reinforcement learning problem with a continuous form and meaning space. We identify two causes for the emergence of discretisation that do not originate in discrete semantics: 1) premature convergence to sub-optimal signalling conventions and 2) topological mismatch between the continuous form space and the continuous semantic space. The insights presented in this paper shed light on the origins of discrete symbols, whose existence is assumed by a large body of research concerned with the emergence of syntactic structures and meaning in language.