Expressivity of Emergent Language is a Trade-off between Contextual Complexity and Unpredictability

Researchers are now using deep learning models to explore the emergence of language in various language games, where simulated agents interact and develop an emergent language to solve a task. Although it is quite intuitive that different types of language games posing different communicative challenges might require emergent languages which encode different levels of information, there is no existing work exploring the expressivity of the emergent languages. In this work, we propose a definition of partial order between expressivity based on the generalisation performance across different language games. We also validate the hypothesis that expressivity of emergent languages is a trade-off between the complexity and unpredictability of the context those languages are used in. Our second novel contribution is introducing contrastive loss into the implementation of referential games. We show that using our contrastive loss alleviates the collapse of message types seen using standard referential loss functions.