  The principle of compositionality, which enables natural language to
represent complex concepts via a structured combination of simpler ones, allows
us to convey an open-ended set of messages using a limited vocabulary. If
compositionality is indeed a natural property of language, we may expect it to
appear in communication protocols that are created by neural agents in language
games. In this paper, we propose an effective neural iterated learning (NIL)
algorithm that, when applied to interacting neural agents, facilitates the
emergence of a more structured type of language. Indeed, these languages
provide learning speed advantages to neural agents during training, which can
be incrementally amplified via NIL. We provide a probabilistic model of NIL and
an explanation of why the advantage of compositional language exist. Our
experiments confirm our analysis, and also demonstrate that the emerged
languages largely improve the generalizing power of the neural agent
communication.
