  Natural language allows us to refer to novel composite concepts by combining
expressions denoting their parts according to systematic rules, a property
known as \emph{compositionality}. In this paper, we study whether the language
emerging in deep multi-agent simulations possesses a similar ability to refer
to novel primitive combinations, and whether it accomplishes this feat by
strategies akin to human-language compositionality. Equipped with new ways to
measure compositionality in emergent languages inspired by disentanglement in
representation learning, we establish three main results. First, given
sufficiently large input spaces, the emergent language will naturally develop
the ability to refer to novel composite concepts. Second, there is no
correlation between the degree of compositionality of an emergent language and
its ability to generalize. Third, while compositionality is not necessary for
generalization, it provides an advantage in terms of language transmission: The
more compositional a language is, the more easily it will be picked up by new
learners, even when the latter differ in architecture from the original agents.
We conclude that compositionality does not arise from simple generalization
pressure, but if an emergent language does chance upon it, it will be more
likely to survive and thrive.
