  Compositionality is an important explanatory target in emergent communication
and language evolution. The vast majority of computational models of
communication account for the emergence of only a very basic form of
compositionality: trivial compositionality. A compositional protocol is
trivially compositional if the meaning of a complex signal (e.g. blue circle)
boils down to the intersection of meanings of its constituents (e.g. the
intersection of the set of blue objects and the set of circles). A protocol is
non-trivially compositional (NTC) if the meaning of a complex signal (e.g.
biggest apple) is a more complex function of the meanings of their
constituents. In this paper, we review several metrics of compositionality used
in emergent communication and experimentally show that most of them fail to
detect NTC - i.e. they treat non-trivial compositionality as a failure of
compositionality. The one exception is tree reconstruction error, a metric
motivated by formal accounts of compositionality. These results emphasise
important limitations of emergent communication research that could hamper
progress on modelling the emergence of NTC.
