  In representation learning, a common approach is to seek representations
which disentangle the underlying factors of variation. Eastwood & Williams
(2018) proposed three metrics for quantifying the quality of such disentangled
representations: disentanglement (D), completeness (C) and informativeness (I).
In this work, we first connect this DCI framework to two common notions of
linear and nonlinear identifiability, thereby establishing a formal link
between disentanglement and the closely-related field of independent component
analysis. We then propose an extended DCI-ES framework with two new measures of
representation quality - explicitness (E) and size (S) - and point out how D
and C can be computed for black-box predictors. Our main idea is that the
functional capacity required to use a representation is an important but
thus-far neglected aspect of representation quality, which we quantify using
explicitness or ease-of-use (E). We illustrate the relevance of our extensions
on the MPI3D and Cars3D datasets.
