  The increasing impact of black box models, and particularly of unsupervised
ones, comes with an increasing interest in tools to understand and interpret
them. In this paper, we consider in particular how to characterise visual
groupings discovered automatically by deep neural networks, starting with
state-of-the-art clustering methods. In some cases, clusters readily correspond
to an existing labelled dataset. However, often they do not, yet they still
maintain an "intuitive interpretability". We introduce two concepts, visual
learnability and describability, that can be used to quantify the
interpretability of arbitrary image groupings, including unsupervised ones. The
idea is to measure (1) how well humans can learn to reproduce a grouping by
measuring their ability to generalise from a small set of visual examples
(learnability) and (2) whether the set of visual examples can be replaced by a
succinct, textual description (describability). By assessing human annotators
as classifiers, we remove the subjective quality of existing evaluation
metrics. For better scalability, we finally propose a class-level captioning
system to generate descriptions for visual groupings automatically and compare
it to human annotators using the describability metric.
