  We address the problem of evaluating the quality of self-supervised learning
(SSL) models without access to supervised labels, while being agnostic to the
architecture, learning algorithm or data manipulation used during training. We
argue that representations can be evaluated through the lens of expressiveness
and learnability. We propose to use the Intrinsic Dimension (ID) to assess
expressiveness and introduce Cluster Learnability (CL) to assess learnability.
CL is measured in terms of the performance of a KNN classifier trained to
predict labels obtained by clustering the representations with K-means. We thus
combine CL and ID into a single predictor -- CLID. Through a large-scale
empirical study with a diverse family of SSL algorithms, we find that CLID
better correlates with in-distribution model performance than other competing
recent evaluation schemes. We also benchmark CLID on out-of-domain
generalization, where CLID serves as a predictor of the transfer performance of
SSL models on several visual classification tasks, yielding improvements with
respect to the competing baselines.
