Expressiveness and Learnability: A Unifying View for Evaluating Self-Supervised Learning

We propose a unifying view to analyze the representation 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 as the learning speed 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 classification tasks, yielding improvements with respect to the competing baselines.