\alpha -ReQ : Assessing Representation Quality in Self-Supervised Learning by measuring eigenspectrum decay

Self-Supervised Learning (SSL) with large-scale unlabelled datasets enables learning useful representations for multiple downstream tasks. However, assessing the quality of such representations efficiently poses nontrivial challenges. Existing approaches train linear probes (with frozen features) to evaluate performance on a given task. This is expensive both computationally, since it requires retraining a new prediction head for each downstream task, and statistically, requires task-specific labels for multiple tasks. This poses a natural question, how do we efficiently determine the "goodness" of representations learned with SSL across a wide range of potential downstream tasks?