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Self-supervised learning (SSL) has shown impressive results in downstream classification tasks. However, there is limited work in understanding their failure modes and interpreting their learned representations. In this paper, we study the representation space of state-of-the-art self-supervised models including SimCLR, SwaV, MoCo, BYOL, DINO, SimSiam, VICReg and Barlow Twins. Without the use of class label information, we discover discriminative features that correspond to unique physical attributes in images, present mostly in correctly-classified representations. Using these features, we can compress the representation space by up to 40% without significantly affecting linear classification performance. We then propose Self-Supervised Representation Quality Score (or Q-Score), an unsupervised score that can reliably predict if a given sample is likely to be mis-classified during linear evaluation, achieving AUPRC of 91.45 on ImageNet-100 and 78.78 on ImageNet-1K. Q-Score can also be used as a regularization term on pre-trained encoders to remedy low-quality representations. Fine-tuning with Q-Score regularization can boost the linear probing accuracy of SSL models by up to 5.8% on ImageNet-100 and 3.7% on ImageNet-1K compared to their baselines. Finally, using gradient heatmaps and Salient ImageNet masks, we define a metric to quantify the interpretability of each representation. We show that discriminative features are strongly correlated to core attributes and, enhancing these features through Q-score regularization makes SSL representations more interpretable.