Joint embedding (JE) architectures have emerged as a promising avenue for ac-quiring transferable data representations. A key obstacle to using JE methods,however, is the inherent challenge of evaluating learned representations withoutaccess to a downstream task, and an annotated dataset. Without efficient and re-liable evaluation, it is difficult to iterate on architectural and training choices forJE methods. In this paper, we introduce LiDAR (Linear Discriminant AnalysisRank), a metric designed to measure the quality of representations within JE archi-tectures. Our metric addresses several shortcomings of recent approaches basedon feature covariance rank by discriminating between informative and uninforma-tive features. In essence, LiDAR quantifies the rank of the Linear DiscriminantAnalysis (LDA) matrix associated with the surrogate SSL task—a measure thatintuitively captures the information content as it pertains to solving the SSL task.We empirically demonstrate that LiDAR significantly surpasses naive rank basedapproaches in its predictive power of optimal hyperparameters. Our proposed cri-terion presents a more robust and intuitive means of assessing the quality of rep-resentations within JE architectures, which we hope facilitates broader adoptionof these powerful techniques in various domains.