Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. However, a key obstacle to using JE methods is the inherent challenge of evaluating learned representations without access to a subsequent task and an annotated data set. Without efficient and reliable evaluation, it is difficult to repeat architecture and training choices for JE methods. In this article, we present LiDAR (Linear Discriminant Analysis Range), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance range in discriminating between informative and non-informative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task, a measure that intuitively captures the information content as it relates to the resolution of the SSL task. We empirically demonstrate that LiDAR significantly outperforms naive range-based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of evaluating the quality of representations within JE architectures, which we hope will facilitate broader adoption of these powerful techniques across diverse domains.
