The paper proposed a metric for evaluating compressed embeddings and also a method to choose between different embeddings without having to run downstream tasks and check performance. The theoretical properties of the metric and empirical results generated a lot of interest among the reviewers. Further, I feel the paper addressed simple obvious though previously overlooked questions around embedding like how well does simple dimensionality reduction generalize? how do various compression techniques compare? Is it possible to choose between different embeddings without having to run downstream? Defining of eigenspace overlap and deriving its theoretical properties is significant. Thus, I am happy to recommend the paper an acceptance to NeurIPS.