Reviews: Breaking the Glass Ceiling for Embedding-Based Classifiers for Large Output Spaces

There is some disagreement about the significance of the paper among the reviewers. Three steps can be distinguished. First, to refute the common belief that low-dimensional embeddings act as bottlenecks that limit the accuracy in the extreme classification case. Here, while it is true (raised by reviewer 1) that a representation result does not imply computational achievability, I feel that it reverses the direction of justification. If someone could show that common optimization methods fail to find embeddings (which "exist"), then this would re-instantiate the argument, yet in a more refined/precise form.