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. I still feel that the paper makes an important argument in an ongoing discussion. Second, the finding that overfitting is the key problem. I agree here with reviewer 2 that overfitting has been observed in many papers before, but I feel the current submission makes a more focussed claim and it proposes a novel regularizer to address it in a specific manner. All in all, while the paper can certainly be improved in many ways, I feel it does enrich and advance our understanding of embeddings based methods for extreme classification,