the liberty to group and reword some of the reviewers comment (in blue italic) to save space. 3 General answer on the usefulness of gradient descent, its theoretical guarantees, and its scalability

We thank the reviewers for the time they spent evaluating our manuscript and for their valuable comments. We agree that having theoretical guarantees would be a big plus. As for scalability, the bottleneck of our method is the single-linkage algorithm. Similarly to Monath et al. (NeurIPS 2017), our idea consists Given the significant body of additional material, we feel that this topic is best left to a future publication. Line 8,56,70,93: I would suggest a more cautious usage of the word "equivalent".