Thanks for your submission to NeurIPS. This paper had somewhat mixed reviews, with two positive reviews and one negative review. After the rebuttal, I also took a look at the paper and initiated a discussion with the reviewers. The main concerns of the negative reviewer were in the comparison to existing non-linear metric learning approaches; I also had a similar concern when reading the paper. I think the rebuttal responded well to this (also, it's unrealistic that one could compare with many of the existing non-linear approaches, given how many exist); please include the new results in the final version. My other concern was that the writing is often not super clear---for example, terms like "measurer lines" are not ever precisely defined, and may be unfamiliar to readers who work on metric learning. Whatever can be done for the final version to clarify the text would make for a more effective presentation. Generally speaking, please keep in mind all the reviewer comments when preparing a final version.