We thank the authors for their submission. The quality of their work was appreciated by all reviewers. I feel a bit more uneasy about the quality of their experimental validation. Several choices are surprising. For instance using matlab's linprog is borderline dishonnest given the importance of comparing oneself with a proper network flow solver, and not a generic off-the-shelf LP solver. Comparisons with the sinkhorn algorithm also denote a lack of familiarity with these solvers and their implementation (as highlighted by R2 some of the computational times initially reported are not realistic). Claims about lack of parallelization by R2 were also left unanswered. For all these reasons, and for the interest of the paper, I would strongly recommend that the authors spend significant time improving the experimental section for the camera ready. A Neurips requires this to have visibility (as opposed to other more TCS conferences)