The paper consider a particular class of neural ODEs and shows that constraining the flow to lie in O(d) improves the stability of training. Initially, the paper received mixed reviews (1 below threshold 2 above threshold). On the positive side, the contribution is found interesting and novel, the idea of restricting to a compact manifold to be tractable and effective. On the negative side, the reviewers had some issues with technical details, would have liked the paper to be a little bit more clear, and would have liked more experiments. The reviewers were satisfied by the rebuttal: R1 writes he/she will increase his/her rating, with the other two reviewers remained positive. In the end, all three reviewers agree the paper is above threshold.