Reviews: Learning nonlinear level sets for dimensionality reduction in function approximation

In particular, the additional experiment on optimizing the dimensionality reduced functions for the real-world example looks quite persuasive, and the explanation about adding a dummy variable to address odd dimensional functions is also super valid. I also appreciate the authors for providing the detailed content of the modified paragraphs that they will include for the mathematical examples. The only small remaining issue is that for my point 6, the authors didn't seem to understand that the issue with Section 4.1 is that some of the sample points in the validation set may (almost) coincide with those in the training set, and the authors should make sure that they have excluded points that are sufficiently closed to the training set ones when generating the validation set, and clearly state this in the main text. That being said, I have decided to improve my score to 7 to acknowledge the sufficient improvement shown in the rebuttal. This paper considers the problem of dimensionality reduction for high dimensional function approximation with small data.