We thank all reviewers for the constructive critique and would be happy to follow their suggestions, in particular, 1 improve the presentation of our theoretical analysis

Our analysis provides full distribution information on the joint outputs. A detailed comment for Reviewer #3: Thm. 2 is not difficult to derive but certainly not standard in MF theory. This is rather obvious however. We agree that we have to extend our literature discussion. Y et, its main focus is on resNets and convNets.