Reviewer

We thank all the reviewers for the unanimous positive comments! Below we address questions raised by each reviewer. Q:"The operator on edges is never defined" " means stitching two adjacent paths (i.e., they share one endpoint) into a longer path. " Is this really an okay assump-6 Is anything given up by this assumption? Most parametric maps will not be injective." This is to define the cycle-consistency basis. Q:" It would be nice to show this form of cycle-consistency optimization enables novel capabilities, rather than Improved testing accuracy indicates better-learned representations.