Appendix A Proof of Theorem 2

Recall the operation in the i -th layer, i.e., the function F We introduce additional descriptions on the datasets with regression labels. All images are resized to 256x256 in both training and testing times. All images are resized to 256x256 in both training and testing times. Note that when training CycleGAN, only the first sub-group is adopted as a source domain, and the rest of the groups are all blended together as a target domain. For each population, we used 100 different cell images for training and testing.