This paper proposes a deep learning approach to predicting functional maps for shape matching. The reviewers agree that the paper makes a useful contribution, is clearly presented, and should be published. They raise concerns in their reviews and in the discussion about two issues that we strongly recommend the authors address in the camera ready version. First, the use of technical terms like "minimum" and "sufficient" imply theoretical claims that are unproved. Second, the derivation of the method needs to be more carefully presented. For example, the paper does not consider that the constraints imposed amount to imposing bijectivity on the composition of two matrices. See R3's review for more details.