This paper considers the theoretical learnability of a multi-class classifier when supervision comes in the form of a variable that has nonzero mutual information with the true label. The reviewers agree this is an important problem and the paper makes useful, sound contributions, including the notion of separation to characterize generalization bounds. The major concern was the relationship between this work and earlier work, particularly Ben-David and Schuller (COLT '03), which uses a notion of transition functions F that are seemingly similar to this work's transformation functions. After the author response and discussion, the reviewers identified several key distinctions in this work. These distinctions include that the transformations are non-deterministic, that the pre- and post-transformation label cardinalities can be different, and that only the post-transformation samples are available for training. We suggest that the reviewers clarify these differences in the camera ready version. (We also note that R3 indicated in discussion that they would like to raise their score to a 6, but did not officially update it.)