text: Summary of paper and review: The paper presents the instability issue of training GANs for semi-supervised learning.  Then, they propose to essentially utilize a wgan for semi-supervised learning.  The novelty of the paper is minor,  since similar approaches have been done before.  The analysis is poor,  the text seems to contain mistakes,  and the results don't seem to indicate any advantage or promise of the proposed algorithm. Detailed comments: - Unless I'm grossly mistaken the loss function (2) is clearly wrong.  There is a cross-entropy term used by Salimans et al. clearly missing. - As well, if equation (4) is referring to feature matching, the expectation should be inside the norm and not outside  (this amounts to matching random specific random fake examples to specific random real examples, an imbalanced form of MMD). - Theorem 2.1 is an almost literal rewrite of Theorem 2.4 of [1], without proper attribution.  Furthermore, Theorem 2.1 is not sufficient to demonstrate existence of this issues.  This is why [1] provides an extensive batch of targeted experiments to verify this assumptions.  Analogous experiments are clearly missing.  A detailed analysis of these assumptions and its implications are missing. - In section 3, the authors propose a minor variation of the Improved GAN approach by using a wgan on the unsupervised part of the loss.  Remarkably similar algorithms (where the two discriminators are two separate heads) to this have been done before (see for example, [2], but other approaches exist after that, see for examples papers citing [2]). - Theorem 3.1 is a trivial consequence of Theorem 3 from WGAN. - The experiments leave much to be desired.  It is widely known that MNIST is a bad benchmark at this point,  and that no signal can be established from a minor success in this dataset.  Furthermore, the results in CIFAR don't seem to bring any advantage, considering the .1% difference in accuracy is 1/100 of chance in this dataset. [1]: Arjovsky & Bottou, Towards Principled Methods for Training Generative Adversarial Networks, ICLR 2017 [2]: Mroueh & Sercu, Goel, McGan: Mean and Covariance Feature Matching GAN, ICML 2017