text: Training GAN in a hierarchical optimization schedule shows promising performance recently (e.g. Zhao et al., 2016).  However, these works utilize the prior knowledge of the data (e.g. image)  and it's hard to generalize it to other data types (e.g. text).  The paper aims to learn these hierarchies directly instead of designing by human.  However, several parts are missing and not well-explained.  Also, many claims in paper are not proved properly by theory results or empirical results.  (1) It is not clear to me how to train the proposed algorithm.  My understanding is train a simple ALI, then using the learned latent as the input and train the new layer.  Do the authors use a separate training ? or a joint training algorithms.  The authors should provide a more clear and rigorous objective function.  It would be even better to have a pseudo code.  (2) In abstract, the authors claim the theoretical results are provided.  I am not sure whether it is sec 3.2  The claims is not clear and limited.  For example, what's the theory statement of [Johnsone 200; Baik 2005].  What is the error measure used in the paper?  For different error, the matrix concentration bound might be different.  Also, the union bound discussed in sec 3.2 is also problematic.  Lats, for using simple standard GAN to learn mixture of Gaussian, the rigorous theory result doesn't seem easy (e.g. [1])   The author should strive for this results if they want to claim any theory guarantee. (3) The experiments part is not complete.  The experiment settings are not described clearly.  Therefore, it is hard to justify whether the proposed algorithm is really useful based on Fig 3.  Also, the authors claims it is applicable to text data in Section 1, this part is missing in the experiment.  Also, the idea of "local" disentangled LV is not well justified to be useful. [1] On the limitations of first order approximation in GAN dynamics, ICLR 2018 under review