Variational Autoencoder plays an important role in disentangled representation learning. However, it is found facing posterior collapse problem and learning multiple variants in one factor. What would be learned by variational autoencoder (VAE)  and what influence the disentanglement of VAE? This paper tries to preliminarily address VAE's intrinsic dimension, real factor, disentanglement and indicator issues theoretically in the idealistic situation and implementation issue practically through noise modeling perspective in the realistic case. On intrinsic dimension issue, due to information conservation, the idealistic VAE learns and only learns intrinsic factor dimension. Besides, suggested by mutual information separation property, the constraint induced by Gaussian prior to the VAE objective encourages the information sparsity in dimension. On disentanglement issue, subsequently, inspired by information conservation theorem the clarification on disentanglement in this paper is made. On real factor issue, due to factor equivalence, the idealistic VAE possibly learns any factor set in the equivalence class. On indicator issue, the behavior of current disentanglement metric is discussed, and several performance indicators regarding the disentanglement and generating influence are subsequently raised to evaluate the performance of VAE model and to supervise the used factors. On implementation issue, the experiments under noise modeling and constraints empirically testify the theoretical analysis and also show their own characteristic in pursuing disentanglement.
This paper proposes to modify how noise factors are treated when developing VAE models.  For example, the original VAE work from (Kingma and Welling, 2013) applies a deep network to learn a diagonal approximation to the covariance on the decoder side.  Subsequent follow-up papers have often simplified this covariance to sigma^2*I, where sigma^2 is assumed to be known or manually tuned.  In contrast, this submission suggests either treating sigma^2 as a trainable parameter, or else introducing a more flexible zero-mean mixture-of-Gaussians (MoG) model for the decoder noise.  These modeling adaptations are then analyzed using various performance indicators and empirical studies.
The primary issues I have with this work are threefold:  (i) The paper is not suitably organized/condensed for an ICLR submission, (ii) the presentation quality is quite low, to the extent that clarity and proper understanding are jeopardized, and (iii) the novelty is limited.  Consequently my overall impression is that this work is not yet ready for acceptance to ICLR.
First, regarding the organization, this submission is 19 pages long (*excluding* references and appendices), despite the clear suggestion in the call for papers to limit the length to 8 pages: "There is no strict limit on paper length. However, we strongly recommend keeping the paper at 8 pages, plus 1 page for the references and as many pages as needed in an appendix section (all in a single pdf). The appropriateness of using additional pages over the recommended length will be judged by reviewers."  In the present submission, the first 8+ pages contain minimal new material, just various background topics and modified VAE update rules to account for learning noise parameters via basic EM algorithm techniques.  There is almost no novelty here.  In my mind, this type of well-known content is in no way appropriate justification for such a long paper submission, and it is unreasonable to expect reviewers to wade through it all during a short review cycle.
Secondly, the presentation quality is simply too low for acceptance at a top-tier international conference (e.g., it is full of strange sentences like "Such amelioration facilitates the VAE capable of always reducing the artificial intervention due to more proper guiding of noise learning."  While I am sympathetic to the difficulties of technical writing, and realize that at times sufficiently good ideas can transcend local grammatical hiccups, my feeling is that, at least for now, another serious pass of editing is seriously needed.  This is especially true given that it can be challenging to digest so many pages of text if the presentation is not relatively smooth.
Third and finally, I do not feel that there is sufficient novelty to overcome the issues already raised above.  Simply adapting the VAE decoder noise factors via either a trainable noise parameter or an MoG model represents an incremental contribution as similar techniques are exceedingly common.  Of course, the paper also invents some new evaluation metrics and then applies them on benchmark datasets, but this content only appears much later in the paper (well after the soft 8 page limit) and I admittedly did not read it all carefully.  But on a superficial level, I do not believe these contributions are sufficient to salvage the paper (although I remain open to hearing arguments to the contrary).