Venue: ICLR 2023 TinyPapers

Reviews:

final_score: rating: High Potential (HP): a submission which meets the reviewing criteria and has potential to make an impact on the field
review_content: summary_of_contributions: The polarized regime, i.e., is well-studied in the context of vanilla VAEs. In this paper, the authors have shown that iVAE, where the mean and the variance of the prior are learned, behave in a polarized regime, and display similar active variables as standard VAEs, whose priors are fixed. Finally, they have shown that the properties of “passive variables” of standard VAEs are a specific case of those of iVAE where the mean and variance of the prior are fixed to 0 and I.
strengths_and_weaknesses: The contribution of the paper is clearly presented, but needs some fixes regarding English and grammatical aspects. In the Appendix are all the necessary demonstrations relative to the theorems and prepositions stated. The article, therefore, turns out to be correct and reproducible from a theoretical point of view.
suggested_changes: It would have been nice to see one experimental result. 
Finally, the paper could provide information about the limitation of the proposed approach.
review_title: null

final_score: rating: Great Start (GS): a submission which meets some of the reviewing criteria but has room for improvement
review_content: summary_of_contributions: Descriptions of math theorems -- I encourage you to improve on clarity if you have a longer version
strengths_and_weaknesses: This paper provides theoretical results to show whether iVAE in training also has behaviours that can be classified into the polarised regime.

Just to say that in quite some other papers this phenomenon is called "posterior collapse", see:
https://arxiv.org/abs/1901.03416 

I believe the results in the paper are correct (as they are extensions to conditional vat with Gaussian prior conditioned on u).

The main issue for this paper is that the presentation is a bit too dry -- it's a collection of math theorem text with very little explanation. The paper starts from background that listed existing work with little discussions. See my comments below for my suggested changes.
suggested_changes: I encourage you to consider the following changes:
1. Motivate what is "polarised regime" and why people are interested in studying it;
2. Why studying this problem for iVAE is interesting: how would it impact on the specific claims (e.g., practical identifiability) of iVAE?
3. Does your result extend to general exponential family for the conditional prior?
4. Translate your theorem results (in math notations) to "layman text", e.g., if Theorem 2 holds, then what's the indication in practical iVAE training?
review_title: null

Meta-review: metareview: Good paper with all reviewers arguing for acceptance. Some changes are suggested.
confidence: 4: The area chair is confident but not absolutely certain
Decision: Invite to present