Paper:
Compositional structures between parts and objects are inherent in natural scenes. Modeling such compositional hierarchies via unsupervised learning can bring various benefits such as interpretability and transferability, which are important in many downstream tasks. In this paper, we propose the first deep latent variable model, called RICH, for learning Representation of Interpretable Compositional Hierarchies. At the core of RICH is a latent scene graph representation that organizes the entities of a scene into a tree structure according to their compositional relationships. During inference, taking top-down approach, RICH is able to use higher-level representation to guide lower-level decomposition. This avoids the difficult problem of routing between parts and objects that is faced by bottom-up approaches. In experiments on images containing multiple objects with different part compositions, we demonstrate that RICH is able to learn the latent compositional hierarchy and generate imaginary scenes.

Review:
Update: I thank the auhors for the detailed response. The updated paper does look more convincing, but my main concern remains - all considered datasets and tasks are synthetic and specifically made for the method. I think experiments on more real data would be crucial to show the potential of the method. Some examples I can imagine would be part segmentation in images or 3D models, or robotic control.
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The paper proposes an unsupervised approach to learning objects and their parts from images. The method is based on the "Attend, Infer, Repeat" (AIR) line of work and adds a new hierarchy level to the approach, corresponding to object parts. The method is evaluated on two custom synthetic dataset: one composed of simple 2D geometric shapes and another one with 3D geometric shapes. On these datasets the method successfully infers the object-part structure and can parse and reconstruct provided images.
While the general topic of the paper is interesting, I do not think it is fit for publication. First and foremost, the experiments are very incomplete: the method is only evaluated on two custom synthetic datasets and not compared against any baselines or ablated versions of the method. Moreover, the proposed approach seems like a relatively minor modification of SPAIR (Crawford & Pineau).
Pros:
1) The topic is interesting and the method generally makes sense.
2) The method works on the tasks studied in the paper, including relatively challenging scenarios with 3D occlusions or ambiguity in assigning parts to objects.
3) The paper shows generalization to a number of objects different from that seen during training.
Cons:
1) Experiments are limited:
1a) The method is evaluated on custom and relatively toy datasets. It is unclear if it would apply to more practical situations. While I agree that at the high level the question of decomposition of object into parts is interesting, it is still important to connect research in this direction to potential practical applications. Where could the proposed method be used? Perhaps in some control tasks, such as robotics? Could it be applied to more realistic data, such as for instance ShapeNet objects?
1b) There are no comparisons to baselines. One might argue that baselines do not exist since there are no methods addressing the same task. Generally, it is the job of the authors to come up with relevant baselines to show that the proposed model actually improves upon some simpler methods. One variant of obtaining baselines is via ablating the proposed model. Another is by taking prior approaches, for instance object-based ones without the part decomposition, and showing that the part decomposition allows to improve upon those in some sense.
2) The novelty is somewhat limited: the method seems like a relatively straightforward extension of SPAIR by adding another hierarchy layer. It might be sufficient if the experimental results would be strong, but given that they are not, becomes somewhat concerning. If the method does indeed include significant technical innovation, it might be helpful to better highlight it.
3) The related work overview is extremly limited. It is authors' job to provide a comprehensive ovreview of prior literature and I cannot do it for them here, but below are a few papers that come to mind. This is by no means a complete list.
[1] Zhenjia Xu, Zhijian Liu, Chen Sun, Kevin Murphy, William T. Freeman, Joshua B. Tenenbaum, Jiajun Wu. Unsupervised Discovery of Parts, Structure, and Dynamics. ICLR 2019
[2] Shubham Tulsiani, Hao Su, Leonidas J. Guibas, Alexei A. Efros, Jitendra Malik. Learning Shape Abstractions by Assembling Volumetric Primitives. CVPR 2017
[3] Jun Li, Kai Xu, Siddhartha Chaudhuri, Ersin Yumer, Hao Zhang, Leonidas Guibas. GRASS: Generative Recursive Autoencoders for Shape Structures. SIGGRAPH 2017.
[4] Gopal Sharma, Rishabh Goyal, Difan Liu, Evangelos Kalogerakis, Subhransu Maji. CSGNet: Neural Shape Parser for Constructive Solid Geometry. CVPR 2018.
[5] Adam R. Kosiorek, Hyunjik Kim, Ingmar Posner, Yee Whye Teh. Sequential Attend, Infer, Repeat: Generative Modelling of Moving Objects. NeurIPS 2018.
4) Presentation is at times suboptimal:
4a) It would be very helpful to have more visuals and intuitions about the functioning of the method, as opposed to equations. Equations are definitely good to have, but they are not the easiest to parse, especially by those not intimately familiar with this specific line of work. 
4b) It is quite unclear to me how and why is the memory used in the model. If this is described in another paper, it would be useful to point there, but still briefly summarize in this paper to make it self-contained.