Venue: ICLR 2022 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper addresses a challenging problem in 3D representation learning of point clouds, which aims to generalize the representations well to arbitrary orientations. The proposed CSGNN uses a convolutional framework to learn over concentric spherical feature maps, which is incorporated with both intra-sphere and inter-sphere information. The idea is interesting and reasonably well presented. In general, the proposed CSGNN is practical on spherical representation learning. However, there still remains some issues that should be addressed.
main_review: Strengths:
1. The author proposes a new volumetric representation as the basis for convolutional learning, which consists of multiple nested spheres discretized by the icosahedral grid.
2. The proposed CSGNN integrates both intra-sphere and inter-sphere convolutions to learn volumetric representation over concentric spheres.
3. The proposed CSGNN is practical in classifying arbitrarily rotated 3D objects and is also effective in molecular environment description.

Weaknesses:
1. The architecture is not novel enough, which is only based on hierarchical graph convolutions followed by radial convolutions, and the performance is restricted by the size of radius, as illustrated in Fig. 1 and the experimental results on Table 2.
2. It is time-consuming and redundant to adopt all the points to calculate the contribution to vertices, the reviewer is curious about how to select the effective points or how to avoid the redundant information when converting the point cloud to concentric spheres. Are there any adaptive strategies other than thresholding on some scores?
3. There are some adjustable hyper-parameters, i.e., the threshold of RBF, the number of spatial concentric spheres, the input channels, the kernel size, etc. It is not clear whether the method is robust.
4. How to calculate the DOS and FDOS loss items, the author is expected to give explanations.
5. Experimental results in some aspects are not state-of-the-arts, and some failure cases should also be discussed if there exists.

summary_of_the_review: This paper presents a new volumetric representation to learn 3D representations. However, some technical details should be further discussed and analyzed. Strengths and weaknesses are both discussed on the proposed CSGNN in terms of data process, method design, and experimental settings and results. Therefore, the reviewer gives rating of 6: marginally above the acceptance threshold.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a graph convolution based multiscale spherical deep neural network. In particular, radial convolutions over concentric spheres of different radii are used in conjunction with the typical spherical convolution. A simple 5-layer architecture is presented to fuse the rich features extracted by both convolutions. Experiments on point cloud classification under arbitrary SO(3) transformations as well as predicting electronic state density of graphene allotropes, demonstrate the validity of the devised method.
main_review: PROS
- The paper makes a very sensible contribution that extends a variant of spherical CNN to be multiscale. As such, better accuracy is expected because the finer grained details can be better captured. 
- The presentation is quite clear and I did not spot significant problems.
- The chosen experiments are quite relevant and span two different communities. 

CONS

- I feel like the paper presents what I would call a 'multi-resolution spherical CNN'. In other words, the only addition to the known graph based spherical CNN is the notion of multiple concentric spheres. However, the experiments seem to distinguish between Spherical CNN and the CSGNN with R=1, C=1. This confuses me a little bit. Would it be possible to discuss the differences or can we recover Spherical CNNs as a special case of the proposed approach? 

- 'Representation' is a fundamental aspect in 3D analysis. I would suggest the paper to be more careful or conscious with the use of the word 'volumetric'. First, why are volumetric features desirable to begin with? Second, I feel like the concentric spheres can better capture the narrow band around the point set while still leaving parts of the space unexplained. This is not necessarily a negative, as it might amount to avoiding the storage of unnecessary information. In that sense, the representation might fall somewhere between a point cloud and a dense volume - say a sweet spot maybe. I might also be wrong, but these points could be better described in the paper.

- The related work does not really discriminate the proposed approach from the others so as to position this method among the state of the art. In particular, it could be good to discuss what properties/goals are not met by the prior approaches. Regarding the related works, it is also good to mention the initial attempts to develop invariant point cloud classification networks:
* Thomas, Nathaniel, et al. "Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds." arXiv preprint arXiv:1802.08219 (2018).
* Zhao, Yongheng, et al. "Quaternion equivariant capsule networks for 3d point clouds." European Conference on Computer Vision. Springer, Cham, 2020.

- The paper seems to lack some details of the rotational invariance capabilities of the convolutions. Especially invariant/equivariant design of the radial convolutions carry importance as being the main contributions of this paper.

- The paper seems to decouple two convolutions (radial and angular). Would it be possible to have a single convolution fusing information from both dimensions? (e.g. just like volumetric 3D convolutions) Could the paper explain why such a design choice is better?

- The paper argues for a spherical distribution to represent the point cloud. However this introduces some discretization artifacts. So it is of wonder to see whether the benefit brought by concentric spheres outdoes the discretization error. 

- As shown in Fig. 2, it is possible to obtain a subset of the spheres at certain radii. As far as I understand this is somewhat a pruning mechanism. Is this only hypothetical or does it also happen with real point clouds? Could we see an example?

- The spheres seem to have more structure than a simple graph. I feel like resorting to GNNs can yield some information loss. Have we ever thought about this aspect?

- Can the approach estimate the pose of the object or is invariance property all we get? In case the pose can be estimated, can we see a study on this?

- In Fig. 6, I notice an architectural/design difference compared to the point cloud one. In fact, this seems to have spheres anchored on local patches (an operation also applicable to point sets). Do we necessarily need this change? Can we cover both problems with similar architectures?

- I feel that some kind of a theoretical analysis on the minimum number of concentric spheres required for rich feature extraction would be a nice to have. 

Minor Remarks:
- such the underlying -> such that the underlying
- challenging to invariance -> challenging to introduce invariance (maybe?)
- 'over over' -> over
- Are all point sets normalized to the unit ball? Can we hear some more details here?
- What about the connections in Fig. 5? Are those used or is the discretization same as the point cloud experiment?
summary_of_the_review: Simple idea, clear writing, but lacks thorough discussions and evaluations.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper proposed a concentric spherical representation of 3D space, formed by nesting spatially-sampled spheres resulting from the highly regular icosahedral discretization. It utilizes separate intra-sphere and inter-sphere convolutions over the resulting concentric spherical grid, which are combined into a convolutional framework for learning volumetric and rotationally equivariant representations over point clouds.
main_review: This paper proposes a new volumetric representation that consists of multiple nested spheres, each discretized by the icosahedral grid. It proposes to learn the 3D volumetric representation over concentric spheres by combining intra-sphere and inter-sphere convolutions. The proposed convolutions are rotationally equivariant, and also scale (near) linearly with grid resolution. It shows some experiments in 3D object classification, and resolving electronic structure of atomistic systems.

The paper overall is technical sound with some interesting results. The application in atomistic systems is interesting and seems new at least to the reviewer for the 3D point clouds.

The results in 3D object classification is not very detailed or sufficient. There are a lot of datasets I wished the paper can test. Also it doesn't reference sufficient papers in the 3D point clouds deep learning domain which is related and very relevant. e.g the KPConv paper should be referred. The shellnet paper which also uses concentric shells should be mentioned. It seems to me the authors might not be very familiar with the literature in this area. I would like to see the paper has side by side comparisons with some of these leading papers in some of the standard benchmark datasets.
summary_of_the_review: Overall the paper is sound and interesting with good results. The application in atomic system is interesting and new. However the paper doesn't do a good comparison with leading papers in this field thus it is hard to judge the effectiveness of the proposed method.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: The paper presents a concentric sphere representation and icosahedron-based spherical CNNs for 3D point clouds. The contributions are two folds. First, the concentric sphere representation enables learning features volumetrically. Second, two types of convolutions: intra-sphere and inter-sphere are combined towards rotation equivariant and scalable computations. 
main_review: Strengths:  
1. motivation: the motivation to use multiple resolution spheres with varying radius sounds valid and may help feature learning of 3D shapes, comparing to previous approaches using single unit sphere; 
2. architecture: the multiple resolution approach is widely used in image deep learning architecture, this is the first time it is extended to spherical cnn and the proposed architecture could lead to many follow-up work in both 3D point cloud processing and spherical CNNs.

Weakness:  
1. rotation-equivariant: authors claims the proposed method to be rotation equivariant and results on ModelNet40 also support this claim. This is the most important property of the proposed method. It is advisable to have a better explanation of both proposed method and related method mentioned in related work, i.e. why some methods are not rotation-equivariant. 
2. ModelNet40: results of [1] (Cohen etal. 2019) is missing in Table 1. 
3. DOS experiments: 
(1). meaning of parameters R/C: in the experiments, R=1 and C=32 are used. Does this mean 32 spheres are combined into 1?
(2). loss functions: from A.2 and Eq.5, \alpha=0.1 is used, does this mean loss(DOS) is less important than loss(FDOS)? If previous works using \alpha=1.0, could the authors provides the results using the same setting? In other words, how does disabling loss(FDOS) hurt?
I'm also keen to know if it is fair to compare to other methods using additional loss term. 
(3) Effectiveness of the methods: On DOS experiments, authors use simplified version of the architecture (R=1) and reported strong performance than baselines. Does this mean that DOS estimation is too easy for the proposed method? 
(4) Spherical CNNs baseline: Considering the baselines use in DOS experiments, nearly all SOTA spherical CNNs are not compared.


Ref: 
[1] Gauge equivariant convolutional networks and the icosahedral CNN.
summary_of_the_review: In summary, the paper is easy to read and follow. Description of the method is clear and complete. Experiments include one for 3D point cloud classification and one for DOS estimation. For the latter one, I'm not familiar with the experiment difficulty and details and thus could not evaluate the methods from the results. Overall, I appreciate the efforts of the work to propose multi-resolution version of spherical CNNs. The downside is that evaluations are limited, and some baselines are not compared.
review_title: null

Meta-review: This paper addresses the problem of learning representation of 3D point clouds and introduces an interesting approach of concentric spherical GNN with the property of rotationally equivariant. It shows some promising results on point cloud classification under SO(3) transformations and on predicting electronic state density of graphene allotropes. The reviews suggest that, while it does not suffer from any major flaws, the paper has a fairly large number of minor issues that add up to make it subpar for publication. The proposed approach have several hyperparameters, but the authors do not seem to be up front about how the parameters are selected except for stating that they use "standard tuning techniques" --- this is not a satisfactory answer and appears to be dodging the question. Many technical details and specific choices could use more thorough explanation and analysis. The distinction of the proposed approach in relation to the large body of existing literature could be more clearly spelled out. Collectively, these issues made the contribution of this paper less clear.
Decision: Reject