Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 8: Accept
review_content: 
The paper presents DeepSphere, a method for learning over spherical data via a graphical representation and graph-convolutions. The primary goal is to develop a method that encodes equivariance to rotations, cheaply. The graph is formed by sampling the surface of the sphere and connecting neighbors according to a distance-based similarity measure. The equivariance of the representation is demonstrated empirically and theoretical background on its convergence properties are shown. DeepSphere is then demonstrated on several problems as well as shown how it applies to non-uniform data.

The paper is interesting and clear. The projection of structured data to graphical representations is both efficient in utilizing existing algorithmic techniques for graph convolutions and useful for approaching the spherical structure of the data. The theoretical analysis and discussion of sampling is interesting, though should be more clearly stated throughout and potentially visualized in figures.

The experiments performed are thorough and interesting. The approach both outperforms baselines in inference time and accuracy. However, one wonders the performance on the well-researched tasks such as the performance on 3D imagery, e.g., Su & Grauman, 2017; Coors et al., 2018. 

The unevenly sampled data is a nice extension showing the generality of the approach. How does the approach work for data connected within a radius rather than a k-nearest approach?

Minor:
- A figure detailing the parameters and setup for theorem 3.1 and figure 2 would be useful.
- The statement on the dispersion of the sampling sequence states “the smallest ball in \R^3 containing \sigma_i”, but I believe it should be “containing only \sigma_i”.
review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: The paper studies the problem of designing a convolution for a spherical neural network. The authors use the existing graph CNN formulation and a pooling strategy that exploits hierarchical pixelations of the sphere to learn from the discretized sphere. The main idea is to model the discretized sphere as a graph of connected pixels: the length of the shortest path between two pixels is an approximation of the geodesic distance between them. To show the computational efficiency, sampling flexibility and rotation equivariance, extensive experiments are conducted, including 3D object recognition, cosmological mode classification, climate event segmentation and uneven sampling.
Pros: 
1. The application and combination of different techniques in this paper are smart.
2. The experiments show that the proposed method outperforms other baseline methods.
3. The paper is well organized and written. 
Cons:
1. It is a good application of known techniques, but the novelty is limited.
2. It is suggested to add more baselines in the experiments.

[1] Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In Advances in Neural Information ProcessingSystems, 2016
review_title: Official Blind Review #3

final_score: rating: 6: Weak Accept
review_content: In this paper, CNNs specialized for spherical data are studied. The proposed architecture is a combination of existing frameworks based on the discretization of a sphere as a graph. As a main result, the paper shows a convergence result, which is related to the rotation equivalence on a sphere. The experiments show the proposed model achieves a good tradeoff between the prediction performance and the computational cost. 

Although the theoretical result is not strong enough, the empirical results show the proposed approach is promising. Therefore I vote for acceptance. 

The paper is overall clearly written. It is nice that the authors try to mitigate from overclaiming of the analysis. 

As a non-expert of spherical CNN, I don't understand clearly the gap between the result Theorem 3.1 and showing the rotation equivalence. It would be nice to add some counterexample (i.e., in what situation the proposed approach does not have rotational equivalence while Theorem 3.1 holds).
review_title: Official Blind Review #1

Meta-review: This paper proposes a novel methodology for applying convolutional networks to spherical data through a graph-based discretization.   The reviewers all found the methodology sensible and the experiments convincing.  A common concern of the reviewers was the amount of novelty in the approach, as in it involves the combination of established methods, but ultimately they found that the empirical performance compared to baselines outweighed this.
Decision: Accept (Spotlight)