Venue: ICLR 2022 Conference

Reviews:

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This work aims at the representation learning of 3D molecular graphs and proposes a principled message passing framework to unify existing works. Besides, a novel message passing approach is presented by incorporating 3D geometric information including distance, angle, and torsion. In experiments, the performance of the proposed model is validated on three benchmark datasets.
main_review: Strengths:
- The idea of incorporating torsion information when representing 3D molecules is novel and helpful. The proposed MP approach can better distinguish certain structures than some existing models. 
- The proposed model performs well on benchmark datasets, which validate the strong expressive power when representing 3D molecules.

Weaknesses:
- The proposed SMP scheme in Eq. (1) lacks novelty since it basically enriches the GN framework in [1] with geometry features.
- I feel that the architecture of the proposed SphereNet is similar to DimeNet [2] except addressing torsion information. The importance and power to embed both distances and angles in 3D molecules have already been addressed by DimeNet. The ways of representing and embedding distances and angles are nearly the same in SphereNet and DimeNet. By comparing Figure 4 in this work and Figure 4 in DimeNet work [2], it's not hard to find the corresponding similarities in their architectures (each row below represents a correspondence):
+---------------+----------------+

|    DimeNet  | SphereNet    |

+---------------+----------------+

| Embedding | Input Block        |

| Interaction | Interaction Block |

| Residual    | Residual              |

| Output      | Output Block         |

+---------------+----------------+


[1] Relational inductive biases, deep learning, and graph networks

[2] Directional message passing for molecular graphs
summary_of_the_review: The main issue of the proposed model is the lack of novelty. Although introducing torsion is helpful when representing 3D molecules, the proposed model doesn't have novel architecture when embedding it as compared to existing models. The proposed framework also just follows the idea of existing work. Thus I think this work is below the acceptance threshold of ICLR.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper provides a novel geometric GNN: SMP. SMP is based on the SCS, and can reduce the complexity by an order of magnitude. Besides, it is a unified framework that can cover some mainstream geometric GNN methods. The empirical results support the effectiveness of SMP.
main_review: 
Strengths:

(1) The SMP introduces an interesting method to alleviate the computation cost issue in SCS from O(nk^3) to O(nk^2). This method is important and can be generalized to more broad types of tasks.

(2) The paper structure, i.e., from motivation to solution, is generally smooth. (Some potential points are listed below).

(3) This is an empirical work, and the experimental results support the effectiveness of SMP.


-----
Weaknesses:

(1) About motivation: Why SMP is better than Cartesian coordinate system (CCS) is not well explained. Authors give an example in Sec 2, but it is a little confusing for me.
1. It says atomic connectivity is based on a cut-off distance and `considering all pairwise distances will lead to severe redundancies`, thus only local distance pairs are considered. But my understanding is the cut-off distance is merely a hyper-parameter, and it can include the H-H bond in the example in Fig 1.
2. SMP alleviates the high computation cost issue when using SCS. However, its computational cost is still quite large, and is larger than the computational cost in CCS given the same cut-off threshold.
3. From my point of view, SMP can better reflect the chirality property where models using pairwise distance cannot. This might be one point authors can try. 

(2) One question about the SMP model.
So SCS takes 3 atoms to define the reference plane. In SMP, it reduces it by introducing an interesting trick. However, I’m not quite sure how to pick the atom q_1 (in Figure b). Will the choice of q_1 have an effect on SMP? I didn’t find it in Sec 3.


(3) Categories in related work.
About the categories, I’m not sure why authors split the existing works into EGNN and relative information. From my understanding, models like SE(3)-Trans and EGNN are also using relative distance.



-----
Minor:

(1) Typo in Intro: `... relative location of each atom in a 3D graph … `

(2) In Intro, the authors say that `integrating the SMP and physical solutions to the Schrodinger equation`, can authors further explain what this means?

summary_of_the_review: This paper is generally good, in terms of story-telling, method description, and technical novelty.
There are three main concerns: motivation/example, model description, and related work. This work can be further polished after fixing these points.

-----

After checking the replies from the authors and polished-up version of the paper, most concerns on the story have been addressed. I would like to raise the score to 8.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper proposes a message passing scheme using spherical coordinates. It is tested on three datasets of 3D moleclular graphs. The paper offer an in depth analysis of different aspects, with an extensive experimentation of the method.
main_review: As a premise, I am not an expert of molecular studies; in my review, I will focus on the technical and geometrical perspective, but I cannot assess the relevance of the method\results for the biology community.

==STRENGTHS==

ANALYSIS & REPLICABILITY
The experiments investigate different aspects of the method, providing insights on performance vs efficiency, ablation of used schema, and all the details of experimental setups and implementation. I think the paper can be replicable, and the claims are motivated.

NOVELTY
To my best knowledge, the idea is novel. While message passing methods on graphs exploit only the connectivity, this work shows an interesting method to include the embedding information in the case of geometrical graphs. On this point, however, I would suggest a better contextualization. Geometrical graphs are well explained in this book [1], and other works propose methods to exploit such geometrical prior (e.g., [2]). I would consider this in the related work section.

==WEAKNESSES==

COMPARISONS
The majority of the results are taken from other papers without re-running the experiments. I think this could be ok, but it is not completely clear if the split of training\val\test is preserved across the works (i.e., they are given by dataset) or if each method uses its own. I think it would be good to provide an average across multiple runs or reimplement at least the more recent competitors in this second case.

APPLICABILITY
The method explicitly addresses a specific domain, and I am not sure that it could be exported to other ones, e.g., meshes. How would it perform on geometrical graphs with thousands of nodes? The paper left such question for future works, but I think at least a computational timing on different domains would be useful to understand which kind of interest\impact it could receive in ICLR audience. I am not from the biological field, and I do not get the dimensions of the considered graphs (but being molecules, I assume that the order of magnitude is tens of nodes, is it correct?)

[1]: Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges; Bronstein et al., 2021
[2]: Gauge Equivariant Mesh CNNs Anisotropic convolutions on geometric graphs; Haan et al., 2020

summary_of_the_review: While I am not sure that the method can be applied in other contexts, I think the idea is valuable, and the experiments are convincing, and I am prone to accept the paper.
review_title: null

Meta-review: The paper considers representation learning of 3D molecular graphs.
The authors propose a message passing scheme using spherical coordinates. It is
tested on three datasets of 3D moleclular graphs. The authors offer an in depth
analysis of different aspects, with an extensive experimentation of the method.

Strengths:

- The SMP introduces an interesting method to alleviate the computation cost issue in SCS from O(nk^3) to O(nk^2). This method is important and can be generalized to more broad types of tasks.
- This is an empirical work, and the experimental results support the effectiveness of SMP.
- The proposed MP approach can better distinguish certain structures than some existing models.
- Incorporating torsion information when representing 3D molecules is novel and helpful
- While message passing methods on graphs exploit only the connectivity, this work shows an interesting method to include the embedding information in the case of geometrical graphs.

Weaknesses:

- The proposed SMP scheme in Eq. (1) lacks novelty since it basically enriches the GN framework in [1] with geometry features
- the architecture of the proposed SphereNet is similar to DimeNet
- Why SMP is better than Cartesian coordinate system (CCS) is not well explained.

Overall, a majority of reviewers are in favor of acceptance and a third reviewer is happy with either acceptance or rejection and does not give strong reasons for rejecting the paper. My recommendation is, therefore, acceptance. I recommend the authors use the reviewers comments to improve the paper for its camera-ready version.
Decision: Accept (Poster)