Venue: ICLR 2022 Conference

Reviews:

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper proposes a generative models for learning over the space of geometric graphs -- those graphs whose nodes are associated with geometric coordinates (point clouds). The point cloud serves as basis for decoding graph structure. This makes the entire system efficient. An extensive suite of experiments on chemical benchmarks (QM9 and ChEBML) show that the proposed method is competitive against state-of-the-art rivals on a variety of measures and tasks.

main_review: Overall this is a well-written paper with clear motivations and description of each model component. The problem of generating geometric graphs is important and the paper demonstrates that the proposed G^3 can leverage both graph structures and the point cloud geometry well. The experiments are extensive and the results are clear with domain-knowledge interpretation.

On the negative side, it looks like many components of G^3 are be studied before, hence reducing the novelty of the paper.
summary_of_the_review: This is a nice paper on an important topic and with a successful proposal evaluated extensively. The novelty may be less than ideal due to the integration of existing ideas.
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final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: The authors propose to combine point cloud and graph encoders with coordinate and feature decoders in order to learn the geometry first, and then try to predict the adjacency matrix of the graph, to obtain a better overall graph representation of the considered applications.

main_review: The paper is clearly written and well motivated, and easy to follow. The network is comprised of multiple parts which are clearly defined and explained.
The numerical experiments indeed show an improvement over other methods, however not in all metrics.

I have a few concerns:
1. If I understand correctly, the authors choose to first learn the geometry, via template folding (as in FoldingNet), and then, once the node features are learned, use a link prediction mechanism to predict the topology of the graph. To the best of my knowledge, the approach of template folding is bound to its original topology (e.g. genus 0), which is limited. It would be beneficial and enriching if the authors can elaborate on this point. Were other methods considered to learning the geometry, and perhaps the authors can state what is the influence of using such template, which in many cases may not fit to the actual topology of the underlying graph.

2.How did the authors choose the link prediction mechanism? In what sense is it different/better than using something like GAT and its variants ?

3.The authors present their results on 2 popular datasets. However, in order to reach to a more conclusive evidence of the importance and contribution of this work, I would suggest the authors to add more applications, such as learning the geometry and topology of meshes (e.g., ModelNet, ShapeNet). Also, the task of protein folding (e.g., AlphaFold) seems to be appropriate for the suggested method.


summary_of_the_review: The authors propose an interesting combination of known methods to learn the geometry and topology of the  graph for molecular-based applications. The results reveal that some improvements over existing method is obtained. Some of the limitation could be further discussed, and more experiments would strengthen the contribution of the paper.
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final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper studies the problem of geometric graph generation (mainly focusing on molecule graph generation). Specifically, the authors propose a new method,  namely Geometric Graph Generator (G3), which generates three-dimensional geometric graphs. Different from others, G3 can capture both the combinatorial and the geometric information of graphs. The proposed algorithm can successfully generate molecule graphs and runs faster than other baseline methods. The key parts of G3 are the point encoder and graph encoder, and the three-step decoding process, that is the coordinate decode, feature decoder, and finally graph decoder.  The experimental results show that G3 has better performance than other generators in terms of validity, uniqueness, and novelty.

main_review: Strengths: The run time of G3 is impressive compared with strong baselines such as  GraphAF and JT-VAE due to the one-shot nature while obtaining as good in quality as these baseline methods. The designed method may be applied to the application of drug discovery, etc.

Weaknesses: The technical contribution is unclear/limited. The comparison (from both the theoretical side and architecture design side) between G3 and other popular baseline methods is missing. It is unclear why G3 is better than others and why it is so efficient but not other methods. How this designed architecture is useful to guide other works? The other concern is the generalization ability of the proposed method since the proposed method was only tested on two datasets.
summary_of_the_review: Overall, the problem studied is interesting. The authors aim at designing new NN architecture to generate geometric graphs. The experimental results look promising. Moreover, G3 is much faster than current strong baseline methods. 

However, the generalization ability of the proposed architecture to other datasets is unknown. The encoding part seems heavily based on other works (similarly decoder parts). Compared with other methods, the reviewer does not see the real novelty part of the technical section. (The problem of graph generation is out of my research area. I may miss something important.)
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final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper is well written and focuses on an interesting problem, to design a better framework for a molecular generation while incorporating 3D geometry, using connections between 3D point clouds and GNNs.
main_review: **Strength**

1. It is true that restoring a graph is challenging. Works [1][2] at the same period tackle it via matching the representations in the latent space instead of defining reconstruction loss on the data space. This paper proposes a different way via separating (or..cascading) 3d and feature decoding processes, whose effectiveness and efficiency are empirically validated.

2. a good integration of previous works, especially connecting generative models in point clouds and molecules.


**Weakness**

1. Link predictor is quite interesting (and overselling), more empirical results and interpretations will be helpful to support the claim of "We highlight that our link predictor works remarkably well as a standalone module for molecules, ..."
2. Unclear when interpreting tables 1 & 2. How to determine the angle directions? In comparisons with all the baselines or a certain subset of baselines (e.g., methods without using hard valency checks)?
3. Table 3 seems not to well support the claim of "It is clear that both ablated models are inferior to G 3 in nearly all molecular metrics, which attests to the efﬁcacy of G 3 ’s overall architecture.", for instance, Validity and Novelty are decreasing when combining both encoders, and so on. More elaborations?

**Comments**

1. What do you mean by the term "large inner product in 3D" (page 5)?
2. It would be helpful to bold the best results in the tables.

**Open Questions**

Not addressing the following comments won't have negative effects on my rating. 
But it would be nice if the authors can make a few clarifications, which also helps with my understandings!
1. explorations on the template design in the coordinate decoder
2. interpretability on the learned geometrical information in the point cloud encoders for molecules (something like [3])
3. a better (analytical/empirical) way to support the claim that geometry and structure are "complementary"? I don't find an inspiring explanation in [1] or in this draft.

**Reference**

1. Pre-training Molecular Graph Representation with 3D Geometry, arXiv 2021
2. 3D Infomax improves GNNs for Molecular Property Prediction, arXiv 2021
3. Unsupervised Point Cloud Pre-Training via Occlusion Completion, ICCV 2021
summary_of_the_review: In general, I like the idea but given the fact a lot of concerns need to be addressed, I tend to give a borderline. 

However, I am willing to adjust my scores based on the reviewer's reply.
review_title: null

Meta-review: This paper presents a generative model for geometric graphs.  The main contribution is to separate the representation and generation of geometry from that of graph structure and features.  Based on this idea the authors assembled a set of existing ideas and built an auto-encoder style generative model for geometric graphs.

This paper sits on the borderline, with reviewers split on both sides.  I appreciate the clarifications from the authors during the rebuttal and the interactions with the reviewers.  The main concern is the novelty of this approach, as the main contribution is the idea of separating geometry from graph structure, and most other components of the pipeline already exist in the literature.  Because of this I think the paper can probably devote a bit more to this ablation study.  In particular the paper currently lacks detail about whether the size of the models were controlled when doing the ablation, which could be a confounding factor that explains why the joint model with both geometry and graph structure works better.  Also the different architecture choices may also factor into the difference, it would be more convincing if for example the same combination of multi-head attention blocks and GINE networks are used for the ablated graph encoder (you can simply concatenate the features from both on all layers, or even at the end).

Based on this I would recommend rejection at this time but encourage the authors to improve the paper and send it to the next venue.
Decision: Reject