Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: The authors study the molecule representation problem from a novel aspect based on the surface Riemannian manifold. Specifically, the authors adopt the Shape-DNA techniques to obtain surface representation and propose the information aggregation for the surface. The authors further design the frameworks for molecular property prediction and binding prediction.
strength_and_weaknesses: 
### Strengths

(+) The studied problem of the “shape-activity” relationship as an alternative to the “structure-activity” relationship is interesting and can provide some insights into understanding the system.

(+) The proposed method itself, including surface representation and information aggregation, is interesting and novel for geometric graph learning. I’m sure it can also be applied to many other scenarios than molecules.

(+) The proposed rigid protein docking framework has additional technical contributions.

### Weaknesses

(-) The use of surface only is not well-motivated nor justified. Although the authors claim that “molecular surface displays chemical and geometric patterns which fingerprint a protein’s mode of interactions with other biomolecules”, some analysis or empirical results are needed to justify the claim and make the proposed surface representation more convincing. Moreover, I agree that the surface may be important for binding problems to some degree, but the claim “this possibly explains the success of predicting these properties using only molecular surface information, since the surface is approximately an isosurface of the molecular electron density field” is not convincing enough and may need additional justifications.

(-) Current experimental results are not convincing enough to show the significance and effectiveness of the proposed methods. The experimental results on QM9 do not show a significant improvement to the baselines (some are worse). It indicates the practical application of the proposed method may be limited to only a few specific tasks. For the binding task, the EquiDock can be a relatively weak baseline. The authors may want to include stronger baselines such as EquiBind [1].

(-) There is a lack of details or comparisons on the method's computation complexity in terms of runtime and memory cost. Also, it would be better if the authors include results on how increasing the dimensions (surface resolution) can improve the performance and increase the computation cost.

[1] Stark et al. EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. ICML 2022.

clarity,_quality,_novelty_and_reproducibility: Clarity: the paper is overall well-written, and the descriptions of methods are clear.

Quality: Some statements regarding the motivation for using surface representations are not fully justified.

Novelty: the idea and methods are novel.
summary_of_the_review: Overall I like the idea in this paper. Using representation and message passing of surface is a pretty natural approach to the binding problem. The proposed idea is novel. However, there are concerns that some important claims are not fully justified and experimental results are not strong enough.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper develops a harmonic representation of a molecular surface using the Laplace-Beltrami eigenfunctions. The approach is applied to predict the properties of small molecules and predict the docking pose of proteins.
strength_and_weaknesses: Strengths:
- The Laplace-Beltrami operator as a harmonic filter provides a principled approach to encode interactions at different resolutions of molecular surfaces.
- The model outperforms EquiDock in the protein rigid docking task. 

Weaknesses:
- The comparison with GNN baselines is not very informative. It is well-known that molecular surface representation captures very different information compared with GNNs. The HMR also uses surface geometry features and chemical features which are not present in the GNN baselines. It is not surprising that HMR can outperform the GNN based EquiDock baseline due to the additional information. I think comparing it with another protein-surface representation baseline like MaSIF [Gainza et al., Nature Methods 17.2 (2020): 184-192.] or Multi-Scale Protein Representation [Somnath et al., NeurIPS 2021] is needed to demonstrate the usefulness of this new molecular surface representation approach.
- In Table 2, the runtime of the HMR approach is not reported. The key advantage of EquiDock is its significantly faster inference compared conventional docking software. The surface construction might be slow for the HMR method. How does the inference time compare with EquiDock, Attract, and Hdock?

clarity,_quality,_novelty_and_reproducibility: The paper is well-motivated and the technical part is clear and easy to follow. The experiments are not designed properly to evaluate the surface representation approach. I am not an expert in protein surface representation, but the approach is novel to the extent of the reviewer’s knowledge. The authors provide code in the supplementary material to reproduce their results.
summary_of_the_review: In summary, this paper develops a novel harmonic representation of the molecular surface and applies the approach to two tasks: QM9 and protein rigid docking. Despite the potential improvement in the rigid docking task, the HMR approach may benefit from the additional geometric and chemical features in the surface representation. Comparing it to another surface representation baseline which encodes the same information is needed to demonstrate the advantage of the harmonic representation from the reviewer’s perspective.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper proposes propose a Harmonic Molecular Representation learning (HMR) framework,which offers a multi-resolution representation of molecular geometric and chemical properties on 2D Riemannian manifold. In order to realize efficient spectral message passing over the surface manifold for better molecular encoding, a harmonic message passing method is proposed. The proposed method outperforms the state-of-the-art deep learning models for the rigid protein docking challenge, and shows comparable predictive power to current models in small molecule property prediction tasks.
strength_and_weaknesses: The paper addresses an important problem of encoding 3D molecular structures in deep neural networks. The paper is well written and the proposed methods are examined in various tasks.

Some parts of the presentation can be improved and additional results can be provided as suggested below.
clarity,_quality,_novelty_and_reproducibility: The paper is well-written in general. However, some figures are not clear. For instance, the notation given in the figures should be defined clearly in the captions or the figures should be given as the notations are defined.

In the analyses, the proposed method outperforms various state-of-the-art. Could you please also elaborate dynamics of networks by analyzing learning curves obtained during training? Do you also follow a particular recipe while designing network architectures? An ablation study of different networks and optimizers can highlight network dynamics as well.

summary_of_the_review: The paper is well written in general, and the proposed method was examined in comparison with state-of-the-art in various experimental analyses.

The recommended updates can improve presentation of the paper and elucidate dynamics of the proposed learning methods and networks.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper proposes a framework to learn Riemannian manifold representation using harmonic message passing. To this end, the authors (1) pre-process molecules (or macromolecules like proteins) as a surface function using triangulation, (2) decompose the surface function into components with LB eigenfunctions and coefficients, and (3) perform spectral message passing between the component-wise features. Importantly, the proposed harmonic message passing is motivated by the interpretation of heat diffusion as a message passing between surface regions (LB eigenfunctions and coefficient) with different temperatures (eigenvalues). The proposed methodology is applied for molecular property prediction, binding site prediction, and rigid docking simulation. The empirical results are promising and competitive with respect to the recently proposed molecular representation learning algorithms. 
strength_and_weaknesses: Strength. 

This paper proposes a novel molecular representation learning framework inspired by molecular surface representation and harmonic analysis. To my knowledge, various geometric deep learning works have focused on message passing between mesh vertices rather than the surface regions (LB eigenfunctions). If my knowledge is correct, I believe this work to be quite significant. 

I also appreciate how the experiments are done on both molecules & proteins with various tasks (molecular property prediction, binding site prediction, rigid docking simulation). This makes the empirical benefit of the proposed method convincing.

The proposed method looks quite scalable, so I think this method might be potentially useful in large-scale scenario where computation time is important.

Weakness. 

In the experiments, it is not clear whether if the complexity of preprocessing molecular surface is considered. I find this confusing since the EquiDock authors mentioned how they avoided molecular surface preprocessing due to high complexity. 

The experimental results for molecular property prediction is not exactly state-of-the-art, but I think this is fine given novelty of the work. Nevertheless, I suggest comparing with more recent works like "Geometric and physical quantities improve e(3) equivariant message passing, ICLR 2022" for molecular property prediction (QM9) for completeness of the paper.

I think clarity the description of harmonic message passing could be improved. For example, the input and the output of harmonic message passing is expressed as a function. However, to my understanding, the features being actually updated correspond to different coefficients for the LB eigenfunctions. I think the matrix representation of the function operator (Fig 3) should be described in the text. Also, the symbols in Fig 3 has no corresponding explanation, e.g., what is $\Phi$? 

The authors claim this method to be scalable to large scale molecules and proteins. However, although the logic is convincing, the authors do not design any experiements to support this fact. When HMP is compared to Equidock in term of preprocessing + inference time, is it faster?

(minor) I find that the experimental setting differs from Equidock. Could you explain the reasoning behind this?



clarity,_quality,_novelty_and_reproducibility: Clarity: While I was able to understand this paper (despite being new to LB eigenfunctions), I think the clarity is suboptimal (see weakness). 

Quality: I found it convincing for the method to be potentially impactful for molecular representation learning. However, empirical evaluation is could be improved to enough to support this fact. 

Novelty: I am aware of existing works on spectral graph convolution between point cloud, graph, and mesh representation of molecules/proteins. However, The idea of harmonic message passing between LB eigenfunctions is very new to me. If this is truly novel, I believe the novelty of this work is very strong.

summary_of_the_review: This paper proposes a very novel idea for molecular representation learning. While the experiments could be slightly improved, I think this paper is potentially very impactful and interesting for molecular representation learning community
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: The paper uses spectral geometry techniques (that are common in the CG community) for molecular tasks, such as small molecule property prediction and protein docking. The reviewers appreciated the paper, and the authors provided an extensive rebuttal. 
We recommend accepting. 

justification_for_why_not_higher_score: paper is based on techniques well-known in other field 
justification_for_why_not_lower_score: sufficiently interesting application and novelty for ML community
Decision: Accept: poster