Molecule Joint Auto-Encoding: Trajectory Pretraining with 2D and 3D Diffusion

Recently, artificial intelligence for drug discovery has raised increasing interest in both machine learning and chemistry domains. The fundamental building block for drug discovery is molecule geometry and thus, the molecule's geometrical representation is the main bottleneck to better utilize machine learning techniques for drug discovery. In this work, we propose a pretraining method for molecule joint auto-encoding (MoleculeJAE). MoleculeJAE can learn both the 2D bond (topology) and 3D conformation (geometry) information, and a diffusion process model is applied to mimic the augmented trajectories of such two modalities, based on which, MoleculeJAE will learn the inherent chemical structure in a self-supervised manner. Thus, the pretrained geometrical representation in MoleculeJAE is expected to benefit downstream geometry-related tasks. Empirically, MoleculeJAE proves its effectiveness by reaching state-of-the-art performance on 15 out of 20 tasks by comparing it with 12 competitive baselines.

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Peer review

Reviewer oitq5/10 · confidence 3/52023-06-24

Summary

The paper introduces a pretraining method for molecule joint auto-encoding (MoleculeJAE) for 2D molecular topology and 3D molecular geometry. Their approach adopts SE(3) symmetry and is trained by fitting the joint distribution of the trajectories from the forward process of the diffusion model. The authors treat the 2D molecular structure and 3D geometry as continuous objects, which are perturbed by Gaussian noise in the diffusion process. Unlike traditional diffusion models that denoise data by marginal distribution modeling, their 'auto-encoding' approach focuses on learning the joint distribution of data pair $(x_0, x_t)$. The overall task is then optimized by two objective functions, including a reconstruction loss and a contrastive loss, as well as a surrogate model. Experimentally, MoleculeJAE is pre-trained on the PCQM4Mv2 dataset and is used to perform downstream tasks on QM9 and MD17 datasets. The experimental results are competitive on property prediction and dynamics prediction tasks. Overall, this work is well-motivated and novel, with a theoretical justification for their approach. This paper presents good quality work.

Strengths

First of all, this work is well-motivated, as jointly learning 2D and 3D molecular representations by diffusion models is still at the stage of development. MoleculeJAE can learn both 2D bond topology and 3D conformation geometry information and is designed to respect the SE(3) symmetry of molecule data and is trained by fitting the joint distribution of the data’s augmented trajectories extracted from the forward process of the diffusion model. It is also novel that the joint 2D and 3D learning of diffusion models is trained in a self-supervised learning manner and optimized by a contrastive learning objective function. MoleculeJAE unifies both contrastive and generative learning approaches from a trajectory perspective, providing a versatile and powerful molecular representation that can be applied to various downstream applications. Unlike traditional diffusion modeling, MoleculeJAE uses a contrastive learning paradigm to fit the trajectory of pairwise molecules, while also utilizing the reconstructive task to perform denoising for each individual molecule. By using contrastive learning, it allows the model to align the augmented views of the same data and simultaneously contrast the augmented views of different data. Also, ablation studies show the importance to have a contrastive loss in the task.

Weaknesses

For methodology, the authors treat the 2D graph topology as a continuous object that is perturbed by Gaussian noise. I understand it is easier and reasonable to put the three things, atom features, bonds, and coordinates, under a single SDE framework. However, following previous works [1][2], describing the 2D graph topology as a discrete object with a discrete diffusion process is more reasonable, and their models show superior results. Experimentally, MoleculeJAE shows better results with only small margins. However, the authors do not compare the number of model parameters, the overall training time, and the error bars (standard deviation) with existing methods, so it is unclear to me how well MoleculeJAE surpasses those methods. [1] Vignac, Clement, et al. "DiGress: Discrete Denoising diffusion for graph generation." arXiv preprint arXiv:2209.14734 (2022). [2] Hua, Chenqing, et al. "MUDiff: Unified Diffusion for Complete Molecule Generation." arXiv preprint arXiv:2304.14621 (2023).

Questions

1. Jointly learning 2D and 3D molecular data is not completely underdeveloped. Previous works on diffusion models, [1][2], have shown that diffusion models can be used to learn 2D and 3D latent molecular representations effectively jointly. They perform better on molecular generation tasks than single-modal diffusion models, and it is proper to cite these works and mention the difference. 2. I wonder if the authors consider extending this auto-encoding framework to discrete graph topology, as a discrete representation and diffusion process is more reasonable for graph-like objects. If not, I would like to hear the reason. 3. I would like to see the error bars (standard deviation), the number of model parameters, and the total training time compared with different methods. [1] Hua, Chenqing, et al. "MUDiff: Unified Diffusion for Complete Molecule Generation." arXiv preprint arXiv:2304.14621 (2023). [2] Vignac, Clement, et al. "Midi: Mixed graph and 3d denoising diffusion for molecule generation." arXiv preprint arXiv:2302.09048 (2023). Typo: 1. Line 257, the log-likelihood logp is also achieves $\rightarrow$ the log-likelihood logp also achieves

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

N/A

Reviewer s6Nt6/10 · confidence 4/52023-07-06

Summary

The paper proposes MoleculeJAE, an auto-encoder for both 2D and 3D molecule diffusion trajectories. The model learns the trajectories jointly in a self-supervised manner. Empirically, MoleculeJAE achieves competitive results on property and force prediction benchmarks.

Strengths

The joint diffusion of 2D and 3D is novel. It is widely concerned that point cloud diffusion is less aware of 2D information. I admire the authors' contribution to this problem. I would also thank the authors for providing a detailed theoretical analysis.

Weaknesses

1. I did not really get the motivation of modeling diffusion trajectories. Personally, I think the intermediate states are less informative than x_0. Could you please further explain your idea, and provide some additional ablation results if possible, for it seems that the current ablation study shows that the role of the contrastive loss is not very significant in many cases? Thanks. 2. I believe the baselines of QM9 experiments are not state-of-the-art. Please consider this work: https://openreview.net/forum?id=tYIMtogyee

Questions

There is another work that introduced timestep embeddings in their diffusion process: https://ojs.aaai.org/index.php/AAAI/article/view/25639/25411 What are the advantages of contrastive learning?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

N/A

Reviewer fgxq5/10 · confidence 3/52023-07-07

Summary

This paper proposes a new representation learning method for molecules using 2D and 3D structures. The joint distribution between original molecules and augmented molecules is decomposed into reconstructive and contrastive tasks. The proposed model, MolecularJAE, simultaneously tackles both tasks with the help of SE(3) equivariant GNN models. MolecularJAE is evaluated on quantum property prediction and molecular dynamics prediction and achieves a competitive result against baseline models.

Strengths

- Diffusion over two different modalities hasn't been explored as far as I know. - The decomposition of joint distribution into reconstructive and contrastive tasks is new and interesting.

Weaknesses

- It is known that the 3D structure of a molecule follows certain physical rules. The diffusion process used in this paper does not account for the prior knowledge from the domain. - The performance of the proposed model is worse than some recently proposed models, which hasn't been included in the experiment section. For example, the performance of Equiformer[1] and PaiNN[2] on QM9 is better than the proposed model across almost all tasks. - The presentation of this paper can be improved further. For example, Figure 1 does not provide any meaningful information to readers. Figure 2 is also difficult to digest. Polishing these figures with additional details and proper explanations would improve the accessibility of the manuscript. - There are too many typos throughout the main text and appendix. [1] Liao, Yi-Lun, and Tess Smidt. "Equiformer: Equivariant graph attention transformer for 3d atomistic graphs." ICLR 2023. [2] Schütt, Kristof, Oliver Unke, and Michael Gastegger. "Equivariant message passing for the prediction of tensorial properties and molecular spectra." ICML 2021.

Questions

- Why does the energy function formulation (Eq 7) reformulate the maximum likelihood estimator to the one above line 196, even though the normalizing constant depends on theta? - The reconstructive task with score matching is advertised as a tool for generating new samples (line 222). Are there any experiments on the generative perspective? Given that the gain from the contrastive task is not significant in the experiments, the score-matching model seems well modeling the underlying distribution of graphs.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

I couldn't find any negative societal impact.

Authorsrebuttal2023-08-16

Gentle Reminder

Hope this message finds you well. We have carefully addressed your questions and have incorporated additional generative experiments (in the general response) based on your valuable advice. We are eager to know if our response has effectively addressed the concerns you raised in your initial review. Should you need further clarification or have any additional points you would like us to consider, please do not hesitate to share your thoughts. We are committed to ensuring that all your concerns are fully addressed. Thanks!

Reviewer fgxq2023-08-17

I appreciate your comprehensive response regarding my questions and concerns. Based on the rebuttal, I think my biggest concern about the paper on the experimental performance has been properly addressed. I hope the authors add the new results with missing details to the revised manuscript to make it more concrete. In this regard, I am happy to raise my original score.

Authorsrebuttal2023-08-17

Thanks

We sincerely appreciate your time and effort in re-evaluating our work. We will make the suggested revisions as promised in our updated manuscript.

Reviewer LUAH6/10 · confidence 3/52023-07-07

Summary

The authors propose an auto-encoding method for learning molecular embeddings from both 3D and 2D information jointly. The method is loosely related to diffusion methods in that embeddings of data augmentation trajectories are learned via a score-based reconstruction loss and contrastive loss. The embeddings give SOTA performance on a number of QM and activity prediction tasks.

Strengths

### Originality The method is original in that it encodes both 3D and 2D molecular information via learning to embed data augmentation trajectories. ### Quality The results indicate that the resulting embeddings are SOTA. ### Clarity The paper could be made much clearer (see Weaknesses). ### Significance Optimal molecular embeddings are a perennial desire for all kinds of downstream molecular tasks. The SOTA performance of these embeddings suggests that this method represents a significant contribution.

Weaknesses

- Section 2 Background is a meandering presentation of a number of related ideas, some of which are not immediately relevant for the main paper. Those should be moved to the appendix, and the remainder should be made much crisper so that it is clear to the reader how the remaining sections will proceed. - the unnumbered equation after Eq. 4 is missing an $e_m$. - It is not at all clear what data augmentations are used in this paper. E.g. what are $\mu_1$ and $\mu_2$ in Eq. 6? - The presentation of the MLE in Section 3.2 is unnecessarily confusing. There is no need to introduce energy-based models, Eq. 9 can be derived without the energy functions. Note that the energy functions are never referred to again. The only thing is the surrogate gaussian KDE, but again that does not need to be motivated by energy functions. Typos: - The statement $E_θ(x0) = \log q_θ(x_0)$ is incorrect since it is missing a $\log Z_\theta$. - Most of the score expressions in section 3.2 are missing a $\log$.

Questions

- The unnumbered equation after Eq. 5 does not make sense - how does one apply a rigid transformation to time t? - How are the results in Tables 1 and 2 obtained? What model is trained on the learned embeddings? - What is the intuition behind this entire paper? Why does embedding a trajectory give better performance than embedding just the stationary data? How do these results depend on the choice of trajectories?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

Some limitations are addressed in the appendix.

Authorsrebuttal2023-08-18

A Kind Reminder

I hope this message finds you in good health. I wanted to take a moment to express our sincere gratitude for your positive evaluation of the novelty and methodology of our paper, as well as your insightful suggestions for improving our presentation. Your feedback has been invaluable, not only in addressing critical typos that play a crucial role in ensuring readers' understanding of our method, but also in shaping the overall organization of our revisions. We have carefully considered your feedback and have made efforts to address the concerns you raised. As we approach the conclusion of the discussion period, we are eager to ensure that our response effectively addresses your concerns and aligns with your expectations. If there are any lingering questions or if you require further clarification on any aspect of our work, please don't hesitate to reach out to us. We are committed to ensuring that your concerns are fully addressed before the deadline.

Reviewer s6Nt2023-08-11

Thank the authors for the rebuttal

I think my concerns are well-clarified by the authors. I am updating my rating from 4 to 6.

Reviewer oitq2023-08-14

Response by Reviewer

I thank the authors for their response. I will keep my score for a borderline accept. I hope the authors can properly cite and mention [1][2] in their revised version. [1] Hua, Chenqing, et al. "MUDiff: Unified Diffusion for Complete Molecule Generation." [2] Vignac, Clement, et al. "Midi: Mixed graph and 3d denoising diffusion for molecule generation."

Authorsrebuttal2023-08-14

Response from authors

Thank you for your feedback and for taking the time to consider our revisions. As we still have time within the discussion period, if there are particular aspects of our paper that you feel we should concentrate on or enhance further, we are willing to incorporate your further suggestions.

Authorsrebuttal2023-08-21

A simple update

Following the reviewer's suggestion, we update the **Lumo** downstream task for our supplementary Painn pretraining model (missed in the last period of experiment due to GPU shortage): | Model | Lumo | | ---- | ---- | | no-pretraining | 20.16 | | Distance Prediction | 18.26 | | 3D InfoGraph | 20.16 | |GeoSSL-EBM-NCE | 17.89 | |3D InfoMax | 17.69 | |GraphMVP | 17.02 | | GeoSSL-DDM | 16.95 | | 3D-EMGP | 23.99 | |**Molecule-JAE** | **16.89** |

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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