MoleBridge: Synthetic Space Projecting with Discrete Markov Bridges

Dear reviewer,

We sincerely appreciate your thoughtful and constructive feedback. Thank you for your positive assessment of our work! We now address the raised questions as follows.

---

W: No comparison to previous methods in other experimental settings (SBDD and Target-directed).

We sincerely appreciate this valuable suggestion. However, we would like to clarify that we actually compared previous methods in the SBDD and target-directed settings, and the results included in the supplementary materials. This may have been overlooked because we did not highlight the results sufficiently in the main text, and we apologize for that. We appreciate your insightful comments. Thank you once again for your valuable time!

Q1: Building block tokens have an extremely large vocabulary size and it is predicted as fingerprints, so Markov Bridge cannot be applied to fingerprints? What do the authors think the contributions of building block tokens to the error accumulation? Are errors in reaction tokens more detrimental?

Thank you for raising this question. We clarify that the Markov Bridge can be applied to building blocks, although there are still further improvements required in our current implementation. However, we agree that the larger vocabulary size of building block tokens indeed presents technical challenges for the direct application of the Markov Bridge. In contrast, the Markov Bridge performs better in lower-dimensional discrete spaces. For instance, it has been successfully applied in protein modeling with only 20 amino acids [1]. Of course, considering that there is still room for improvement in the discrete Markov Bridge, we also hope to further design more advanced modeling techniques. We will further consider the contributions to this specific modeling aspect.

We have analyzed 7314 cases and found that 1178 cases of pathway errors were caused by building blocks, which is indeed a significant proportion. Therefore, it is also essential to address this issue. However, given the recent significant progress in guided model learning, we acknowledge that there are also better potential solutions to this issue. We will further discuss this in response to your next question (Q2). Thank you again for your invaluable suggestions.

Q2: For future work, what do the authors think about the potential solution to implementing error correction on building blocks?

To further optimize the issue of error correction in building blocks, we propose three better potential solutions.

• First, fingerprints are essentially "encodings," which we believe are not a complete representation of the molecule but a form of information compression. If their length is too large, they even tend to cause more information loss. The Markov Bridge faces the issue of large fingerprint dimensions in its modeling process. We can draw on advanced theories from information compression to optimize its encoding process, thus generating more informative yet easier-to-handle low-dimensional representations.

• Second, inspired by guided training methods in LLMs, we could introduce erroneous blocks as random noise in the training data, which might help the model learn erroneous patterns, potentially improving robustness to building block errors.

• Third, akin to the second approach, during inference, we could design highly reliable reference templates for comparison to evaluate the model's performance, helping it identify modeling flaws and potentially serving as a correction strategy.

Of course, these are just our preliminary technical ideas. Thank you again for your valuable professional feedback!

---

Thank you once again for your thoughtful and positive review!

Best wishes,

All authors of Paper 1834.

[1] Yiheng Zhu, Jialu Wu, Qiuyi Li, Jiahuan Yan, Mingze Yin, Wei Wu, Mingyang Li, Jieping Ye, Zheng Wang, Jian Wu: Bridge-IF: Learning Inverse Protein Folding with Markov Bridges. NeurIPS 2024

Dear reviewer,

We sincerely appreciate the time you have taken to review our work and your positive comments about our paper! We aim to address your questions below.

---

W1: Some more discussion on the chemistry aspects of MCSP. Is there a way to add temperature/pH dependence into your reaction templates?

Thank you for the insightful suggestions! We completely agree that many chemical reactions are often dependent on specific experimental conditions and additional reagents. Different experimental conditions, such as the temperature and pH you mentioned, can indeed lead to enantiomers. However, our Markov Bridge framework is highly scalable, allowing for the integration of additional constraints and prior knowledge, offering flexibility for modeling conditional dependencies, and thus can accommodate the expansion requirements for such settings. For instance, after obtaining a dataset containing condition information such as temperature and pH, the most direct approach would be to integrate these conditions as additional context into the neural network inference process. We believe this is a technically feasible extension. The primary limitation at present is the absence of high-quality datasets containing this kind of data. We look forward to future contributions from the community in providing data resources that include detailed reaction condition information.

We believe that drawing from recent advancements in contrastive learning techniques could also be a promising solution. Contrastive learning works by minimizing the distance between positive sample pairs and maximizing the distance between negative pairs, allowing for the learning of more discriminative molecular embeddings, which is useful for distinguishing enantiomers that have similar structures but different chemical properties.

Additionally, your observation about the influence of molecular fingerprint choice on the results is highly insightful. We believe that molecular fingerprints are essentially vector hash representations of atomic connections, local environments, paths, and other features. Regardless of the method employed, molecular fingerprints serve as encoding systems that compress a subset of the overall molecular information. We acknowledge that any molecular fingerprint systems inherently introduce some information loss. Our molecular fingerprint method iteratively updates the encoding for each atom, combining its characteristics with those of neighboring atoms, thus integrating the local environmental context of the atoms. This design allows for capturing specific substructures and local chemical environments in the molecule [1], providing molecules with similar structures whenever possible, which alleviates the issue of enantiomer differentiation to some extent. However, we also acknowledge that the current methods still require further development and optimization. Ideally, we hope that in the future, a universal encoding system can be developed that both encompasses complete molecular information and adapts to various application scenarios, including deep learning.

W2 and Q1: How does varying the group size affect the performance of your model?

We conduct a sensitivity experiment on the group size, keeping other experimental conditions constant while changing only the group size. The results are shown in the table below. When the size is 1, the model generates tokens one by one, which is formally equivalent to an autoregressive model. However, it shows that the performance is worse compared to when the block size is 4. With a size of 6, performance slightly decreases again. This indicates that too large a size reduces the ability to model semantic dependencies, leading to limited gains. Therefore, we recommend setting the optimal size to 4.

Q2, Q3 and Q4: Notations.

We sincerely appreciate your thorough review of our paper and your careful examination of the mathematical details! We deeply apologize for the notation representation errors that appeared in the paper. Your understanding of the meaning of these notations is correct. We will correct all the notation issues you pointed out in the revised version. Thank you once again for bringing these issues to our attention!

Q5: Equation 9 is not the actual transition probability.

We appreciate you pointing out this issue! Equation 9 actually defines the approximation process of the Markov Bridge. When $v_\tau$ = 1, in the Markov Bridge, the forward transfer process can be equivalently expressed as $(1-\beta_\tau)y^c+\beta_\tau t_\tau^c$. This approximation process is its reverse operation. To clarify, we will revise this claim.

Q6: The callout to Proteína seems quite unnecessary, especially because it is a protein generative model, not a small molecule generative model.

Thank you for your valuable insight. We find your perspective very reasonable. After your suggestion, we realized that citing the protein generation model here is indeed inappropriate. We will follow your advice and remove the inappropriate reference to Proteína in the revised version, refocusing on the challenges of synthesizability in small molecule design. We will highlight the enormous waste of development resources caused by designing non-synthesizable molecules.

Q7: I feel like the first part of the title “Semi-autoregressive Your Bridge” is a little ill-formed and unclear.

Thank you for your valuable feedback. We acknowledge that there is a lack of clarity in the title. If possible, we will remove "Semi-autoregressive Your Bridge" and revise the title according to your feedback. Once again, we sincerely thank you for your highly valuable feedback!

---

Thank you again for your constructive feedback! Your feedback has been very helpful in improving our paper, and I believe you are a very responsible reviewer.

Best wishes,

All authors of Paper 1834.

[1] Jiatong Li, Yunqing Liu, Wenqi Fan, Xiao-Yong Wei, Hui Liu, Jiliang Tang, Qing Li: Empowering Molecule Discovery for Molecule-Caption Translation With Large Language Models: A ChatGPT Perspective. IEEE Trans. Knowl. Data Eng 2024

Dear reviewer,

Thanks for your further valuable feedback. Here, we provide an explanation. Considering the existence of very short synthesis pathways, larger groups limit the model's ability to capture local causal dependencies. In this case, such extensive modeling may be unnecessary for inferring these synthesis pathways. Hence, larger groups result in more potential states, which can lead to convergence difficulties, thereby affecting the model's performance.

We sincerely appreciate your insightful and constructive comments, which have significantly enhanced the overall quality of our paper.

Best wishes,

All authors of Paper 1834.

Dear reviewer,

We are grateful for your valuable suggestions! Our detailed responses to the concerns are provided below.

---

W1: The author could also discuss some earlier methods, such as JT-VAE, that also generate molecule graphs by sub-parts.

Thank you for sharing this paper. JT-VAE primarily involves continuous embedding and generation of molecular graphs, recursively constructing them through chemical substructures, with the aim of automating molecular design based on specific chemical properties [1]. It serves as a foundational work in the field of molecular research. Specifically, their junction tree variational autoencoder generates molecular graphs in two phases: first by creating a tree-structured scaffold over chemical substructures, and then combining them into a molecule using a graph message passing network. This is an excellent method for graph generation. We recognize the important contributions of methods such as JT-VAE in molecular structure generation.

We clarify that it can generate molecular structures with specified properties, but whether these molecules can actually be synthesized through existing chemical methods remains an open question. Hence, our work tackles a distinct yet complementary problem, addressing downstream challenges related to its application. Thank you for your valuable suggestion. We will cite this work and discuss it. Specifically, we will further discuss the development of this field in the introduction of the revised version, providing the necessary academic discussion and recognition for important works such as JT-VAE.

W2: Could the author provide more analysis and discussion on the generated synthetic process compared to the pathway used in the real-world chemical reactions or molecular rectification?

Thank you for this suggestion. Here, we provide additional discussions compared to the pathway used in the real-world chemical reactions from three aspects:

• First, real-world chemical reactions typically depend on specific experimental conditions and additional reagents. Similar to most related computational methods, our model does not directly predict these conditions nor provide explicit information about the required reaction types. However, our Markov Bridge framework offers good scalability, allowing for the integration of additional constraints and prior knowledge, which offers flexibility in modeling conditional dependencies. Thus, it can accommodate the extended needs of such a setup.

• Second, the chemical validity of our generated results primarily depends on the RDKit product prediction in the inference process. We acknowledge that this validation approach lacks direct evaluation from chemistry experts. To address this issue, we have further evaluated the accuracy of RDKit predictions (please refer to our response in Q1). Our analysis indicates that the prediction accuracy of RDKit is acceptable.

• Third, we acknowledge that the reaction templates currently used are primarily derived from combinatorial chemistry libraries and may not fully represent the diversity of actual synthesis. These templates are based on validated actual reactions, ensuring chemical feasibility, and cover the most commonly used reaction types in chemistry, fulfilling the needs of most application scenarios. Additionally, future extensions and updates of the templates are also feasible.

Finally, through this work, we hope to improve the design of synthesizable molecules in molecular design. As experiments in real-world scenarios are an extremely time-consuming and costly process. We believe that our contribution will provide a more reliable and practical computational foundation for chemical space projection. In the future, we hope that more excellent works in various fields will benefit from our technical ideas!

Q1: How accurate is the RDKit prediction of the reaction product?

To evaluate the accuracy of RDKit's prediction of the reaction product, we filter all 11,818 single-step synthetic reactions generated. We evaluate the chemical validity rate (CVR) and prediction coverage (PC). CVR denotes the proportion of chemically valid predicted products, while PC indicates the proportion of samples with successfully generated predictions. As presented in the table below:

The results indicate that the RDKit predictions are reliable.

Q2: Could the author elaborate more on why completing at least 50% of the synthesis steps is considered a success?

Your feedback is very important to us. We have realized that there is a problem with our expression. It is computationally equivalent to the percentage of valid postfix notations, and further multiplied by 1/2. We acknowledge that our explanation is unclear and caused confusion, so we will restore the definition ("the percentage of valid postfix notations") and values in the revised version. We sincerely apologize and hope that this explanation clarifies the issue.

Q3: How is the number of notation blocks determined? Does the choice of the number of notation blocks affect the performance?

We sincerely appreciate your insightful suggestion. We conduct a sensitivity experiment on the block size, keeping other experimental conditions constant while changing only the size. The results are shown in the table below. We can observe that when the size is 1, its performance is not as good as when the size is 4. When the block size is increased to 6, the performance slightly decreases again. This indicates that too large a block size reduces the ability to model semantic dependencies, leading to limited gains. Therefore, we recommend setting the optimal size to 4.

---

Thank you again for your efforts and time. We sincerely appreciate the feedback, which helped improve our work!

Best wishes,

All authors of Paper 1834.

[1] Wengong Jin, Regina Barzilay, Tommi S. Jaakkola: Junction Tree Variational Autoencoder for Molecular Graph Generation. ICML 2018

Dear reviewer,

We deeply appreciate your thoughtful review and your recognition of our contributions. Below, we provide point-by-point responses to your concerns and suggestions.

---

W1: Empirical advantage.

We clarify that the test set comes from the largest and most comprehensive source of medchem building blocks in the world, and it is a standard data source. The reconstruction rate is the percentage of proposed synthesis pathways that lead to products identical to the input molecules. MoleBridge improves the error accumulation issue at the algorithmic level, leading to a higher reconstruction rate. An example can be seen in W3. Additionally, given the inherent difficulty of the tasks, our improvements in other evaluations have been relatively significant. In drug discovery, due to the time-consuming and labor-intensive nature of the process with low success rates [1], even a small improvement of a few percentage points could translate into millions of dollars in value. Hence, we hope that in the future, we can better demonstrate the practical application value of the algorithm. Furthermore, we hope that other excellent works in various domains will benefit from our technical ideas!

W2 and Q1: Can the authors compare the empirical results with those of SynFormer?

Thank you for providing this paper. We observe that SynFormer is currently only published on arXiv and has not yet been peer-reviewed. Despite this, we take the suggestion seriously and have included a comparison with SynFormer.

Although SynFormer is an excellent parallel work, MoleBridge has advantages on most metrics. While SynFormer has a slight edge on success, we clarify that in practical studies, the primary focus is on finding synthetically viable analogs similar to the target molecule. Despite this, the comparison reveals interesting research directions, and we are exploring how to combine SynFormer’s strengths to enhance success. We will further discuss this work in the revised version.

W3: Case studies where the autoregressive formulation leads to incoherent, invalid sequences that MoleBridge otherwise can correct.

We believe the suggestion you mentioned has unique value. To address this, we have further analyzed 7314 cases, where sequence error accumulation occurred in 5441 cases in the autoregressive formulation. We present a typical example of an early error for the target molecule, "NCCCC(=O)N(CC(=O)NN)C(N)=O". The autoregressive model generates "CC(=O)Cl" in an inference step, which is an invalid pathway, leading to the errors of subsequent steps. This is because this step cannot lead to the target structure. MoleBridge corrects the step to "NCCCC(=O)NC(N)=O", generating a complete pathway and successfully reconstructing the target molecule.

Q2: What are the computational costs associated with the Markov bridge-based method compared to the simpler autoregressive method?

Thank you for your suggestion. With your suggestion, we have discovered an additional advantage. We conduct a computational cost comparison on the NVIDIA 4090:

Our method is slower in inference for short sequences due to the additional overhead from the Markov Bridge. However, this slight difference in inference time is minimal, with a difference of only 0.17s, which is within an acceptable range. In contrast, for longer synthesis pathway sequences, it is faster, owing to the parallel inference of tokens within blocks.

Q3: Could Figure 1 be made clearer to illustrate how the algorithm works?

Thank you for your revision suggestion. Since the conference reply format limits us to text only, we will follow the excellent presentation formats of ChemProjector and RetroBridge that you suggested, further simplify the process, and provide clearer and more intuitive module divisions and labeling improvements, which will be reflected in the revised version.

Q4: The definition of "success rate" in the evaluation.

Your feedback is very important to us. We clarify that the definition of the success rate we use is the same as the one in ChemProjector, and it is computationally equivalent to the percentage of valid postfix notations, but further multiplied by 1/2, which has caused some confusion. We acknowledge that our explanation was unclear, and we will restore the original definition in the revised version.

---

Thank you once again for your valuable and insightful review!

Best wishes,

All authors of Paper 1834.

[1] Kang Zhang, Xin Yang, Yifei Wang, Yunfang Yu, Niu Huang, Gen Li, Xiaokun Li, Joseph C. Wu & Shengyong Yang: Artificial intelligence in drug development. Nature Medicine 2025