The paper proposes a graph neural network based method to solve the retrosynthesis prediction problem, that is the identification of the reactions which lead to a particular target. In particular, the proposed graphical model exploit ideas from graph neural networks, in order to learn informative representation. Furthermore, expert knowledge from chemistry rules can be integrated in order to consider known restrictions and to provide interpretable solutions. The paper well describes the background and task of interest. However, I find the notation and model derivations to be hard to follow. The results show very promising performances, but could be more comprehensive and I find the methodological contribution to be limited. Detailed comments are provided below. 1) Overall, I found the model design choices to be not properly justified. I would suggest to clarify the arguments and formula derivations in section 4, in order to make the text smoother and easier to follow. 2) I would also recommend to properly introduce the notation and definitions before presenting the model. 3) Graph Neuralization. The design and model choices seem to be arbitrary. Could the author(s) discuss further on it? 4) Since the paper seems to be heavily focused on the application and the strong experimental results, I would suggest to explore additional options for the update operator of the graph neural network (additionally to structure2vec). This would validate the actual benefit of the learning component. 5) Using only one dataset is restrictive in order to assess the generalisability of the method. I would consider to validate the model on additional real and/or simulated datasets %%%%%%%%%%%%%%% Thank you for your rebuttal and for answering my concerns. I found the new experiments and arguments provided to be convincing.

I really enjoyed reading this paper - it is well motivated and the theory is also well described in my opinion. Originality: The combination of merging a rule-based approach with a neural approach appears to be very well suited for the problem at hand. It has to the best of my knowledge not been studied using graphical models, exploiting the compositional structure of these rules, which is a significant step forward. The compositionality of the rules has been studied in a purely symbolic way by Segler et al in https://onlinelibrary.wiley.com/doi/abs/10.1002/chem.201604556 which I would suggest to additionally cite. Approaching the problem by decomposing the the rule application into several matching and reaction scoring steps is very elegant. Do the authors think the choice of the graph neural network for the encoding plays a large role? ___________ EDIT after authors response: I want to thank the authors for addressing the questions. With the additional data provided during the rebuttal (which should be added to the final version), I raise my score accordingly.

Positives: The paper is well organized, with each section clearly defined and good use of notation to clearly mark research objectives and contributions made by the authors. The introduction sets up the contributions clearly, and the background/method sections manage to cover a lot of material with varying degrees of success. The figures/graphics provided by the paper also do a good job of expressing what the machine learning task that is being solved is and the proposed solution as it relates to retrosynthesis. The authors focus on a specific ML task, retrosynthesis, is also refreshing as it’s applications in the industry are clear. The mathematical equations provide a means to implement the model as well, this also extends to descriptions for the model including layers and optimization functions. In the experiment section, the authors model also appears to beat out the baselines. Negatives: The paper would have benefited with a pseudo-code algorithm describing the graph neutralization for v1, v2 and w2. The equations, while well written, are frequently written inline and the clarity of the overall algorithm is a little unclear. Overall the focus on retrosynthesis as the main ML task leads to equations being described from that perspective solely. It would have helped if the authors described the methods agnostic of the data or ML task. The related work section is also fairly short with citations to other works infrequently mentioned in the paper. In particular, the paper mentions markov logic networks, which seem structurally similar to the proposed GLNs. The authors mention an appendix A which explains the differences, but this was not available for review. Given the strong similarities between the two frameworks, GLNs novelty is called into question. It would seem this is just an application of MLNs in the context of retrosynthesis. Related work: The paper provides a related work section, which very quickly mentions approaches dealing with the second goal of the paper, hierarchical classification. The authors do a well enough job citing previous methods which they base their model off of. The baseline methods are also cited and explained. Conclusion: The following paper does a good job describing the model proposed, and the solution does appear to improve upon previous approaches dealing with retrosynthesis. The authors focus on a specific ML task is also a step in the right direction, however their focus in describing the model in regards to the task makes applying the model to other ML tasks difficult. The use of inline equations also removes some clarity in their approach. The novelty of the approach is also called into question since there are clear similarities with MLNs, and the appendix was not available. Given that, I would give this paper a weak reject as it is unclear if this is simply an application paper or a truly new method.