MapSelect: Sparse & Interpretable Graph Attention Networks

Thank you for your thoughtful review and insightful observations regarding our manuscript. We appreciate the time you took to analyze our work and provide constructive feedback. Below, we address your concerns and questions:

1. Novelty and Theoretical Contribution: We understand your point about the mathematical novelty appearing limited. Our aim was to address a specific practical limitation in GATs by combining SparseMap with GATs in a novel way. However, we believe the paper, as is, offers valuable empirical analysis alongside a clear mathematical description of our method.

2. Code and Tool Update: We appreciate your note on the usage of SparseMap and its code update status. We agree that maintaining and updating the tools we rely on is crucial. For this reason, we have documented the SparseMap part of the code, ensuring that it remains a viable tool in the field.

3. Consistency in Writing Style: Your observation regarding the inconsistent use of American and British English is well taken. We apologize for any confusion this may have caused and we have revised manuscript to maintain consistency in spelling and grammar.

4. Benefits Over Existing Approaches: We acknowledge that the improvements in terms of accuracy might not seem significantly higher than state-of-the-art methods. However, the primary advantage of our approach over SGAT, lies in its ability to offer precise control over attention density. This control facilitates a more interpretable and sparse representation (see answer to Reviewer EqGL). On top of this, in contrast to SGAT, MapSelect also works locally, and from our evaluation, is the best performing local-based method. We believe these two points make a significant step forward in understanding how the model allocates attention.

5. Applicability in Specific Scenarios: MapSelect shows particular strengths in scenarios where interpretability is as important as performance, such as in domains where decisions need to be explainable, justifiable, and adhere to a certain format (e.g., at most three nodes/edges), like healthcare or finance.

Thank you once again for your valuable feedback.

Thank you for your insightful review and constructive criticism of our manuscript. We value your feedback and agree that addressing these points will enhance the quality of our paper. Below, we address each of your concerns:

1. Lack of Sufficient Analysis: We have enhanced the clarity of our motivations in the introduction. Moreover, we maintain that our method is theoretically robust, as substantiated in Sections 2 and 3. Notably, unlike prior approaches, our method has the unique capability to explain both local and global contexts.

2. Improvement in Writing and Symbol System: We regret that our writing style and symbol system were not clear in the introduction and other sections of the paper. To address this, we will undertake a thorough review and revision of our manuscript, focusing on improving readability and clarity. We would greatly appreciate it if you could provide specific sentences or paragraphs where you found the content particularly challenging to follow. This will help us target our revisions more effectively.

3. Performance Comparison with SGAT: Your observation regarding SGAT's performance in comparison to our proposed methods is valid. However, it's important to emphasize that our method works both locally and globally, with superior performance on the local setting. Moreover, it offers significantly greater control over sparsity, which is a crucial aspect of interpretability in GATs. To clarify this advantage, we have included two additional plots in our revised manuscript (see Figures 10 and 11 in Appendix D.3). These plots showcase the relationship between the hyperparameters controlling sparsity (e.g., l1 penalty for SGAT and budget for MapSelect) and the resultant sparsity levels, thus highlighting the controllability and interpretability advantages of MapSelect over SGAT.

We believe these revisions will address your concerns and significantly improve the manuscript. Thank you again for your valuable feedback, and we look forward to resubmitting our improved paper.

Thank you for your thoughtful and detailed review of our manuscript. We appreciate your insights and agree that addressing these points will strengthen our paper. Below, we respond to each of your concerns:

1. Accuracy-Interpretability Trade-off: We acknowledge your observation regarding the comparable performance of MapSelect with SGAT. It is indeed a characteristic of self-interpretable methods to potentially trade off accuracy for increased sparsity and interpretability. We realize this might not have been sufficiently emphasized in our paper. In our revised manuscript, we have clarified this trade-off in the introduction, highlighting that our primary goal is to improve interpretability, even if it sometimes comes at the expense of accuracy.

2. Baseline Selection: Regarding your suggestion to include a baseline combining GAT with a post-hoc explainer, we understand the rationale behind it. However, our work intentionally focuses on self-interpretable models. While the proposed baseline is valuable, it falls outside our paper's scope, which is dedicated to exploring intrinsic interpretability within GNNs rather than relying on external explainers. We have made our scope and the rationale behind our choice of baselines clearer in the revised paper.

3. Scalability Concerns: SparseMAP enjoys a convex optimization problem and has a very efficient implementation in C++. Its convergence can also be controlled via hyperparameters. In practice, we found that MapSelect is 2x (local) and 4x (global) faster than NeuralSparse. This shows that runtime performance is not a bottleneck.

4. Flexibility with Various GNN Models: Your suggestion to demonstrate the flexibility of our method by integrating it with different GNN models is intriguing. While our current focus is on graph attention networks, we acknowledge the potential value in showing the method's applicability to other GNN architectures. However, integrating MapSelect with non-attention-based GNNs might change the nature of the explanations provided, as our method is designed to interpret GATs. We will consider exploring this in future work and we have noted this as a potential benefit of our approach.

Thank you once again for your valuable feedback.

Thank you for your thorough review and constructive feedback on our paper. We appreciate the opportunity to clarify and enhance our work based on your insights. Below, we address each of your concerns:

1. End-to-End Differentiability and Determinism: We acknowledge that our claim regarding determinism and end-to-end differentiability was not fully substantiated in the initial manuscript. We agree that the reparameterization trick, as used in NeuralSparse and SGAT, renders these methods end-to-end differentiable. To clarify, our method's deterministic nature was intended as a strength, following the comparison in SPECTRA (Guerreiro & Martins, 2021) between deterministic and stochastic approaches, including the reparameterization trick. We have added the necessary citation to SPECTRA to support this claim.

2. Comparison with Original GAT: We recognize the importance of comparing MapSelect with the original GAT in terms of performance and efficiency. While MapSelect does incorporate SparseMAP, leading to slower performance compared to standard GATs, our primary focus is not on performance gains over the original GAT. Instead, we emphasize the interpretability and sparsity benefits. You can find the result of a standard GAT (i.e., without sparsity) when looking at the first point of Entmax (alpha = 1.0) and MapSelect (budget = 100%). However, to provide a comprehensive view, we have made this distinction clearer in our revised manuscript (see footnote 6).

3. Focus on Self-Interpretable Models in Node-Classification Contexts: We appreciate your suggestion regarding the expansion of our interpretability analysis. It's important to highlight that our main goal in this paper was to investigate self-interpretable models specifically in the context of node-classification datasets. This angle of analysis, focusing on self-interpretability in node-classification, represents a novel contribution to the field, as far as we are aware. We agree that incorporating both node-level and graph-level classification tasks will enrich our study. Do you have recommendations for graph-level classification datasets?

4. Omission of Top-k Attention in Figure 2: The exclusion of top-k attention from Figure 2 was intentional, as its results are similar to those of normal GAT (we only apply top-k at test time, see Sec. 4.1).

5. Comparison with the results in Luo et al. (2020): We have provided the specific section reference in Luo et al. (2020) where the results we mentioned can be found, for the convenience of readers.

6. Clarification on Parameter Use in Section 2.1: Thank you for your observation regarding the parameter usage in our model. We realize there might be a misunderstanding due to the conventional notation used in the field. In our implementation, contrary to what might be inferred from the notation, we actually utilize two distinct matrices (W1 and W2), and not a single matrix as is often represented (W) in other papers. However, note that these two matrices can be seen as a single W applied after the concat operation.

Thank you again for your valuable feedback. We believe these revisions significantly strengthed our paper.