We thank all reviewers for their valuable feedback and comments. Original Manuscript ID: Tracking #: 803-1794 Original Article Title: Towards Semantic Understanding of GNN Layers Embedding with Functional-Semantic Activation Mapping Dear Editor, We sincerely appreciate the opportunity to revise and resubmit our manuscript titled "Towards Semantic Understanding of GNN Layers Embedding with Functional-Semantic Activation Mapping". We are grateful to the reviewers for their insightful comments, which have significantly strengthened our work. Please find enclosed: A point-by-point response to all reviewer comments (attached below) Revised manuscript with changes highlighted in green ("FSAM_highlighted.pdf") Clean version of the revised manuscript ("FSAM_Cleaned.pdf") without highlights. Thanks and best regards Kislay et al. Reviewer 1, Concern # 1: Lack of Baseline Comparisons While FSAM is compared with some existing explainability methods, a direct comparison with state-of-the-art GNN explainability models (e.g., GNNExplainer, XGNN, PGExplainer, SubgraphX) on the same datasets is missing. A more quantitative benchmark comparison would help demonstrate FSAM’s advantage in real-world interpretability. Author response: Since FSAM differs fundamentally from local explainability techniques, such as GNNExplainer, PGExplainer, SubgraphX, etc., which focus on local-level explanations, these methods are not directly comparable. We focus on global explainability. As a result, we relate FSAM against XGNN, which is also a global explainability method.. It is worth noting that FSAM aims to map the deep representations learned by the GNN into a Functional-Semantic graph, and this work is focused on validating that the obtained representation represents the behaviour of the network. The generation of global (per-class) explanations is the next step we aim towards, from which quantitative comparison will follow. XGNN and the more recent GLG-Explainer entirely skip the step in which the deep representation is translated into something that can be exploited for more than just global explainability, including local explainability, integration with background knowledge, bias detection to mention a few, and this is why we believe it is a fundamentally different starting point. As noted in recent work (Agarwal et al., 2022; Azzolin et al., 2023), XGNN’s synthetic graphs often fail to reflect real-world graph structures or model internals. FSAM, conversely, reveals why predictions occur. In the appendix, fig. (12) XGNN’s prototype for Class 0 in the Cora dataset is presented. As XGNN generates one graph per class, assuming a single prototype can explain the class. The sparse structure suggests limited explanatory power for complex citation patterns, while FSAM evaluates semantic consistency of activations, and FSAM diagnoses semantic overlap across layers in Fig (13-16 ) ar cora dataset. As FSAM is more geared towards the (Global + semantic degradation) as it is a diagnostic tool, not yet an explanation generator, this work validates that the FSAM graph accurately reflects network behaviour. As XGNN evaluates prototype quality, FSAM evaluates semantic coherence, and these metrics measure fundamentally different aspects of explainability. In the future, we will derive an explanation from the FSAM graph for direct comparison. Reviewer 1, Concern # 2: Limited Discussion on Computational Complexity FSAM involves tracking neuron activations across multiple layers and performing correlation-based analyses, which could be computationally expensive for large-scale graphs. There is no mention of FSAM’s scalability when applied to larger graphs. A discussion on computational cost and possible optimisations would be valuable. Author response: To address your concern, the revised manuscript's conclusion now includes observations on how execution time increases as graph size grows and potential optimisations to tackle scalability issues in section 5.8. The analysis indicates that scalability can be problematic, especially regarding execution time for larger graphs. This limitation also applies to XGNN and GLG-Explainer, as mentioned on page 3, lines 39-44. Reviewer 1, Concern # 3: Over-Reliance on FSAM as a Ground Truth The paper assumes that FSAM-generated graphs always represent correct semantic relationships. However, no external validation (e.g., human domain experts) is provided to confirm whether FSAM representations align with true semantic structures. A qualitative evaluation or expert validation could strengthen FSAM's reliability. Author response: Despite our understanding of the reviewer’s concern, it is worth pointing out that we have focused on a more objective analysis of FSAM-generated graphs (e.g. via community analysis and p-score) where we look at the correlation between classification error and similarity of classes (Table 3) and quantitative evidence that model depth exhibits diminishing returns, supported by layer-wise Jaccard similarity analysis in fig(5,6,7). This indicated the benefits of the FSAM representation, for example, in characterising when correct predictions may be made for incorrect reasons due to over-smoothing or loss of semantic clarity, particularly in deeper layers. The choice of citation datasets also makes it easier to assess the quality of communities identified by the analysis on FSAM, but this is not an evaluation of the quality of explanations (which we have not generated yet) but instead of the quality of the representation we aim to use. Our next steps, which include generating per-class explanations and validating them against the metrics used for XGNN- such as fidelity, accuracy, and human evaluation- are part of our future work. Reviewer 1, Concern # 4: Statistical Consistency in Results The Pearson correlation values in Table 2 (ranging from 0.589 to 0.917) indicate high correlation but do not necessarily prove causation. It would be beneficial to perform: Significance testing (p-values) Confidence intervals Statistical ablation studies (e.g., what happens if certain neurons are artificially suppressed?) Author response: We greatly appreciated your suggestion and implemented several statistical measures to provide a more comprehensive analysis. In Tables 2 and 3, we have added the mean ± standard deviation for correlation values across all the different layers for each dataset. We also conducted the significance test and included the P values in Table 3. The p-values we calculated show that the Pearson correlation values are statistically significant. This means that the relationship observed between layer depth and accuracy is unlikely due to random chance; we also provided the 95% Confidence interval in the updated Table 3, we also explained that on page no 10 line no 8-12, which is narrow, confirming that the Pearson correlation values are reliable and robust across different data points. We have not conducted ablation studies to see the impact of suppressing specific neurons on the model’s representation, as we believe this requires further consideration to define what neurons to suppress and what should be the expected effect, but this is certainly part of our next steps. Reviewer 1, Concern # 5: Ambiguities in Community Analysis While the paper states that overlapping neuron activations contribute to misclassification, it does not quantify the degree of overlap that leads to significant misclassifications. A threshold for defining critical neuron overlaps would provide a clearer interpretation. The Table 3 (Community Structure Analysis) could be enhanced by showing per-class misclassification rates instead of just total mistakes. Author response: We have moved the Jaccard similarity analysis from the appendix to the main body of the paper. Specifically, we calculate the Jaccard similarity and overlap coefficient between neuron activations in different communities to assess the degree of overlap that leads to misclassifications. As shown in Figure 4, we observed a positive correlation between Jaccard similarity and misclassification rate across the layers of the Amazon Photos dataset. The plot indicates that as the overlap between neuron activations increases (measured by Jaccard similarity), the number of mistakes also increases. This finding suggests that higher similarity between classes leads to more significant confusion during the classification process, causing more misclassifications. The rest of the Jaccard similarity plots were added in the appendix because of space constraints. As I also indicated in table 4 now (previously table 3). This threshold for significant overlap is discussed in the revised paper to provide a more precise interpretation of how neuron overlap contributes to misclassification. We have provided additional figures for the per-class misclassification rates across all layers for only one dataset due to space constraints for the PubMed dataset. These can be found in Figures 8 to 11 in the appendix. Please refer to the updated manuscript, lines from 2 to 5 on page 16 Reviewer 1, Concern # 6: Experiment Reproducibility The paper lacks clear implementation details: What hyperparameters were used for GNN training? What batch sizes, learning rates, and optimizers were employed? Were all experiments conducted under controlled settings (same random seed)? Author response: We appreciate your feedback and have added a new section (Section 5.1) to provide detailed information about the experimental setup. This section outlines the hyperparameters used for GNN training, including batch sizes, learning rates, and optimisers. Additionally, we have clarified that all experiments were conducted under controlled settings, with the same random seed used to ensure reproducibility. Reviewer 2, Concern # 1: One of the claims of the paper is that FSAM quality decreases due to over-smoothing (page 2, L20-26). A small introduction on the concept of over-smoothing, and a summary of related works on the topic, would strengthen and clarify the contribution of this paper. Over Smoothing has long been studied in the machine learning literature [1], what are the unique advantages of FSAM, if any, in detecting oversmoothing? Or conversely, is the fact that FSAM output indicates over smoothing proof of its validating, since over smoothing is a well-studied problem? Author response: We have updated the manuscript on Page 2, Lines 9-26, to include a brief introduction to the concept of oversmoothing. We would like to clarify that FSAM does not aim to solve the problem of oversmoothing but instead serves as a tool to quantify and track the effects of oversmoothing at the neuron level. It provides valuable insights into when and where oversmoothing occurs during model training. This has been discussed more clearly on page 2, lines 9-22. Reviewer 2, Concern # 2: In Table 1, the content of each column should be clarified, ideally in the caption. While type or black-box is self-explanatory, task, target, flow, and design are less so. Abbreviations used in the Table should be defined in the caption or in the text. Author response: We have updated Table 1 to provide more precise definitions for the terms used in each column. Reviewer 2, Concern # 3: I like the idea of having Section 4 with the detailed contribution, but a lot of content is repeated from the introduction. The introduction could be shortened to avoid repetition. Author response: Thank you for your valuable comment. We have revised the Introduction to reduce redundancy and avoid repetition with Section 4 and also updated the manuscript. Reviewer 2, Concern # 4: It is not clear to me what cross-domain validation means in the context of FSAM validation (page 6, line 9). I think validation on multiple domains would be clearer, as often cross-domain is used to entail that the system is trained/configured on one domain, and tested/used on another domain Author response: We acknowledged the potential ambiguity in using the term "cross-domain validation" on Page 6, Line 23-28. To avoid confusion, we have revised the manuscript by replacing "cross-domain validation" with "validation across multiple datasets", ensuring that our intended meaning is clear. Reviewer 2, Concern # 5: The description of FSAM is much more concise than in the NeSy paper. I understand that this choice leaves room to expand on the experimental validation and limits repetition. However, in the interest of a more self-contained manuscript, I believe it would be useful to at least briefly define all elements of the methodology. In particular, the following concepts are mentioned but not defined or explained: the notion of ego-graph (page 5, line 10); how each activated neuron is mapped to the final predicted class (page 7, line 34-38); how communities are extracted (Section 5.4) Author response: We acknowledge the concise description of FSAM in this manuscript. While we intended to minimise redundancy from our conference NeSy paper and allow more space for experimental validation, we agree that key concepts should be clearly defined for better readability. To address this concern, we have now provided a brief explanation of ego-graphs, describing them as subgraphs centered around a specific node, including its direct neighbours and edges (Page 5, Line 28-33). We explained the mapping in our previous paper. We started mapping the neurons from the first layer to the predicted class and added the Overall proposed system architecture in Fig 1. For each subsequent layer, we track how neuron activations are influenced by previous layers, using attention scores to progressively map these activations to the final class at the output layer. Because of space constraints, we moved all the community graph and the FSAM semantic graph in the appendix, as the FSAM semantic graph is our previous contribution and explained thoroughly in our earlier paper. We updated pages no 10, line 38-45 to discuss how communities are extracted. Reviewer 2, Concern # 6: In Fig.1 there are two nodes which are separately from the rest of the graph. Is it an artifact of the visualization or are they nodes with distinct characteristics? Author response: The two separately positioned nodes in Figure 1 are not artefacts of visualisation but represent distinct neuron activations that do not strongly associate with the primary activation communities. When nodes are isolated in the visualisation, it suggests that their feature activations are less coherent with the larger group of nodes. These isolated nodes help diagnose problems with the network’s semantic alignment or representation quality. We plan to investigate in more detail the activation behaviour of these nodes in future work as this relates to ablation studies discussed in previous comments Reviewer 1, Concern#4. Reviewer 2, Concern # 7: It is not entirely clear, to me, why the graphs in Fig. 1-4 are “semantic graphs”, since most of the nodes are layers, and thus are labelled with strings that do not carry, by themselves, any semantic meaning. If I understand the paper correctly, the semantics are given by the connections with the predicted labels, but these are hard to interpret visually. It is also not evident which neurons correspond to each layer, and thus how layer-by-layer comparison can be obtained. In Figs 2-4, all labels appear to refer to the first convolutional layer (Conv1*), thus it is not self-evident how the structure changes in different layers, or with networks of different depths. Author response: A Functional Semantic Graph describes how neuron activations and their relationships to the predicted class labels are represented, capturing both the network's functional behaviour and semantic structure. Moreover, the graphs in Figures 13-16 show the semantic relationships inferred from the activation patterns at different layers, which are referred to as functional-semantic graphs. Due to space constraints, we have added only one dataset, FSAM, for all four layers. This indicates how the model's behaviour evolves as the network depth increases. In Figure (1-4), since FSAM maps activations from the last layer to the final class, the semantic meaning is derived from how neurons interact to form class-specific activation communities rather than from the individual layer labels themselves. Reviewer 2, Concern # 8: In Table 2, how is the layer-wise accuracy calculated? Or, if the table compares the accuracy of separate networks characterized by different depths, then the caption should be revised (by layer-wise accuracy, I understand that the network has four layers, and the accuracy is computed at the end of the first, second, third and fourth layer). Author response: To avoid misinterpretation, we have revised the caption to explicitly state that the table compares the final accuracy of models with different depths rather than the accuracy computed at different layers of a single model. Reviewer 2, Concern # 9: Table 3 includes the absolute mistake count, however, also including the percentage figure would clarify. Author response: In the updated manuscript, Table 4 now reports the percentage of mistakes relative to the total predictions per class. Reviewer 2, Concern # 10: Sections 5.4 and 5.5 are quite long and would benefit from a revision to better summarize the substantial number of experiments described in the paper. Section 5.5 also refers to several key figures (page 15, 1-24) but does not refer to the actual content of the paper. Some references are unclear: for instance, there is a reference to Section 8, which does not exist in the paper, or to visualization of community structures that are not present in the manuscript. Page 15, line 25 refers to Table 2, but the sentence seems more consistent with Table 3 instead. I think that revising these two final sections to improve readability, clarify conclusions, and better connect them with the experimental results would strengthen the paper. Author response: We acknowledge that Sections 5.4 and 5.5 contain extensive experimental details and require better structuring for clarity. We have summarised key experimental findings while maintaining the necessary information to enhance readability and have revised the manuscript. The reference to Table 2 (Page 16, Line no 1-5) has been revised, as the discussion aligns more closely with Table 3. Some references pointed to visualisations that were not present in the main text because of page limitations; I added those in the appendix. Reviewer 2, Concern # 11: Typos: Page 6, line 8 (and 16/24/31): in the subsection 5.2 We are extending -> in Subsection 5.2, we are extending Page 6, line 9: what is 5.1? subsection I image I would avoid capitalization in the sentence (e.g., page 6, line 8) Page 7, line 44: However, As shown -> However, as shown Page 11 lines 31-48: the same paragraph is repeated twice Author response: All typos have been checked and corrected. Reviewer 3, Concern # 1: The soundness of the paper is good. The experimental setup is sound, with evaluations across multiple datasets and layer configurations. However, the paper lacks a deeper theoretical analysis or comparison with other XAI methods. Author response: As discussed in response to Reviewer 1, Concern #1, we acknowledged the need for direct quantitative benchmarking against the two global GNN explainability methods available in the literature, namely XGNN and GLGExplainer. We also added Tables 2 and 3 for rigorous statistical validation. As of now, we have not generated global class-level explanations, which would enable quantitative comparison. However, in Table 1, we have indicated how our methods compare in relation to their characteristic features and potentials. Reviewer 3, Concern # 2: The clarity of the paper is suboptimal. The FSAM method is not well-presented. The contributions are repeated excessively, making the text feel redundant. The figures are poorly presented. Additionally, the writing style often feels repetitive. Author response: We have revised the manuscript to improve clarity, conciseness, and overall presentation. Reviewer 3, Concern # 3: Page 2 line 3&4: "This ambiguity complicates the interpretation of learned embeddings, making it essential to understand model behaviour through detailed activation analysis." What is the ambiguity in this context? Please be more concrete. Author response: We use the term "ambiguity" to refer to the similarity in node embeddings as the model deepens, which hinders interpretability. Activation analysis via FSAM helps us understand how the model makes decisions and ensures that the embeddings are meaningful. We have clarified this in the paper. Reviewer 3, Concern # 4: Page 3 line 13: Abbreviation definition in header. Please do not do this. Author response: We have removed the definition of abbreviation from the header, ensuring consistency with standard academic writing conventions. Reviewer 3, Concern # 5: Page 3 Line 36-38: "Additionally, these methods tend to provide explanations that are difficult for humans to interpret, as they do not reveal the underlying relationships between the GNN’s learned representations and the data’s inherent structure." Please provide evidence for this claim. I would argue this heavily depends on how concise an explanation is, and various methods provide concise explanations for GNNs (e.g., GraphLime). Author response: We agree on the fact that the effectiveness of explainability methods depends on how concise and clear the explanation is. Despite local explainability methods like GraphLIME that can provide reasonably clear explanations, we focus on global explainability, which is still under-investigated. Specifically, the FSAM approach aims to provide access to an interpretable representation that reflects GNN behaviour. We focus on building and validating this representation, and argue it can be exploited to generate global (and also local) explanations as we intend to do in future work. (see response to Reviewer 3, Concern # 1). As discussed in future work, FSAM could be a foundation for designing local explainability methods that identify relevant nodes and understand the relationships between the input data and potentially external knowledge. In the Conclusion and Future Work section, we discussed this as a future direction. Reviewer 3, Concern # 6: Page 3 Line 40-43: "However, XGNN’s assumption that a single synthetic graph can represent an entire class oversimplifies the complex relationships within real-world datasets." Please justify this claim. Author response: As mentioned in Reviewer 1, Concern #1 and Reviewer 3, Concern # 1 in real world datasets classes often have variations within the class – and different structural patterns can lead to the same class. XGNN’s single synthetic graph cannot effectively capture these subtleties, as discussed in Azzolin et al. (2023) and Yu and Gao (2024). This happens because XGNN builds graphs edge-by-edge (“atom-by-atom”), which can struggle to capture a complex motif that requires adding a set of edges together (closing a ring). XGNN’s inability to capture multiple modes or diverse substructures within the same class means its explanations can be incomplete or biased toward one pattern. Fig 12 we added for cora dataset for class 0 and Fig (13-16) FSAM all layers representation for cora dataset. Reviewer 3, Concern # 7: Page 3 Line 43 & 44 (This claim is made more often, but no substantial reasoning is provided) "Such approaches, while offering some insight into the final predictions, fail to account for how intermediate layers contribute to the learned representations" Why is the contribution of the intermediate layers inherently important? Intermediate steps are not enforced to be linked to semantic and human-interpretable concepts, and thus, the model may learn a non-human-accessible representation as an intermediate step. This is not necessarily a downside of the model. Author response: We agree that intermediate layers in GNNs are not necessarily associated with human-interpretable concepts. However, it is also true that subsequent embedding steps might relate to intermediate concepts and relations between those concepts in the same way as the layers of a CNN relate to concepts from simple to complex as we move towards the final layers. This means that if we want to translate deep representations (in this case, layers of embeddings) into composable and interpretable concepts and relations, we need to be able to identify how intermediate embeddings relate to classes in the final layer. Hence, although XGNN provides a final synthetic explanation, it does not provide a layer-wise decomposition needed for compositionality in the interpretation. This prevents one from knowing which sub-patterns of embeddings are being detected at each layer, what concept they relate to (if any) and how they contribute to the final decision. FSAM aims to do this. Reviewer 3, Concern # 8: Page 4, Line 30 & 31: "Furthermore, soft masking techniques [29], which are effective in image domains, compromise the integrity of graph structures when adapted to GNNs." Why is that important here? The sentence feels out of place. Author response: In the updated manuscript. Yes, it has been removed as it is deemed out of scope. Reviewer 3, Concern # 9: Page 4 Line 37 & 38: "FSAM enhances both transparency and accountability, providing explanations that are intuitive and accessible to non-experts" Non-experts of what? GNNs? Author response: We have updated this sentence to clarify that FSAM does not generate explanations as subgraphs. Currently, FSAM does not produce human-interpretable explanations in the classical sense. We have revised the statement to reflect FSAM’s role in mapping GNN representations and its potential future application in explanation generation and updated on page 3 line no 45-50. Reviewer 3, Concern# 10: Page , line 43: A nice figure would help to relate better to the method. Author response: We have included Fig 1 as an overview of the methods Reviewer 3, Concern # 11: Page 5 Line 19-20: "To capture the behaviour of neurons within the GNN, we calculate neuron activations using Graph Convolutional Networks (GCNs)" Do you use GCNs to calculate the neuron activation for any underlying GNN architecture? And please use a reference here. Author response: The neuron activations in FSAM are computed by extracting layer-wise activation values from the hidden layers of the GCN. While GCNs serve as the primary model in our experiments, the same methodology could be extended to other GNN architectures. We have revised the manuscript to explicitly state this general applicability and have added an appropriate reference to GCNs (Kipf & Welling, 2017). Section 3.1, pages 29 to 33, is updated. Reviewer 3, Concern # 12: Page 5 Line 43&44 "We visualize these graphs using thresholding techniques to identify the most influential neurons in decision-making." It would help to see an example visualization of these graphs to understand what is going on here. Author response: Examples of the co-activation visualisations are provided in Appendix Figures 13-16 for the Cora dataset. These examples show that we apply dynamic thresholding (Yan et al., 2018) to highlight the most influential neuron activations. The specific p-value threshold (p < 0.01) and its justification are detailed in Table 3 and the explanation on page 10 lineno 6-10. Reviewer 3, Concern # 13: Page 5 Line 46 -51: "We find that additional layers beyond a certain threshold do not yield significant new information. Instead, the overlap between neuron activations for different classes intensifies, undermining class-specific representation and confirming our hypothesis that over-smoothing impairs the model’s ability to distinguish classes effectively. This extended analysis substantiates our hypothesis that beyond an optimal point, adding layers fails to enhance the GNN’s knowledge capacity. The FSAM framework thus proves to be an insightful tool, not only for visualizing these limitations but also for guiding the design of more efficient GNN architectures." You state the same claim twice in a row without substantiating it in those five lines. Author response: We have revised the manuscript to remove repetition and improve clarity and coherence, introducing over-smoothing and discussing the importance of the layer-wise analysis (see response to Reviewer 3, Concern # 12) Reviewer 3, Concern # 14: Page 7 Line 1 and 2: "testing our hypothesis that deeper layers may not always provide additional knowledge and could hinder class differentiation" Your hypothesis describes over-smoothing, which has already been studied and confirmed to happen in GNNs. Author response: We have clarified our insights in relation to layer-wise activations and over-smoothing and the contribution of our analysis (see responses to Reviewer 2, Concern #1) Our layer-wise semantic activation analysis can help quantify and visualise the effects of over-smoothing at the neuron level. Instead of merely confirming that over-smoothing occurs, FSAM provides a structured way to track when and where neurons lose class-specific activations, offering deeper insight into how model depth impacts representation quality. To clarify this distinction, we have revised the manuscript to frame our findings as an interpretability-driven analysis of over-smoothing rather than restating a known hypothesis. Reviewer 3, Concern # 15: Page 7 Line 36-38: "This layer-wise mapping approach enabled a deeper understanding of the model’s behaviour across layers and allowed us to evaluate the effects of increasing model depth." How did that help you? Author response: It revealed where semantic collapse occurs (e.g., CoauthorCS accuracy drop at Layer 3 despite correlation increase) in figure 2 and table 3, and it also showed deeper layers (≥3) lose neuron specialization in Table 3, so it helped demonstrate the correct predictions for wrong reasons phenomenon and it tracked how misclassified samples shared neurons in deeper layers in fig 6. Reviewer 3, Concern # 16: Page 8 Fig.1.: This figure is not human-interpretable ("Ball of Edges and Nodes") Author response: We understand the confusion and highlight that the visual representation of FSAM aims to help us in community analysis to understand the progression of class-specific neuron activations across layers. This analysis, presented in Table 4 and fig no (8 to 11), offers more insights into the community structure per layer based on what the GNN has learned rather than trying to interpret the dense graph directly. Reviewer 3, Concern # 17: Page 15 Line 49 -51 "These insights suggest that tuning efforts should focus on reducing overlap in the co-activation graph for similar classes to enhance the GNN’s ability to differentiate between them. By targeting overlapping nodes, we can potentially decrease misclassification rates and improve overall model accuracy." I really like this insight because it is actionable. More actionable findings from your experiments deserve a whole subsection. Author response: We agree there is the need to highlight the potential of the approach through a list of actionable insights. We have added a dedicated subsection focusing on actionable insights derived from FSAM analysis. We expanded on tuning strategies, particularly how reducing co-activation overlap can enhance class separability and lower misclassification rates. Reviewer 3, Concern # 19: - Page 5, Line 6-8: (You make this claim repeatedly, and it is also part of your contributions) "Our extended analysis suggests that after a certain number of layers, additional neurons contribute less meaningful information due to over-smoothing, resulting in decreased model performance". This is a well-known phenomenon. There are even medium articles about that. https://towardsdatascience.com/over-smoothing-issue-in-graph-neural-netw... Author response: To clarify the role of FSAM in over-smoothing, we emphasise that FSAM does not directly resolve the problem. Instead, it serves as a tool to quantify and track the effects of over-smoothing at the neuron level. FSAM allows us to visualise and monitor how neuron activations become increasingly overlapping as additional layers are added, providing a detailed understanding of how over-smoothing impacts model performance (see previous discussion and responses on over-smoothing and layer-wise analysis). Reviewer 3, Concern # 20: - The contributions are basically some experiments with FSAM - an existing method by the author. The findings, misalignment and over-smoothing are not novel. They are well-studied effects in GNNs. Author response: Thanks, we discussed in reviewer2 concern #4. Reviewer 3, Concern # 21: - Why is FSAM not compared to other global explanation methods for GNNs? Author response: As discussed in Reviewer 1, Concern #1,