We sincerely appreciate your thorough review and invaluable feedback. Below, we provide detailed responses to all your comments or concerns.

Q1: BA-HouseOrGrid-nRnd Generated is a Bit Confusing

Thank you for pointing this out! We clarify the label definitions as follows:

• Label 0: The graph contains neither houses nor grids.
• Label 1: The graph contains (a) only houses, (b) only grids, (c) an equal number of houses and grids.

We do not consider cases where houses and grids appear simultaneously in different quantities, as this would introduce significant combinatorial complexity. To ensure a balanced dataset and avoid potential bias in model training or evaluation, we first guarantee that the number of graphs with label 0 and label 1 is equal. Furthermore, within label 1, we generate an equal number of graphs for conditions (a), (b), and (c), so as to maintain a stable and unbiased distribution across subcategories.

Q2: Are the Assumptions in Theorem 3.5 Realistic for Real-world Graphs?

We consider the assumptions made in Theorem 3.5 to be reasonably realistic for a range of real-world graphs, especially in structured domains such as molecular graphs. For instance, in datasets like MUTAG and BENZENE, there often exists a relatively small rationale subgraph (e.g., a specific functional group) embedded within a larger graph, which aligns well with our assumption of a distinguishable and minimal rationale G_X​.

Our theoretical assumptions, while idealized, significantly relax the strict conditions required by previous works, making our method theoretically better suited for handling variable rationale structures. Empirical evidence strongly supports the practical validity of these assumptions. Specifically, previous works (e.g., GSAT, GMT, DIR) assume that within each category, the corresponding rationale substructure is globally invariant across the entire data distribution—a much stronger and less practical condition compared to ours. This stricter requirement explains why existing methods struggle with variform rationales.

Regarding more real-word dataset

We acknowledge requests for additional real-world datasets. However, graph interpretability requires not just graph labels, but also ground-truth rationale annotations identifying causal subgraphs. The scarcity of such comprehensively labeled datasets is a recognized challenge in this field (Zhang et al., 2024). Our experiments follows established benchmarking practices. Furthermore, we have tested out-of-distribution (OOD) generalization by training TopInG on BA-HouseOrGrid-nRnd with fixed motif count (n=4) and testing on varying counts (n=2,3,5,6). Despite the distribution shift, TopInG maintains stable prediction and interpretability performance without degradation, as shown in Figure 14 (Appendix).

To further mitigate the concern, here we conducted an additional experiment on MNIST-75sp [1]. This dataset contains noisy rational subgraphs with more complex and varied topologies.

[1]Knyazev, B., Taylor, G. W., and Amer, M. R. Understanding attention and generalization in graph neural networks. In Advances in Neural Information Processing Systems, pp. 4204–4214, 2019.

Our results, with details in the table below, show that TopInG achieves the best interpretation and good prediction scores compared to existing SOTA methods. This suggests that our topological signal contributes meaningfully to explanation quality, even when tested on a real-dataset with more complex and noisy varing rationale subgraphs.

Regarding the typo of 'variiform'

Thank you for pointing this out. We will correct the spelling.

Post-hoc methods missing for Fig3 experiment

We prioritized comparing interpretable methods (DIR, GSAT, GMT) since our work specifically addresses the variform rationale challenge observed in these approaches. Post-hoc methods show diverse performance on BA-HouseOrGrid dataset, suggesting this is not neccessarily a common challenge across post-hoc methods. We tested MAGE on the dataset BA-HouseOrGrid-nRnd for n=(2,3,4), and observed that MAGE has consistent performance close to 100%. It indicates that post-hoc methods like MAGE are not very sensitive to the variation of rationale structures.

Regarding the notations in Fig.1

To improve its readability and self-containment, we will revise the figure caption to explicitly define all notations used, including:

• F, which denotes the filtration applied to the graph.

• T, which refers to the resulting topological invariant (e.g., persistence diagram).

We sincerely appreciate your thorough review and invaluable feedback. Below, we provide detailed responses to all your comments or concerns.

Regarding the weakness "Persistent homology computation is computationally intensive on large-scale graphs."

For larger graphs, we have mentioned several promising directions for speedup the computation, in Appendix D. For example: (1) Development of efficient GPU implementations. (2) Using carefully designed GNN models to approximate persistent homology computations.

Regarding more real-world dataset evaluation

We acknowledge requests for more real-world datasets. However, graph interpretability requires not just graph labels, but also ground-truth rationale annotations identifying causal subgraphs. The scarcity of such comprehensively labeled datasets is a recognized challenge in this field (Zhang et al., 2024). Our experiments follows established benchmarking practices. Furthermore, we have tested out-of-distribution (OOD) generalization by training TopInG on BA-HouseOrGrid-nRnd with fixed motif count (n=4) and testing on varying counts (n=2,3,5,6). Despite the distribution shift, TopInG maintains stable prediction and interpretability performance without degradation, as shown in Figure 14 (Appendix).

To further mitigate the concern, we conducted an additional experiment on MNIST-75sp [1], which contains noisy rational subgraphs with richer topologies.

[1]Knyazev, B., Taylor, G. W., and Amer, M. R. Understanding attention and generalization in graph neural networks. In Advances in Neural Information Processing Systems, pp. 4204–4214, 2019.

Our results (table below) show that TopInG achieves the best interpretation and good prediction scores compared to existing SOTA methods. This suggests our topological signal contributes meaningfully to explanation quality, even when tested on a real-dataset with more complex and noisy varing rationale subgraphs.

Regarding "The method requires simultaneous optimization of multiple loss components and the adjustment of several hyperparameters, which may increase engineering complexity and tuning burden in practical applications."

We appreciate the reviewer's concern regarding the potential complexity introduced by optimizing multiple loss components and tuning associated hyperparameters. While this may appear to increase the engineering burden in theory, in practice, we fixed most hyperparameters across all datasets without extensive tuning. Despite this, TopInG consistently achieved strong performance, suggesting that the method is not heavily sensitive to hyperparameter choices, and the additional loss components can be integrated in a stable manner.

We believe this demonstrates that while the design includes multiple components, the practical tuning burden is low, and the framework remains accessible for real-world applications.

Regarding "There are also studies about rationalization in the field of NLP. Would it be possible to discuss some of them in the related work?"

We appreciate the reviewer's suggestion to incorporate discussions on rationalization studies from the Natural Language Processing (NLP) domain into our related work section. Incorporating insights from NLP rationalization studies inspire advancements in graph-based interpretability methods.​

Rationalization has been extensively studied in NLP literature, emphasizing causal feature selection, faithful rationale-input alignment, and stable training dynamics. Recent advances include alternatives to the maximum mutual information (MMI) criterion, highlighting input utilization and causal feature isolation [1,2,4]. Other studies enhance rationale fidelity by enforcing semantic alignment with original inputs [3], and propose methods to stabilize joint rationale-predictor training through asymmetric learning rates, multi-generator ensembles, and unified encoders [5,6,7]. However, unlike NLP domains where rationales often manifest as contiguous text spans, graph domains often exhibit "variform rationale subgraphs" that can differ significantly in form, size, and topology even among instances of the same class.

We will include a brief discussion in the related work section to acknowledge related NLP studies.

Clarifications and Corrections

We thank the reviewers for their detailed feedback and appreciate the opportunity to clarify a few misunderstandings and highlight concerns already solved in our Appendix:

• BA-2Motifs do include cycles in their rationale subgraphs. All datasets used in our work contain complex topological structures.
• MUTAG graphs contain cycles, even if the rationale subgraphs may not. Appendix E.5 contains illustrative examples of every dataset we used.
• "overfitting" refers to poor generalization from training to test data, which does not fit the content since all scores we reported are based on test data. We discuss a more related topic called "out-of-distribution (OOD) generalization" in Q1 below.
• The formula "\mathcal{L}{\text{topo}} \leq W{\text{GH}}(\mathbb{P}, \mathbb{Q})" is not from our submitted manuscript.

Methodological Notes

• GSAT’s hyperparameter r is tunned following author-recommended strategy: initially set to 0.9 and gradually decay to 0.7 (Appendix E.3, line 892).
• Additional ablation studies are provided to support the impact of topological discrepancy vs. Gaussian(Appendix E.3, Table 5).
• Backbone choices have been discussed in Appendix E.3 line 914.

Q1: To evaluate on more Real-World Datasets

We acknowledge requests for more real-world datasets. However, graph interpretability requires not just graph labels, but also ground-truth rationale annotations identifying causal subgraphs. The scarcity of such comprehensively labeled datasets is a recognized challenge in this field (Zhang et al., 2024). Our experiments follows established benchmarking practices. Furthermore, we have tested OOD generalization by training TopInG on BA-HouseOrGrid-nRnd with fixed motif count (n=4) and testing on varying counts (n=2,3,5,6). Despite the distribution shift, TopInG maintains stable prediction and interpretability performance without degradation, as shown in Figure 14 (Appendix).

To further mitigate the concern, we conducted an additional experiment on MNIST-75sp [1], which contains noisy rational subgraphs with richer topologies.

[1]Knyazev, B., Taylor, G. W., and Amer, M. R. Understanding attention and generalization in graph neural networks. In Advances in Neural Information Processing Systems, pp. 4204–4214, 2019.

Our results (table below) show that TopInG achieves the best interpretation and good prediction scores compared to existing SOTA methods. This suggests our topological signal contributes meaningfully to explanation quality, even when tested on a real-dataset with more complex and noisy varing rationale subgraphs.

Q2: Test on Graphs with Conflicting Topologies

TopInG is evaluated on the two datasets, SPMotif (synthetic) and MUTAG (real-world), which include non-informative or spurious cycles irrelevant to labels. The experiment results (Table 1) confirm that our model is robust.

Q3: Regarding Theorem 3.5

Our theoretical assumptions in Theorem 3.5, while idealized, significantly relax the strict conditions required by previous works, making our method theoretically better suited for handling variable rationale structures. Empirical evidence strongly supports the practical validity of these assumptions. Specifically, previous works (e.g., GSAT, GMT, DIR) assume that within each category, the corresponding rationale substructure is globally invariant across the entire data distribution—a much stronger and less practical condition compared to ours. This stricter requirement explains why existing methods struggle with variform rationales. We would greatly appreciate it if the reviewer could clarify the intended meaning of "overfitting risks" in the context of |E_X| \ll |E_\epsilon|. As we mentioned before in "Clarifications", "overfitting" does not fit the content. Additionally, the inequality |E_X| \ll |E_\epsilon| is covered by the weaker assumption |E_X| < |E_\epsilon| used in our theorem. Moreover, in our experiments, nearly all datasets tested exhibit the property that rationale subgraphs are significantly smaller than the full graphs (e.g. |E_\epsilon| > 10*|E_X|). TopInG consistently performs well across these scenarios, further supporting that the assumptions underlying Theorem 3.5 do not limit its practical utility.

Q4: How Sensitive are TopInG’s Gains to Backbone Choices?

As disucussed in Appendix E.3, TopInG performs more robustly with backbones that preserve topological structures (e.g., CIN). Some backbones like GCN and GAT can struggle with interpretability or prediction, as noted in (Bui et al., 2024).

Q5: What Specific Strategies Would Address the Scalability Challenges?

For larger graphs, we have mentioned several promising directions for speedup the computation, in Appendix D line 807.

We sincerely appreciate your thorough review and invaluable feedback. Below, we provide detailed responses to all your comments or concerns.

Q1: Evaluation on Datasets with Hierarchical Rationales

We appreciate the reviewer's insight into the importance of hierarchical rationales in interpretable graph neural networks. Indeed, this is an emerging area with significant potential. However, graph interpretability requires ground-truth rationale annotations, and such comprehensively labeled datasets are scarce (Zhang et al., 2024). Our experiments follow established benchmarking practices. Furthermore, we tested out-of-distribution (OOD) generalization by training TopInG on BA-HouseOrGrid-nRnd with fixed motif count (n=4) and testing on varying counts (n=2,3,5,6). TopInG maintains stable performance across these distribution shifts, as shown in Figure 14."

Regarding more real-word dataset

To further demonstrate the practical applicability of TopInG on real-world tasks, we conducted additional experiments on the MNIST-75sp dataset [1], which is widely used for evaluating graph-based models on visual tasks. In this dataset, each MNIST image is converted into a superpixel graph, where nodes correspond to superpixels and edges represent spatial adjacency. Nodes with nonzero pixel values provide ground-truth explanations, making it suitable for evaluating interpretability methods.

This dataset consists of 60,000 graphs for training and 10,000 for testing, with an average of 70.57 nodes and 590.52 edges per graph. Notably, the ground-truth explanatory subgraphs vary in size across samples, adding to the challenge. We trained all models for 30 epochs on a single RTX 4090 GPU (over 26 hours). For TopInG, we used default hyperparameters and only reduced the coefficient of the topological loss, without extensive tuning.

The table below presents both interpretation and prediction performance:

As shown, TopInG achieves the best interpretability performance (AUC = 84.50) while maintaining competitive prediction accuracy. This result demonstrates TopInG's strong potential for real-world graph-based tasks involving complex, variable-sized explanations.

[1]Knyazev, B., Taylor, G. W., and Amer, M. R. Understanding attention and generalization in graph neural networks. In Advances in Neural Information Processing Systems, pp. 4204–4214, 2019.

Q2: Runtime Efficiency of the Proposed Framework

We appreciate the reviewer's concern regarding the runtime efficiency of our framework. In Appendix D, we provided a theoretical analysis of the runtime complexity. In brief, the time complexity can be as fast as O(nlogn), without considering GPU acceleration. Practically, we provide representative results on two datasets to give a sense of our method's efficiency.

On BA-2Motifs, each training epoch takes approximately 0.45 ± 0.12 minutes, and on SPMotif (which is a more complex and larger dataset), the runtime is approximately 9.20 ± 2.35 minutes per epoch. All experiments were conducted on a single RTX 4090 GPU, and importantly, our method consistently converges within 20 epochs across all datasets.

Although our method is relatively slower per epoch due to the incorporation of TDA, this added cost is justified by the significant performance gains. Unlike many baseline models that typically require 50 to 100 epochs to converge, TopInG achieves convergence within 20 epochs, while consistently achieving perfect or near-perfect AUC scores on multiple datasets.

We hope this additional information clarifies the practical efficiency of our approach.

Regarding PersGNN:

Thank you for providing the reference. We will mention this work in the revised version. As a related work, PersGNN applies TDA to analyze the structure of protein graphs by combining persistent homology with GNNs to capture both local and global structural features for improved protein function prediction. While our work focuses on leveraging TDA to enhance the interpretability of GNN models through persistent rationale filtration, PersGNN primarily aims to improve prediction performance on protein structure-function relationships via a novel TDA-enhanced GNN architecture. This distinction highlights complementary applications of topological methods in graph learning.