Paper: GNNX-BENCH: Unravelling the Utility of Perturbation-based GNN Explainers through In-depth Benchmarking (ICLR-2024)

Reviewer comment (Experiments):
Whether adversarially adding the number of edges has an impact on the sufficiency of the factual explainers leading to different experimental results in Figure 2 or Table 4

Author response:
**Q1. Whether adversarially adding the number of edges has an impact on the sufficiency of the factual explainers leading to different experimental results in Figure 2 or Table 4.**

*Response:* We have extended our stability experiments to more datasets for feature perturbation and adversarial attacks (Figures G and H, respectively). The behavior is similar to the topological noise attack explained in Section 4.2; the stability decays with the higher noise and inductive methods handle noise better than transductive.

As requested, we also provide a sufficiency score with explanations generated by the topological noise attack. The results are provided in Figure F. In summary, when the noise increases, the sufficiency drops for most cases, but not in all scenarios. This shows that despite the changes in the explanations caused by the noise, GNNs may still predict the same class under noisy conditions.

Reviewer comment (Evaluation):
Most experimental results do not seem to provide explanations about the experimental phenomena and comparisons of the advantages and disadvantages of different explanation methods. For example, why the stability of CF^2 has dropped significantly on the IMDB-B and AIDS datasets in Fig. 3.

Author response:
**Q2. Most experimental results do not seem to provide explanations about the experimental phenomena and comparisons of the advantages and disadvantages of different explanation methods. For example, why the stability of CF^2 has dropped significantly on the IMDB-B and AIDS datasets in Fig. 3.**

*Response:* We appreciate this feedback and now provide clear insights on trends observed across the experiments in the revised manuscript. CF^2 is a transductive method. This lies at the core of the trends observed. Specifically, transductive methods lack generalizable capability to unseen data. Furthermore, the stability is worse on denser datasets such as IMDB-B since due to the presence of more edges, the search space of explanation is larger. Transductive methods such as CF^2 and GNNExplainer witness higher deterioration in stability in such harder situations due to being transductive.

Reviewer comment (Experiments):
For the experimental results of stability against topological noise, why are the GEM and SubgraphX not used.

Author response:
**Q3. For the experimental results of stability against topological noise, why are the GEM and SubgraphX not used.**

*Response:* We have updated Fig. 3 by adding GEM and SubgraphX. GEM has two-steps (distillation + generation) and one can add noise in any of these two steps. We have added noise before the distillation step, which makes it comparable to other methods. On the other hand, SubgraphX is time-consuming while providing subpar efficacy in terms of robustness compared to other explainers. For example, SubgraphX consumes $\approx 26.5$ hours to run on 435 test graphs in the Mutagenicity dataset. The inclusion of GEM and SubgraphX in Fig. 3 does not affect our conclusions.

Reviewer comment (Evaluation):
There are differences between different factual explainers on different datasets. Is there a benchmark to select a proper explainers in practice.

Author response:
**Q4. There are differences between different factual explainers on different datasets. Is there a benchmark to select a proper explainers in practice.**

*Response:* This is an excellent question and is the ultimate objective of this study! The choice of the explainer depends on various factors and we make the following recommendations. We have now added a flowchart to help the user in selecting the most appropriate. This recommendation has now also been added as a flowchart (Fig. S in App. K). The same flowchart is presented in text below. We have added this discussion in the manuscript (App. K). We have also referred this discussion in the conclusions (Sec. 5).

- For counter-factual reasoning, we recommend RCExplainer for graph classification and CF-GNNExplainer for node classification. 
- For factual reasoning, if the goal is to do node or graph classification, we need to first decide if we need an inductive reasoner or transductive. While an inductive reasoner is more suitable, we want to generalize to large volumes of unseen graphs, transductive is suitable for explaining single instances. In case of inductive, we recommend RCExplainer, while for transductive GNNExplainer stands out as the method of choice. These two algorithms had the highest sufficiency on average. In addition, RCExplainer displayed stability in the face of noise injection.  
- For different task generalization beyond node and graph classification, one can consider using TAGExplainer.
- In high-stakes applications, we recommend RCExplainer due to consistent results across different runs and robustness to noise.
- If computation time is important, we recommend an inductive reasoner since they only involve a forward pass through the corresponding neural network. Transductive reasoners train the parameters on the input and hence is significantly slower in practice.

While the above is a guideline, we emphasize that there is no one-size-fits-all benchmark for selecting the ideal explainer. The choice  depends on the characteristics of the application in hand and/or the dataset. The above flowchart takes these factors into account to streamline the decision process.

Reviewer comment (Evaluation):
The conclusions from the empirical comparison are not clear. It would be better to summarize the conclusions from the empirical comparison and provide conceptual insights, such as how would the results guide the future design of GNN explanation methods.

Author response:
**Q1. The conclusions from the empirical comparison are not clear. It would be better to summarize the conclusions from the empirical comparison and provide conceptual insights, such as how would the results guide the future design of GNN explanation methods.**

*Response:* This is an excellent suggestion. We appreciate the constructive feedback. To incorporate this suggestion, we have now made the following changes. 

* The conclusion section (Section 5) has been expanded to discuss research directions that may potentially yield solutions to the primary limitations identified in this study, namely - incorporating *generative modeling* in counterfactual reasoning to address feasibility concerns, and migrating towards *ante-hoc* reasoning to address instability and non-reproducibility. Current explainers are post-hoc in nature, wherein the explanations are generated post the completion of GNN training. In this pipeline, the explainers have no visibility to how the GNN reacts to perturbations on the input data, initialization seeds, etc. In the *ante-hoc* paradigm, the GNN and the explainer are jointly trained.
*  For each experiment, we have added a paragraph titled "Insights" to clearly discuss the take-aways and provide explanations for the trends observed.

Reviewer comment (Presentation):
Discussion of the existing works needs more structure. Current discussion of the related works are based on the summary for each method. It would be better to provide more structures of the current works, such as what methods the existing ones share in common.

Author response:
**Q2. Discussion of the existing works needs more structure. Current discussion of the related works is based on the summary for each method. It would be better to provide more structures of the current works, such as what methods the existing ones share in common.**

*Response:* We have incorporated this suggestion through the following mechanisms:
* Tables 1 and 2 characterize different factual and counterfactual methods, respectively, along various dimensions such as scoring function, intended task (such as graph/node classification), modeling paradigm (transductive vs. inductive), etc. Through these tables, it is now easy to derive the common principles shared across algorithms.
* We have also re-structured the related work discussion (Sec. 2.1) based on these tables to better elucidate the common design principles and enable easier abstraction of their conceptual designs.

Reviewer comment (Evaluation):
It would be better to clearly define how the sufficiency score is computed.

Author response:
**Q3. It would be better to clearly define how the sufficiency score is computed.**

*Response:* We have added the mathematical formulation of sufficiency as well as all other metrics used in our work (See Table 3 in the revised manuscript). The relevant portion is reproduced verbatim below.

Sufficiency encodes the ratio of graphs for which the prediction derived from the explanation matches the prediction obtained from the complete graph.

$$
    \text{Sufficiency}(\mathcal{S}) = \frac{\sum_{i=1}^{|\mathbb{G}|} \mathbb{1}(\Phi({\mathcal{G}_S^i}) = \Phi(\mathcal{G}^i))}{|\mathbb{G}|}
$$

$$
    \text{Necessity}(\mathcal{N}) = \frac{\sum_{i=1}^{|\mathbb{G}|} \mathbb{1}(\Phi(\mathcal{R}^i) \neq \Phi(\mathcal{G}^i))}{|\mathbb{G}|}
$$

$$
    \text{Stability}(\mathcal{E}_X, \mathcal{E}'_X) = \frac{\vert\mathcal{E}_X\cap\mathcal{E}'_X\vert}{\vert\mathcal{E}_X\cup\mathcal{E}'_X\vert}
$$

$$
    \text{Reproducibility}^{+}(\mathcal{R^+}) = \frac{ACC(\Phi_S)}{ACC(\Phi)}
$$

$$
    \text{Reproducibility}^{-}(\mathcal{R^-}) = \frac{ACC(\Phi_R)}{ACC(\Phi)}
$$

- $\mathbb{G} = \{\mathcal{G}^1, \mathcal{G}^2, \dots, \mathcal{G}^n\}$, the set of all graphs.
- ${\mathcal{G}^i_S}$ is the explanation subgraph of $\mathcal{G}^i$ 
- $\mathbb{G}_S = \{\mathcal{G}^1_S, \mathcal{G}^2_S, \dots, \mathcal{G}^n_S\}$ is the set of explanations.
- $\mathcal{R}^i = \mathcal{G} - \mathcal{G}^i_S$
- $\mathbb{R} = \{\mathcal{R}^1, \mathcal{R}^2, \dots, \mathcal{R}^n\}$ is the set of residual graphs.
- $\Phi$, $\Phi_S$, and $\Phi_R$ are the models trained on $\mathbb{G}$, $\mathbb{\mathbb{G}}_S$, and $\mathbb{\mathbb{R}}$, respectively. All models are trained on the same labels.
- $\Phi(\mathbb{G}^i)$ is the model's prediction on $\mathbb{G}^i$.
- $\mathcal{E}_X$ and $\mathcal{E}'_X$ are the set of edges in the explanations on the original graph and after noise injection.
- $ACC(\Phi)$ is the test accuracy of the model $\Phi$.

Reviewer comment (Evaluation):
Do the authors have any explanation for why the RCExplainer and the GNNExplainer have the highest sufficiency scores? It would be helpful to provide a more structured and conceptual comparison between the explanation methods.

Author response:
**Q4. Do the authors have any explanation for why the RCExplainer and the GNNExplainer have the highest sufficiency scores? It would be helpful to provide a more structured and conceptual comparison between the explanation methods.**

*Response:* GNNExplainer is transductive, wherein it trains the parameters on the input graph itself. In contrast, inductive methods use pre-trained weights to explain the input. Consequently, transductive methods, such as GNNExplainer, at the expense of higher computation cost, has an inherent advantage in terms of optimizing sufficiency. Compared to other transductive methods, GNNExplainer utilizes a loss function that aims to increase sufficiency directly. This makes the method a better candidate for sufficiency compared to other inductive and transductive explainers. On the other hand, for RCExplainer, we believe that calculation of decision regions for classes helps to increase its generalizability as well as robustness. Finally, as a trend, both methods provide consistent sufficiency increase with the size of explanations for all datasets, while we observe an oscillation in sufficiency in Mutag for other explainers. This makes RCExplainer and GNNExplainer more reliable as well.

We have incorporated the above discussion while analyzing the sufficiency results in Fig. 2.

Reviewer comment (Experiments):
What is the definition and scale of the noise shown in Figure 3?

Author response:
**Q5. What is the definition and scale of the noise shown in Figure 3?**

*Response:* In Figure 3, the xticks (Noise) denote the number of perturbations made to the edge set of the original graph. Here, perturbations include randomly sampling $x$ (denoted on x-axis) negative edges and adding them to the original edge set (i.e., connect a pair of nodes that were previously unconnected). We now mention this explicitly in the caption of Fig. 3. 

We note that we also explore adding noise through adversarial attack, where edges are both removed and added. These experiments are in Appendix C.

Reviewer comment (Novelty):
Lack of creativity and significance: The authors conducted an evaluation to measure many explainers' performances, but did not come up with a novel solution to overcome the discovered challenges. Also, the conclusions are not insightful enough with further analysis. Based on this reason, it is hard to regard this paper as a research paper.

Author response:
**Q1. Lack of creativity and significance: The authors conducted an evaluation to measure many explainers' performances, but did not come up with a novel solution to overcome the discovered challenges. Also, the conclusions are not insightful enough with further analysis. Based on this reason, it is hard to regard this paper as a research paper.**

*Response:* The Call for Papers for ICLR 2024 includes 'Datasets and Benchmarks' (refer to https://iclr.cc/Conferences/2024/CallForPapers), and our submission falls within this category. Benchmarking papers are not anticipated to present novel solutions; rather, the focus is on conducting a comprehensive empirical evaluation in a relevant area and offering fresh insights previously undiscovered. It is a reasonable expectation from a benchmarking paper to propose potential directions for addressing identified limitations, as we have done in Section 5. Based on the suggestions provided, we have further expanded our discussion on potential solutions in the revised manuscript.

Reviewer comment (Presentation):
Poor layout: The layout of words and tables is too dense, such as Table 1, 4, 5, and 8. Numbers inside table are too small and hard to read.

Author response:
**Q2. Poor layout: The layout of words and tables is too dense, such as Table 1, 4, 5, and 8. Numbers inside table are too small and hard to read.**

*Response:* We appreciate this constructive feedback. We have thoroughly revisited all sections of the paper and have ensured the fonts are large enough to be comfortably legible in the revised manuscript. We have also increased spacing around tables. We hope these changes have effectively addressed the presentation-related concerns.

Reviewer comment (Novelty):
Authors may want to try to offer some new solutions to the discovered limitations of existing GNN explainers. Finding out these limitations is just a start of a research work. For instance, the feasibility concerns about counterfactual explainations appear due to the deviations in topological distribution. Authors can keep working in this direction and find out some methods to improve feasibility.

Author response:
Dear Reviewer,

Since we are only a day away from the completion of the discussion phase, we are eagerly awaiting your feedback on the revised manuscript. We have addressed all of the presentation related concerns and present a significantly expanded discussion on potential solutions to the previously undiscovered shortcomings of the explainability methods with regards to stability, feasibility and reproducibility.

Finally, we wish to clarify again that our submission has been made to the Dataset and Benchmark category of ICLR.

Please do let us know if there are any additional clarifications or experiments that we can offer. We would love to discuss more if any concern still remains. Otherwise, we would appreciate it if you could support the paper by increasing the score.

regards,

Authors