TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring substructures within the graph, known as temporal motifs. Despite the success and prevalence of current temporal graph neural networks (TGNN), it remains uncertain which temporal motifs are recognized as the significant indications that trigger a certain prediction from the model, which is a critical challenge for advancing the explainability and trustworthiness of current TGNNs. To address this challenge, we propose a novel approach, called Temporal Motifs Explainer (TempME), which uncovers the most pivotal temporal motifs guiding the prediction of TGNNs. Derived from the information bottleneck principle, TempME extracts the most interaction-related motifs while minimizing the amount of contained information to preserve the sparsity and succinctness of the explanation. Events in the explanations generated by TempME are verified to be more spatiotemporally correlated than those of existing approaches, providing more understandable insights. Extensive experiments validate the superiority of TempME, with up to 8.21% increase in terms of explanation accuracy across six real-world datasets and up to 22.96% increase in boosting the prediction Average Precision of current TGNNs.

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Peer review

Reviewer U22B6/10 · confidence 4/52023-06-24

Summary

The work presents TempME, an explanation methodology for temporal graph neural networks that incoporates the idea of temporal motifs. By incoporating temporal motifs, the method demonstrates better cohesiveness, since motifs are constructed to be cohesive, i.e., connected and localized, as well as better explainability compared to prior explainability works.

Strengths

- The work presents an excellent contribution to TGNN explainability by proposing the use of temporal motifs. - The work presents solid technical material to support the proposed methodology. - The work further presents good and extensive results that covers many interesting aspects.

Weaknesses

There are some unclarity in the paper. In particular, the goal of the evaluation and the evaluation setting for the explanation performance is not clear. In particular, the statement "ACC-AUC, which is the AUC value of the proportion of generated explanations that have the same predicted label by the base model over sparsity levels from 0 to 0.3" is hard to comprehend. Currently, the reviewer thinks that: - "generated explanations" are the explanation subgraphs extracted by the expalantion models. - "sparcity level" idicates the ratio of sizes between the the extracted explanation subgraph and the whole temporal graph - perhaps the "predicted label by the base model" is the prediction of the event/edge that the original target model gives when given the extracted explanation subgraph? It could be clearer if at Section 3, it is noted that the budget "K" will be represented as "sparsity" and the objective of Equation 1 is spelled out more intuitively. Besides: - The inline equation for "Fidelity" has typos and the paranthesis does not match up. It also lacks intuitive explanations. Besides, it seems that Fidelity follows that constructed by TGNNExplainer, and a proper citation should be given. - norm of the gradient being utilized for Grad-CAM is essential to understanding the treatment of baseline and should be stated in the main paper. Miscellaneous: The figures (especially the color shades and the lighter colors, when printed out) is not clear.

Questions

Regarding the motivation for presenting an explanation subgraph for TGNN: While with image instances we can verify that the important regions (e.g. highlighted by grad-cam) coincide with semantically meaningful regions in an image using human intuition and understanding, it is unclear if human intuition or logic can be applied to temporal graphs. - Can you provide examples of human intuition or logic applied to temporal graphs? For example, with certain datasets, observing some part of the temporal graph would lead to a understanding on whether some target event should or should not exist. - Can you provide examples of the explanation subgraph presented by TempME and show how such explanation subgraph provides "human intelligible explanation" as stated in line 38? - Can you provide examples of the explanation subgraph presented by TGNNExplainer and Grad-CAM, as well as other baselines, to show how they do not present "human intelligible explanation"?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The paper presents some technical limitations but the discussions on potential negative societal impact could be strengthened by discussing the potential real-world application of explaining TGNNs.

Reviewer NnW17/10 · confidence 3/52023-06-26

Summary

This paper provides a method to extract temporal motifs in order to capture correlated building blocks of networks.

Strengths

The method of extracting temporal motifs is interesting; it is based on information theoretic concepts.

Weaknesses

In my view there are two main weaknesses of this paper. The first weakness is the underlying assumption that network motifs should consist of nodes and edges which are in close time proximity to each other. This assumption is not questioned but often does not hold, as there are often seasonal effects in network time series. These seasonal effects could occur for example only once per week, as Sundays may be special in terms of network behaviour. The second weakness is the presentation. It is stated that the method is in a continuous-time setting, but the events occur at separated time points from the description; there does not seem to be the possibility of having more than one event occurring simultaneously. The large number of questions below indicate that the paper may not be very clearly written. The paper aims to provide an explanation of temporal GNNs; it would be good to see a worked example in which explanation relates to a tangible real-world scenario. Which are the motifs that are found in the different networks? How can they be viewed as builing blocks of these networks; do they point towards fundamental differences between, say, the Wikipedia network and the Enron network? There is a start at this question in the supplementary material E.5 but the analysis may strongly depend on the chosen prior. Finally, the discussion from the supplementary information Section F should have been in the main text.

Questions

It is not clear to me what the mutual information is between a random variable and a graph. Are temporal motifs allowed to overlap each other? Why is there no time component in Figure 1? The elements in the edge set contain an event attribution but the motif definition ignores this event attribution. Why? In Definition 1 why is u_0 = u_1 set ? What is the induced subgraph? What is the graph that this is a subgraph of? If this underlying graph is the union of all temporal graphs, then does it have multiple edges or self-loops? Definition 2: When do two motif instances have the same topology? Is it their induced subgraph that has the same topology? Again, what happens to mutiple edges? Why can the motif of preferential attachment not be represented as a temporal walk? What are `surrounding' motifs in Section 4.2.? Temporal motif encoding: what is T ( t - t_{pq}) ? What is N(p)? Is there an underlying graph with a fixed number of nodes and a fixed topology? Is that a simple graph? How is an importance score generally obtained? It is a crucial ingredient of the method. In Section 5.2 it is stated that ``TempME still surpasses all baselines and achieves the highest connectivity levels, primarly due to it ability to extract and utilize self-connected motifs'' ; how does self-connectedness enter here? what it meant by that? Why is the discussion from the supplementary information section F not in the main text? Is it not important?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The paper discusses limitations only in the supplementary material. Clearly the choice of null model may have a major influence on the analysis, as does the choice of prior.

Reviewer HiZ76/10 · confidence 4/52023-06-27

Summary

TempME is an inductive explainer for temporal graph neural networks (TGNNs) over link prediction tasks. It explains TGNNs using temporal motifs, guaranteeing temporally proximate and spatially adjacent explanations, hence more human interpretable. TempME’s pipeline can be broken down into three parts: sampling, embedding, and explaining. Given a link prediction instance, candidate motifs are sampled starting at either end of the edge. The motifs go through a series of steps to generate rich motif embeddings that encode the event's spatial and temporal roles. An MLP learns a Bernoulli distribution over the embeddings. The distribution is used to mask out the best explanation motifs from the candidates. The MLP is trained using the information bottleneck principle to keep the explanations succinct. The mutual information between the predicted label and the explanation is maximized, while the mutual information between the explanation motifs and the set of candidate motifs is minimized. TempME can also boost a model’s performance. The authors show improved results across datasets by concatenating the aggregation of the motif embeddings around a node of interest prior to a model’s final MLP layer.

Strengths

1. Unlike prior work that measures the impact of singular events, TempME measures the combined effect of events on the black box prediction. 2. Cohesive explanations are more human-interpretable than non-cohesive ones. 3. It has significantly less computational cost compared to previous TGNN explainers. 4. It can generalize to unseen nodes, which is highly desirable. 5. The identified motifs can be utilized during training to boost model performance.

Weaknesses

1. The authors have not experimented with synthetic datasets even though they are available. In graphs, the ground truth explanation is often unknown. Hence, synthetic graphs are vital to ascertain that the explanations comply with the ground truth. Please refer to the following for the synthetic datasets and their case study: *Xia, Wenwen, et al. "Explaining temporal graph models through an explorer-navigator framework." The Eleventh International Conference on Learning Representations. 2022.* 2. The authors have cited the following paper as prior work but have not used it as a baseline. *Wenchong He, Minh N Vu, Zhe Jiang, and My T Thai. An explainer for temporal graph neural networks. In GLOBECOM 2022-2022 IEEE Global Communications Conference, pages 462 6384–6389. IEEE, 2022.* Please either compare or provide a justification for not including as a baseline. 3. The authors have compared with GNNExplainer and PGExplainer for comparison with static graph explainers. However, these are no longer state-of-the-art (SOTA) explainers for static graphs. Table 1 and Fig 3 show that GNNExaplainer and PGExplainer are competitive. Using SOTA static graph explainers might have yielded even better results for static explainers and led to different insights. A comparison with the following will be more fruitful: * *Tan, Juntao, et al. "Learning and evaluating graph neural network explanations based on counterfactual and factual reasoning." Proceedings of the ACM Web Conference 2022. 2022.* * *Yaochen Xie, Sumeet Katariya, Xianfeng Tang, Edward Huang, Nikhil Rao, Karthik Subbian and Shuiwang Ji. Task-agnostic graph explanations. NeurIPS, 2022.* 4. Please provide the hardware details of the experimental setup. 5. Please provide TempME’s training time as well. It is good to have fast inference, and at the end of the day, inference is what matters, but a user should also have an idea of how long it takes to train. 6. The reference for GINE is correct; however, it does not explicitly use the term GINE in it, which may make it difficult for future readers to refer to. Please add a citation that uses the term GINE explicitly. 7. Pip throws an error when using the author’s requirements.txt to setup the experimental environment. 8. Some typos and grammar mistakes: * 158, 622: denotes -> denoted * 190: in this work (unnecessary) * 278: In meanwhile -> Meanwhile

Questions

Overall, I like the paper. I am open to increasing the score if the authors address the weaknesses listed above and address the questions below. * Since we are trying to explain the black box and not the data, what if the black box is prioritizing the distant edges? In that case, will TempME force the explanation to be cohesive? * The authors state the use of a “generative model”. However, it is not found anywhere. The term “generative” brings VAEs and probabilistic graph models to mind, a model that can generate new graph instances that follow a specific distribution or capture the underlying patterns and characteristics of the observed graph data. There is no graph generation involved. Sampling is different from generating. What exactly do the authors mean by a “generative model”? Is it just the ability to generalize to unseen nodes? In that case, the authors should change the terminology as it is misleading. * In line 194, are C motifs sampled from both u and v, totalling 2C?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

4 excellent

Contribution

3 good

Limitations

Yes, the authors have addressed the limitations in the appendix.

Reviewer M5gq5/10 · confidence 4/52023-07-31

Summary

This paper proposes an approach, Temporal Motifs Explainer (TempME), to find out key sub-graph structures from temporal graph neural networks (TGNNs) that mostly influence the prediction for a better ability of explanation. It employs an generative approach including the steps, motif extraction and sampling, to retrieve the structures with explainability. Experiments show that the proposed TempMe improves the state-of-the-art explainable GNNs and TGNNs in prediction.

Strengths

1. Explainable AI in motif exploration is a promising research field that has not been widely studied. 2. This paper is written in good organization. The motivation and the targeted problem are illustrated clearly. 3. The designed procedure of method is clearly stated as well.

Weaknesses

1. The novelty seems not sufficient as claimed. 2. More related research should be compared in the section of related work. 3. The experimental evidence is not sufficient to support the proposed approaches to address the claimed issues in prior research. Please see the detailed comments in the review block - Questions.

Questions

1. The novelty seems not sufficient. It is claimed as the first work that utilizes temporal motifs for explanation. However, the compared state-of-the-art [23] targeted finding out sub-graph structures of TGNNs for explainability enhancement as well. Therefore, the claimed novelty is questionable. 2. More related research should be compared in the section of related work. Following question 1, it is strongly suggested to state the major differences of targeted research problems from the previous work [23]. In addition, as described in Lines 47-53, there are prior studies employing temporal motifs underlying generative mechanisms as well as the proposed work. The differences of contributions are not clearly illustrated in the manuscript though. Hence, the research value of this paper is inadequate accordingly. 3. The experimental evidence is not sufficient to support the proposed approaches to address the claimed issues in prior research. As stated in Lines 34-36, the existing research [20, 21] has not thoroughly studied the characteristics of temporal graphs, the consequent influence on the prediction and explanation is not clearly stated. Moreover, the research is not compared in the experiments. That is, it lacks experimental evidence to support the improvement under consideration of the temporal information over these works. 4. What is the time complexity of TempMe compared with [13, 14, 23]? Are there any trade-offs between the computational costs and the exploration of key motifs under TempMe?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

1. The proposed approach is validated on the graphs with sparsity levels between 0 and 0.3, i.e., dense graphs with richer information. How about the effectiveness on the graphs with higher sparsity?

Reviewer uwpb6/10 · confidence 3/52023-07-31

Summary

The Explainability of TGNN is essential for human understanding of model prediction results. This paper proposed a framework, TempME, to construct meaningful, cohesive explanations by utilizing temporal motifs. The framework consists of temporal motif extraction, motif encoder, information-bottleneck-based importance score generator, and an explanation process. Benefiting from the information bottleneck principle, TempME can balance the explanation accuracy and compression. Experiments on six real-world temporal graph datasets were conducted with three TGNN backbones. The result shows that the selected temporal motifs not only reason the predictions of the backbones but also enhance their link prediction accuracy.

Strengths

-- Connecting the information bottleneck principle with the temporal motif explanation task is considered novel. -- The experiment results are promising. The TempME achieves up to an 8.21% increase in explanation accuracy across real-world datasets. Besides, up to 22.96% improvement in the performance of TGNNs shows the effectiveness of discovered temporal motifs. -- The author provides comprehensive theoretical analysis and extensive experiments. -- The TempME is efficient in terms of the inference time for producing explanations. -- The paper is well-organized and easy to follow.

Weaknesses

-- The performance of the tempME might be susceptible to temporal motif extractions in the first stage, but fewer discussions on other motif mining algorithms. -- The proposed method assumed temporal motifs can capture the dynamics of the graph, which might not hold for real-world scenarios. For instance, external events or user preferences can also affect the explanations. -- The ACC-AUC of TempME in Table 1. outperforms baselines in most cases. However, the performance improvements of the Enron dataset are not significant. The reviewer also finds the results of the Enron dataset in Table 4. show less improvement in the performance of TGNN models with motif embedding. It would be better to investigate the limitation of the proposed method.

Questions

As stated in the weakness.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The proposed method assumed temporal motifs can capture the dynamics of the graph, which might not hold for real-world scenarios. For instance, external events or user preferences can also affect the explanations.

Reviewer HiZ72023-08-12

Thank you for the clarifications.

Thank you for the clarifications. I raise my rating to weak accept.

Reviewer uwpb2023-08-13

Thank you for your clarifications. I am satisfied with the explanations for the first two concerns. However, I am not sure whether the limited performance improvements in the Enron dataset can be simply attributed to dense temporal interactions. In Table 4, US Legis also has a higher interaction density compared to Wikipedia, UCI, and Reddit, but the improvement is significant. The statement “It might be more challenging to analyze temporal graphs with high interaction density with motifs…” would be more convincing if more evidence were provided.

Authorsrebuttal2023-08-14

Response to Reviewer uwpb

Thanks for keeping up the discussion! Your question has motivated us to further investigate the characteristics of the Enron dataset compared with other datasets used in our experiments. Enron is an email network where interaction events are emails exchanged among employees. After more statistical studies, we observed that there are multiple identical interactions in the Enron dataset. For example, the interaction between Node115 and Node124 at timestamp 533820 recurs four times. On average, each distinct interaction is accompanied by **3.284** exactly identical interactions within this dataset. (Refer to the following table for a comparison of the average occurrences of identical interactions across all datasets) | UCI | USLegis | Wikipedia | Reddit | Canparl | Enron | |-------|---------|-----------|--------|---------|-----------| | 1.001 | 1.007 | 1.000 | 1.000 | 1.000 | **3.284** | While this phenomenon might be deemed reasonable within the context of email networks, wherein multiple emails are dispatched to the same recipient at identical timestamps, it is not a common phenomenon in other datasets and many real-world scenarios. For consistency with existing literature [1,2] we restrict the timestamp of the next sampled event strictly earlier than the previous event, which is also a necessary condition of underlying causality between interactions [1]. Consequently, many identical interactions in the Enron dataset are not sampled within a temporal motif, thereby potentially degrading the performance improvement of TempME over this specific dataset. It is crucial to emphasize that **our proposed algorithm adeptly handles scenarios involving multiple interactions at the same timestamp between different node pairs, as well as multiple interactions between the same node pair but at different timestamps.** However, we restate the limitations we articulated earlier: “One limitation of TempME is analyzing temporal graphs characterized by **high interaction density between the same node pairs at the same timestamp**, such as Enron dataset”. We will add more discussion on limitations. Again, thanks for your attention and discussion. [1]Temporal motifs in time-dependent networks [2]Motifs in Temporal Networks

Reviewer uwpb2023-08-15

Thank you so much for the further investigation. The explanations make sense to me.

Reviewer M5gq2023-08-14

Thanks for the detailed response. Most of the issues are addressed. However, there are some some points should be clarified. 1. Following the response to Q2, it is suggested to clearly state that the studies [24-31] verify the important role of temporal motifs by what kinds of analyses or observation. As a meanwhile, it is strongly encouraged to highlight that this work is developed based on those previous verification results. Otherwise, it is confusing if these prior works utilize the temporal motifs for the enhancement of the explainability of TGNNs as well. 2. For the response to Q3, I understand the focused problems are subtly different. What I am looking forward is to see the improvements after the TGNNs are incorporated with the proposed temporal information. In the personal view, it is essential to compare the explainability of the graphs w/. and w/o the motif-level insights based on the evidence of either experimental or theoretical results. Otherwise, it may be hardly to be convinced that the characteristics of the "found motifs" under the proposed approach has a substantial enhancement of the explainability over those previous approaches without incorporating the temporal information as claimed in the section of related works.

Authorsrebuttal2023-08-14

Response to Reviewer M5gq

We appreciate your time and effort spent! We will definitely adopt your suggestions to further improve paper writing on previous works and intrinsic insights in our revised version. To address your concern and ensure a clearer understanding, we'd like to clarify below. 1. Previous works [24~31] have successfully demonstrated the pivotal role of temporal motifs in unraveling the complexity and dynamics of real-world networks. These traditional methods typically investigate the frequency and statistical distribution of temporal motifs to gain insights into the behavior and evolution of real-world networks. For example, in biological networks, the temporal motifs could help in pinpointing critical events in biochemical reactions. In financial networks, the occurrence of specific triadic motifs is a strong indicator of impending financial crisis, offering predictive insights. Inspired by these real-world applications of temporal motifs, we harnessed the potential of temporal motifs to uncover the decision logic of temporal GNNs, thereby improving their transparency and explainability. 2. Compared with previous methods w/o temporal motifs, the enhancements achieved through the incorporation of temporal motifs are mainly three-fold. - **Accuracy and Fidelity Enhancement:** By integrating temporal motifs, we have observed an explainability improvement. First, the accuracy of generated explanations sees a notable increase. This is substantiated by previous research that demonstrates how temporal motifs can effectively model the evolution of dynamic networks. Moreover, the motif-level information bottleneck principle serves as a foundation, ensuring the generated explanations exhibit both maximized fidelity and minimized sparsity. The empirical evidence presented in *Table 1* and *Figure 3* affirms this positive impact on explanation accuracy and fidelity. - **Human-Intelligible Explanations:** The introduction of temporal motifs imparts a unique property of "cohesiveness" to our explanations. This attribute arises naturally due to the inherent nature of temporal motifs. Through the extraction of interaction-related motifs, the explanations transcend singular events and provide an encompassing view of motif importance. Empirical results on the “cohesive” property are shown in *Table 2*. Visualizations of the explanations w/. motif and w/o motif are provided in our general response (please refer to the *1-page pdf*). - **Link Prediction Performance Enhancement:** The benefits of incorporating motif-level insights extend beyond explainability improvements. It also positively influences the link prediction performance of TGNNs. This enhancement is attributed to the appropriate motif encoding that effectively captures both the spatial and temporal roles of each event. The empirical results in *Table 6* and *Table 9* substantiate the consistent link prediction enhancement across various message-passing-based TGNNs, such as TGAT, TGN, and GraphMixer. Thanks again for your suggestions. ​​We hope that the above clarification improves your confidence in our work. Let us know if you have any further questions/concerns.

Reviewer M5gq2023-08-17

According to the provided strengths and improvements on TGNNs, I raise my rating to borderline accept.

Reviewer U22B2023-08-18

Thank you. I am satisfied with your explanations. However, I maintain my score at weak accept based on the impact of this paper.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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