Causality-Inspired Spatial-Temporal Explanations for Dynamic Graph Neural Networks
Authors: Kesen Zhao
Liang Zhang
Venue: ICLR 2024 poster (2024)
Keywords: Dynamic Graph
Graph Explanation
Graph Neural Network
Causal Inference
Primary area: learning on graphs and other geometries & topologies
TL;DR: To the best of our knowledge, we are the first to explain dynamic graph neural networks.

Abstract: Dynamic Graph Neural Networks (DyGNNs) have gained significant popularity in the research of dynamic graphs, but are limited by the low transparency, such that human-understandable insights can hardly be drawn from their predictions. Although a number of existing research have been devoted to investigating the interpretability of graph neural networks (GNNs), achieving the interpretability of DyGNNs is pivotally challenging due to the complex spatial-temporal correlations in dynamic graphs. To this end, we propose an innovative causality-inspired generative model based on structural causal model (SCM), which explores the underlying philosophies of DyGNN predictions by identifying the trivial, static, and dynamic causal relationships. To reach this goal, two critical tasks need to be accomplished including (1) disentangling the complex causal relationships, and (2) fitting the spatial-temporal explanations of DyGNNs in the SCM architecture. To tackle these challenges, the proposed method incorporates a contrastive learning module to disentangle trivial and causal relationships, and a dynamic correlating module to disentangle dynamic and static causal relationships, respectively. A dynamic VGAE-based framework is further developed, which generates causal-and-dynamic masks for spatial interpretability, and recognizes dynamic relationships along the time horizon through causal invention for temporal interpretability. Comprehensive experiments have been conducted on both synthetic and real-world datasets, where our approach yields substantial improvements, thereby demonstrating significant superiority.

Published as a conference paper at ICLR 2024
CAUSALITY-INSPIRED NATIONS FOR DYNAMIC GRAPH NEURAL NETWORKS
EXPLA-
Kesen Zhao
Liang Zhang Shenzhen Research Institute of Big Data Guangdong, China zhangl i anggerridd.rb........... en
City University of Hong Kong Hong Kong, China
kesenzhao2-c@mm cit cityu.edu...
ABSTRACT
Dynamic Graph Neural Networks (DyGNNs) have gained significant popularity in the research dynamic graphs, but are limited by the low transparency, such insights can hardly be drawn from their predictions.
that human-understandall Although a number of existing research have been devoted to investigating the interpretability of graph neural networks (GNNs), achieving the interpretability of DyGNNs pivotally challenging due to the complex spatial-temporal correla- tions in dynamic graphs. To this end, propose innovative causality-inspired generative model based on structural causal model (SCM), which explores the underlying philosophies of DyGNN predictions by identifying the trivial, static, and dynamic causal relationships. To reach this goal, two critical tasks need to be accomplished including (1) disentangling the complex causal relationships. and (2) fitting the spatial-temporal explanations of DyGNNs in the SCM archi- tecture. To tackle these challenges, the proposed method incorporates a con- trastive learning module to disentangle trivial and causal relationships, and a dy- namic correlating module disentangle dynamic and static causal relationships, respectively. A dynamic VGAE-based framework is further developed, which generates causal-and-dynamic masks for spatial interpretability, and recognizes dynamic relationships along the time horizon through causal invention for tem- poral interpretability. Comprehensive experiments have been conducted on both synthetic and real-world datasets, where approach yields substantial improve- ments, thereby demonstrating significant superiority.
INTRODUCTION
Dynamic graphs play a crucial role across wide spectrum of real-world applications (Seo al., 2018; You et al., 2018), including financial networks (Nascimento et al., 2021; Zhang et al., 2021), social networks (Berger- Wolf & Saia, 2006; Greene et al., 2010), and traffic networks (Peng al., 2021; 2020). Unlike the widely studied static graphs, dynamic graphs can represent the spatial- temporal characteristics of real-world data, which is gaining great popularity in practical scenarios despite the high complexity (Pareja et al., 2020). Addressing the challenges posed by this complexity has led to the development of Dynamic Graph Neural Networks (DyGNNs) (Wang et al., 2023; Manessi et al., 2020; Beck et al., 2017; Zaki et al., 2016), which achieves significant advances in predictive tasks through accommodating the intricate interplay of spatial-temporal patterns.
Despite the aforementioned advantages, DyGNNS are usually limited by low transparency, such that human- underssaadddtteebbllleeee insights can hardly be drawn from their predictions. Existing works on the explanation of GNNs, such GNNExplainer (Ying et al., 2019), XGNN (Yuan et al., 2020), and OrphicX (Lin et al., 2022) primarily focus on static networks. Therefore, these methods can hardly be directly adopted for the interpretability of dynamic networks due the following two challenges induced by the complex spatial-temporal correlations in dynamic graphs. 1) Spatial interpretabilitt. The investigation of spatial interpretability critically relies on the extraction of subgraphs that can represent the characteristics of the complete graph in spatial dimension and elucidating outcomes subsequent tasks. In essence, these subgraphs serve as substitutes for the
"Corresponding author.

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Published as a conference paper at ICLR 2024
original graphs, enabling the attainment of analogous results in downstream tasks. However, the sub-graph partition depends on the historical evolution over time as well as the spatial topology of the graph, which cannot be appropriately handled by the conventional methods designed for static graphs. 2) Temporal interpretability.. Temporal interpretability relies on the importance of representative sub-graphs over the time slots. In essence, it's essential elucidate the significance of each time step concerning its impact on the outcomes of subsequent tasks. However, the temporal dynamics of node are also impacted by its topological neighbor apart from its historical states. This makes it infeasible to directly adopt the techniques for time series research.
While causal inference provides an effective framework for investigating the interpretability in graph structures, a critical task to tackle these challenges is to disentangle the complicated types of re- lationships and accommodate them individually. To reach this goal, we propose an innovative causality-nspprred spatial-temporal generative model via constructing the structural causal model (SCM) (Pearl, 2009) for dynamic graphs. In this line of research, previous works for static graphs categorize the relationships within the graph into trivial (or spurious) relationship and causal rela- tionship (Lin et al., 2021; 2022), where trivial relationship captures the dispensable graph informa- tion while the causal relationship exploits the key information for tasks. Inspired by these works, further divide the causal relationships in the SCM into static relationship and dynamic relationship to capture the complex spatial-temporal correlations. However, there remain two critical challenges to implementing such a SCM. The first challenge lies in the approach to disentangling the complex causal relationships as no explicit information is available for the identification of trivial, dynamic, and static relationships. The second challenge is the way to construct the SCM to fit the task of discovering spatial-tempone interpretability due the lack of existing model for dynamic graphs.
To address these problems, we present a novel Dynamic GNN Explainer. Specifically, to disentan- gle the trivial relationship and the causal relationship. we propose contrastive learning module to ensure the semantic similarity between the causal relationship and the original graph while enlarging the semantic distance between the causal relationship and the trivial relationship. To disentangle the dynamic relationship and the static relationship, we leverage the pre-trained target DyGNN model to guarantee the essential temporal correlation between neighboring subgraphs for the dynamic re- lationships and identify the rest independent causal information to the static relationships. We in- stantiate our DyGNNexplaieer with a dynamic variational graph auto-encoder (VGAE) framework, which extracts the causal and dynamic relationships and maps them into a causal adjacency mask and a dynamic adjacency mask to accomplish the spatial explanation of graph-truth label. We fur- ther disentangle dynamic relationships along the time horizon by treating each subgraph as a causal invention and leverage the pre-trained target DyGNN model to measure its causal effect as the tem- poral explanation. To showcase the effectivvness of our approach, we generate synthetic dynamic datasets tailored for dynamic graph interpretability tasks, which fill the blank of dataset benchmarks and would facilitate further research in this domain. Experiments on both synthetic datasets and real-world datasets demonstrate superior performance of our method in both explanation tasks and real predictions. The code and the dataset benchmarks are available !
2 METHOD
2.1 PROBLEM STATEMENT
We denote pre-trained target DyGNN model to be explained as f- f where fa GIT - R the aggregation function of DyGNN to capture temporal structures and feature patterns, G1 is the dynamic graph sets, T is the total number of time steps. R is the aggregated high dimensional graph representation. fa : R + y is the downstream task function, which transforms graph representation to label space. y is the final label prediction. Specifically, the input dynamic graph at the 1hh time step G. (X,, A²), t E [1, includes the node attribute matrix X, glVIDD and corresponding adjacency matrix A, E R IVIxiVV where V is the set of nodes, D is the dimension of node attribute.
graphh
Explanation methods for DyGNNs aim to meet two critical criteria: fudelity and interpretability Fidelity requires that faithful explanation, represented by dynamic subgraphs, should align with how the target DyGNN behaves in the vicinity of the given dynamic graphs of interest (Ribeiro et al., 2016). In other words, when we feed the explanatory dynamic subgraphs to the target DyGNN, the
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Disentanging
trvall and causai
contrastive loss
G
R
O
VGAE
M
G
Spattal-lmmoral
explanation
dynemic loss
prediction loss
0 graph data
T. Uivial factor
G
001
C
spersity loss
C. causal factor
static factor
R reprosantation
D dynamic factor
0 O
prediction
M
Disentangling and dynamic
Figure 1: Overview of DyGNNExplainer and SCM for dynamic explanation.
outcomes should closely resemble those obtained from the original dynamic graphs. Interpretability (Pope et al., 2019) demands that generated explanations should highlight the most important parts of the input while disregarding the irrelevant components. Explanations for DyGNNs require both spatial interpretability and temporal interpretabilify. The spatial interpretability highlights the most important parts of graphs while temporal interpretability identifies the most important time slices. Moreover, an explainer should be versatile enough to explain any black black-box model, adhering to the principle of being 'model-agnostic..
Hence, our ultimate objective is to define generative model, denoted as F, to act as an explainer. This model should have the capability pick out which aspects of the input contribute to the DyGNN prediction while meeting the fidelity and interpretability criteria outlined above. In line with prior research (Lin al., 2021; Yuan et al.. 2020; Lin al., 2022), our focus lies in providing spatial-temporey explanations (dynamic subgraph set) for dynamic graph structures. We operate un- der the black-box setting, wherein we lack information regarding the ground-truth labels of the input graphs and do not require the inner workings of the target DyGNN's output generation process.
2.2 FRAMEWORK OVERVIEW
In this study, we propose a novel causality-inspired spatial-temporal DyGNNExplainer, shown in Figure 1. We first construct Structural Causal Model (SCM) for dynamic graphs with trivial, dynamic, and static relationships, enabling comprehensive understanding of dynamic graphs. Then generate causal and dynamic soft masks, which enable backdoor adjustment, to intervene in the targeting causal and dynamic factors. After that, we employ contrastive loss to separate trivial and causal relationships. To disentangle static and dynamic relationships, we employ dynamic loss, which captures the temporal evolution within graphs and maintains independence from static information. Finally, we improve the generated static and dynamic explanations using prediction loss and sparsity loss, which enhances both prediction accuracy and spatial interpretability.
2.3 A CAUSAL VIEW ON DYGNNS
We first take a casual look at the DyGNN modeling and construct a Structural Causal Model (SCM) in Figure 1. It presents the causalities among variables: dynamic graph data G. trivial rela- tionship T, causal relationship C, dynamic relationship D, static relationship S, node representation R, and prediction Y. where links between variables represent cause-effect relationships. Here some key explanations regarding SCM:
+ 9 + C: represents the genuine causal relationship in dynamic graph data, while T signifies trivial relationships, often stemming from data biases or spurious patterns.
R - C: R is a high aigh-dimensiona representation dynamic graph node data g. To generate R, the conventional strategy leverages both the trivial relationship T and the causal relationship C as inputs to extract discriminative information.
+ R + S: In dynamic graph G, causal relationships C consist of dynamic relationship and static relationship S.
R + y: The ultimate aim of dynamic graph representation learning is to predict graph properties, such node graph label.

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From this SCM, we identify backdoor path between C and V. i..., C + G - T V. In this path, the trivial relationship T acts as a confounder between G and y. Even there's 's no direct link between C. and y/ the backdoor path can cause misleading correlation between C and V/ leading to incorrect predictions. Thus, it's crucial to block backdoor path to enable dynamic GNNs to effectively utilize causal relationships. Similarly, have another backdoor path between 'D and V, i.c., D + C + S + R + V and the static relationship S acts as confounder between C and V.
2.4 BACKDOOR ADJUSTMENT
Our research has emphasized the significance of safeguarding DyGNNs against confounding factors and distinguishing between dynamic and static relationships. This distinction is crucial for effec- tively utilizing causal relationships within dynamic graphs. Instead of modeling the confounded relationship denoted as P(]CC)) in Figure I, our focus shifts towards graph representation learning that eliminates the backdoor path. Fortunately, we can achieve this by applying do-calculus prin- ciples to the variable T. By doing so, can estimate the probability distribution P())dd((C) without interference from the confounder T, utilizing standard backdoor adjustment. Similarly, we apply do-calculus to the variable D and estimate P()]do(D)
eliminate the backdoor path caused by the confounder S. Note that we can't 't directly employ the standard backdoor adjustment method due confounder T. To overcome this challenge, we merge the estimation of P()(do(C) with that of ((Y)do(D)) resulting in the following equations:
P(Y Σ (()) P P())))(())
The first and second equations are based on the backdoor adjustment for confounder S and T re- spectively. Detailed derivation process is shown in Appendix A.4. However, there exist challenges for implementing backdoor adjustment. No explicit information available for the identification of trivial, dynamic, and static relationships. To tackle the above challenges, we propose an effective method shown in the next subsection.
2.5 DISENTANGLING COMPLEX CAUSAL RELATIONSHIPS
Given a dynamic graph set G 1:T AIT)), we formulate the causal soft masks for causal relationship at 9th time step as M E RIVVIVV Each element of the mask represents an attention score, typically falling within the range of [0, 1]. For arbitrary mask M, we define M = 1 - as its complementary mask, where 1 is the all-one matrix. Consequently, we partition the entire dynamic graph set G1TT into two distinct sets: causal set G. = (XI,T, Air0Mf:r) and trivial set GT.r- =
(XI:T, AIT + Mir)). Where t is the element-wise dot product at each time step. Similarly, we formulate the dynamic soft masks as MP | to extract the dynamic relationships and its complementary mask M to extract the static relationships. Then, we have dynamic causal set G. = (XI.T, A 4 Mc 1.r ( MP:r) and static causal set G i:T (XIr, A @ M @ M.T)). Because the ground-truth trivial set, dynamic causal set, and static causal set are unavailable in real- world applications. We aim to capture the trivial dynamic, and static relationships from the full graph by learning the masks.
Estimating soft mask: Inspired by the VGAE framework (Kipf & Welling, 2016), we proposed a dynamic VGAE-based encoder-decoder to estimate the soft masks of explainable subgraphs. We first consider the estimation of the causal soft mask matrix M At the 1-th time step, the causal soft mask matrix can be calculated as
M f. (Xir, 1.r, A Oc) { H.)
G1.)),
(2)
where fo is the encoder-decoder architecture with parameters Oc, q(-) is the encoder module, p(.) is the decoder module. The encoder utilizes posterior probabilities to encode the node embeddings into low-dimensional latent vector representations, which can be formulated as
qHe G = 11 q (hr., G..)) q (h., G = N (hea Pr.i, diag (oī,))
(3)
where H, is the latent matrix. μr and or are means and variances of node latent embeddings learned by GCN, (G.) and GCN, (G.) with different parameters. h,,- Hr.; and o,,, are the tt column of H to p4 and Tt respectively. We use the peaaaeetteiinnooon technique to avoid the problem that the
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sampling operation cannot be pack-propagated and updated by gradient descent. Then the decoder utilizes latent representations to generate the dynamic explainable subgraph as follows
N N
p(M H.)
IIII (M..) he, ha.) . (M,,, = b4. h..) = g (hr,i, hr,))
(4)
where Mi the tth row and jth column of My representing the probability of existence for edge (ot, vf)) at time / in causal graph set and -(+ calculates this probability.
According to the above encoder-decoder framework, the causal soft mask M can estimated based the input of dynamic graph set G1.T. The soft causal mask assists in the formulation of the causal graph set G..T. According to the causal graph in Fig. I, the static relationship S can also be treated the co-founder between DD and Y, just like the trivial relationship TT respect to C and V. Thus, we take the same VGAE- incoder-decoder framework to generate the dynamic soft mask matrix, but with different parameters Qp. have the following estimating process:
M, fo (X1s,, A1:t + M OD)
(5)
Now we have the adjacency matrix causal set A AIT @ M dynamic causal set A P.r
A ArT + M o M.T and static causal set A A 1:T M M I.T- We need to disentangle the trivial, dynamic, and static relationships. We first disentangle the trivial relationship and the causal relationship via contrastive learning method. Then, we propose novel dynamic correlating method to disentangle the static relationship and dynamic relationship.
Disentangling trivial and causal: According to the criteria in Section 2.1, the explanation should meet fidelity. Since the causal subgraph set is the target and the trivial graph set can be treated as noise, the outcome of the target model with the causal subgraph set should be more like the original graph set, while the trivial subgraph set should be treated as negative ones. To disentangle the in- formation in the trivial subgraph set and the causal subgraph set, we need to extract the embedding from them via some dynamic methods. Fortunately, ity for the pre- pre-trained DyGNN. Thus, we utilize the pre- trained aggregation function to obtain such embedding, which is then utilized to assist in disentangling trivial and causal information. During each time step f, the aggregation function fa(-) would generate the embeddings via extracting the essential information until time & for original graph set G1.t. causal subgraph set GC and trivial subgraph set G More formally, we have
target is to provide fidelity and interpretabil-
R4 = fa(G)a), = (G =.. (..
(6)
The above outputs can be the node (graph) embedding for node (graph) classification tasks. We utilize contrastive learning to ensure the semantic similarity between the causal embedding ef and the original embedding e, while enlarging the semantic distance between the causal embedding ef and the trivial embedding e!. Then, we have the following contrastive loss:
exp (s(er,
-
C. T
Σ
log exp (s(e),ef)/r) + on exp (s(e? ef ff/r)) + a2 Exzi exp (s(e? "(ee,et)/T .f)/T)
where is the temperature coefficient, s(::)) measures the similarity, we utilize the dot product here.
Disentangling static and dynamic: According to the structure causal model in Fig. 1, the causal relationship can be further divided into the static relationship and the dynamic relationship. To extract the dynamic relationship and static relationship from the dynamic causal set G and static causal set G
we utilize GCN with learn-able parameters Vp and V.s.
1.7,
H GC, X,; VD) H = GCN(A, X Vs).
(8)
Dynamic relationships evolve over time steps but static relationships are independent across each time step. Specifically, the dynamic relationships in time step can be inferred from the history dynamic causal set G 1i(t-1) while static information in time step f is independent with history static causal graph set G 1:(t-1)) Formally, we have
HP H..
H H H
(9)
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Note that using the history dynamic relationship (i(--)) to predict the dynamic relationship H? directly is trivial since the GCN with parameters VD can map the graph set into embedding space without any useful information. Fortunately, we can use the pre-trained aggregation function fa(+) again, which extracts the dynamic relationship from the original graph set. According the fidelity criteria, the generated dynamic graph set should also guarantee that the pre-trained aggregation function can extract the dynamic relationship from it. Thus, we have the following dynamic loss:
Σ d(aa (G (GR(t-)) HP),
La= T-
(10)
where d(.,-) measures the distribution distance. The dynamic loss guarantees that the dynamic relationships extracted from the dynamic causal graph set are highly correlated. The rest causal information would be independent, which identifies the static causal graph set. To make sure that the dynamic and static relationship can be disentangled separately as possible, we would provide the sparsity constraints for the dynamic causal graph set shown later.
Spatial-temporal explanation: According to the structural causal model, both the dynamic rela- tionship and the static relationship are the key to the prediction and should be utilized to predict the ground-trute label. The learned causal soft mask and the dynamic soft mask can assist in spatial interpretability which highlights the most important causal parts and dynamic causal parts of dy- namic graphs. However, this is not enough for temporal interpretability. Due to the highly temporal correlation for dynamic relationships, it would be difficult to disentangle the dynamic relationship. To address the challenge, we treat the dynamic relationship at time t as an invention. With the help of aggregation function f-(-), we measure the causal effect of this invention via the change of embedding. Formally, we define the causal effect at time / as follows:
AH,- fo (GP.) fa (GR
(11)
We combine the causal effect for the dynamic relationship and the static relationship time as the key causal information for G2 and propose the learn-able weight pooling method to aggregate all the information across all time slots as follows:
H Hr= Σ (AH HHA @ H;, (H) Softmar V /
(12)
where Vp the parameters learn temporal importance 1p (AHP H₂)) ( (AH, H pro- vides importance of subgraphs over different time slots and thus assists in temporal interpretability. Based on pre-trained classifier fa(-), we use aggregated embedding explain the ground-trute label via prediction loss:
Cp = ((r))))),)),,,
(13)
where ((.;) :) is the entropy loss. To ensure human interpretability, the explained causal subgraph set should sparsity. We take the sparsity requirement for both the causal graph set and the dynamic causal graph set via the sparsity loss:
T
AC
+ +| AAll1
C.
(14)
In summary, learn the optimal explainable causal subgraphs, dynamic subgraphs, and temporal importance by solving the following optimization problems:
min C(O, v = X1Lo + deL + >sGp + X4La 8,0
(15)
where O (Oc, Op}. v (Ve, VD, vp and A1, d2. As and da are hyper parameters.
EXPERIMENTS
3.1 EXPERIMENTAL SETTINGS
Datasets: We utilize synthetic datasets and real-world datasets for the node classification task and the graph classification task. Table shows the statisties of all datasets. Since method is

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Table 1: Statistics of datasets for both node and graph classification.
Node classification
Graph classification
Dataset
DBA -hA-pss
DTree- Cycles
D'ree-Grii
Elliptic
DBA-2mon BBA-2mstifs
MemeTracke
#nodes
700
871 1,950
1,231 3410
203,769 234,355
25,000
3.3 mil.
#edges
4.110
51,392
27.6 mil.
#labels
7
3
3
2
2
Table 2: Explanation accuracy of different models (%).
Where best performances bold.
Task
Dataset
GNNExplainer
PGExplainer
Gem
OrphicX
DyGNNExplainer
DBA- ABA--hapes
92.1
92.9
93.6
94.3
97.8*
OTree-Cycles
92.8
93.7
94.4
96
98,2*
Node cls.
DTree-Grid
85.2
85.9
87.1
90.5
94.2
Elliptic
92.4
94.1
94.6
96.1
98.7*
DBA-2motif's
86.5
88.0
90.7
91.4
96.3*
Graph cls.
MemeTrracker
88.2
89.2
91.0
91.9
97.4*
indicates the statistically significant improvements (i.e., two-sided t-test with p < 0.05) over the best baseline. "cls." is short for classification.
the first study dynamic graph interpretability, there are no directly available datasets suitable for the task of dynamic graph interpretability. So we dynamically transformed some commonly used static graph interpretability datasets. For node classification, we process three benchmark synthetic datasets BA-Shapes, Tree-Cycles, and Tree-Grid (Ying et al., 2019), as dynamic graph datasets DBA-Shapes, DTree-Cycles, and DTree-Grid. Furthermore, we utilize real-world dynamic graph dataset Elliptic 2. For graph classification, we process a benchmark synthetic dataset BA-2motifs dataset (Luo et al., 2020) as dynamic graph dataset DBA- And we utilize real-word dataset Meme'Tracke (I (Leskovec et al., 2009). More details of datasets and the generation process are shown in Appendix A.1.
Since we are the first to explain DyGNNs, there are no existing dynamic graph inter- pretability benchmarks for comparison. And graph representation and graph generalization models are the target models we want to explain, there is no comparison between us and them. Conse- quently, we compare our approach against various powerful static interpretability frameworks for GNNs. They are GNNExplainer (Ying et al., 2019), PGExplainer (Luo et al., 2020), Gem (Lin al., 2021), and OrphicX (Lin et al., 2022). For all these static baselines, we treat all nodes and edges as occurring simultaneously. More details about baselines and hyperparameter settings are shown in Appendix A.2.
Baselines:
3.2 RESULTS
Explanation fidelity: Explanation fidelity pertains the accuracy of the explanations provided by various methods. To gauge this, we compare the predicted labels of explanatory subgraphs with the predicted labels of the original graphs as generated by the target model. For the static baselines, we simplify the target model by excluding temporal evolution. From the results presented in Table 2, our DyGNNExplainer surpasses all other baselines by significant margin across all datasets, both for node classification and graph classification tasks. This underscores the fidelity of the explanations produced by our method, which, in contrast to static baselines, adeptly captures the intricate spatial-temporal correlations in dynamic graphs via our -inssiire apatial-tempor structure. Causal- based methods OrphicX and Gem also outperform other baselines, affirming the effectiveness of causal inference in explanation tasks. However, these methods only differentiate between trivial and causal factors, disregarding the dynamic factor. Consequently, they fall short in explaining complex spatial-temporal relationships. In contrast, our method addresses this limitation by imposing two constraints.
Explanation interpretability analysis: Interpretability implies that the explainer should emphasize the most crucial components of the input data while disregarding irrelevant elements. In other words,

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[a] DBA-Shapes
(b) DTrre-Cycles
[c] DBA-shapes
Or
Or
Dy
Dy
98
90
95
Accuracy
Accuracy
Accuracyss
96
85
90
94
80
85
92-
8
9
7
8
DV
W/O. Cd
w/o.
w/o. w/o.VGAE VGAE
#edges
eedge
Figure 2: Interpretability analysis and ablation study. (a) Sparsity analysis on OBA-Shapes dataset (b) Sparsity analysis on "Tree-Cycles dataset. (c) Ablation study DBA-shapes. K is the edge number of each explanation subgraph. 'Or' is the OrphicX model, and 'Dy' is our DxxNNeeel "w/o. La', 'w/o. Le' and 'w/o. VGAE" are DyGNNExplainer without dynamic loss, contrastive loss, and VGAE, respectively.
Table 3: Prediction accuracy of different models (%). Where best performances bold.
Dataset
GNNExplainer
PGExplainer
Gem
OrphicX
Target
DyGNNExplainer
OBA-Shapes 35.5
36.3
38.5
38.7
40.2
44.6*
Elliptic 39.7
45.6
43.5
47.8
84.3
89.2*
*
indicates the statistically significant improvements (i.e.. two-sided t-test with p < 0.05) over the best baseline.
the explanation subgraphs should exhibit a high degree of sparsity. To quantify this sparsity, we measure the number of subgraph edges (denoted as K). A smaller number of selected edges implies a higher sparsity. We compare the explanation accuracy of DyGNNExplainer with OrphicX on DBA-Shapes and DTree- -yclle,, varying the number of edges (K) in the subgraph. As illustrated in Figure 2 (a) and (b), our method outperforms OrphicX with fewer edges in the subgraphs. This superiority arises from our model's adeptness at capturing spatial-temporal correlations in dynamic graphs, allowing it to encapsulate more critical information while ensuring interpretability.
Prediction accuracy analysis: While we aim construct an explainer faithfully elucidates the inner workings of the target model, it is equally imperative to ascertain the consistency of the inter- preted results with real-world facts. Consequently, we also compare the prediction accuracy of our method with other baselines and target model on synthetic dataset DBA-Shapes and real-world dataset Elliptic for node classification task. As shown in the Table DyGNNExplainer outperforms all other baselines by substantial margin on both datasets. Particularly noteworthy is its 41.4% performance advantage over the best baseline, OrphicX, in the real-world Elliptic dataset. This un- derscores that our method generates explanations that align not only closely with the target model but Static baselines, due to their inability to capture spatial-temm temporaal model
also with real-world ground- correlations, fall short in accurately predicting the ground truth. Intriguingly, passes the target model in terms of prediction accuracy. This is attributed to our model's ability disentangle trivial dynamic, and static relationships, thereby better capturing spatial-temporal correlations across graph time steps.
sur-
A Ablaiion study We also delve into ablation study on the DBA-Shapes dataset to dissect the roles of dynamic and static causal relationships. As depicted in Figure (c), we present several variants for comparison. In 'w/o. VGAE', we replace the encoder with simple GCN layer. Our findings reveal that DyGNNExplainer consistently outperforms the 'w/o. L,¹ and 'w/o. L." versions. The 'w/o. La version, lacking the dynamic loss component, fails to effectively differentiate between dynamic and static factors, leading to an inability to capture temporal correlations across dynamic data. On the other hand, the 'w/o. L. version experiences a significant drop in performance. This decline can be attributed to its inability to distinguish between causal and trivial factors, resulting in noisy independence that hinders the DyGNN explanations. These observations underscore the efficacy of our imposed constraints in disentangling trivial, dynamic, and static factors. Furthermore, GyNNxpllaeee also outperforms the 'w/o. VGAE' version. This is primarily due to the superior capabilities of VGAE in harnessing spatial graph information generate soft masks.
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DyGNNExolainer
OrphicX
Time step
2
$
t
Original graph
Explanation
0.031
0.172
0.225
0:237
Figure 3:
Case study on DBA DBA-Shapes. The red node, designated as the target node for explanation, also serves as connecting node between the 'house' motif and the base graph.
Case study To provide present a case study on DBA-Shapes dataset. As depicted in Figure 3, we visually represent both the original graph and the top six weighted edges of the generated causal subgraph across all time steps using DyGNNxxplainer, Additionally, we compare our results with those obtained using OrphicX. To streamline the visualization, we have omitted edges and nodes that do not belong to the 'house' motif or are not directly linked to the target node. The variable Ep denotes the importance of each time step. Notably, there is a gradual upward trend in lp values. This trend can be attributed to the increasing completeness of the "house" motif in later time steps, rendering them more crucial for the final interpretation. The weight assigned to the first time slice is considerably lower than that of subsequent time steps. This discrepancy is due to the fact that the recognizable pattern of 'house' motif has not yet to fully materialize in the initial time step. Additionally, the weight for the fourth time step does not significantly surpass that of the previous one, to the motif during this interval. This observation underscores the excellent temporal interpretabil- ity of our approach. Furthermore, DyGNNExplainer effectively identifies the 'house" motif from the original graph in the final time step, which explains the target node label. In contrast, OrphicX erroneously attributes an edge outside of the 'house' motif. This discrepancy vividly illustrates the superior spatial interpretability of our method.
vivid demonstration of DyGNNExplainer's interpretability.
new edges added
RELATED WORK
A host of recent methods has emerged to provide explanations for Graph Neural Networks (GNNs) (Sui et al., 2022), focusing on identifying the most influential features (e-g., nodes, edges, sub- graphs) in input graphs to explain model predictions. These methods predominantly aim generate input-dependent explanations. GNNExplainer (Ying al., 2019) seeks soft masks for edges and node features through mask optimization explain predictions. And Shokri et al. extend expla- nation methods designed for Convolutional Neural Networks (CNNs) to GNNs. However, these methods typically explain each instance individually and lack the ability generalize graphs, lim- iting their global interpretability of the target model. Recognizing the issue of hindsight bias and the compromise of faithfulness when separately optimizing for each instance, PGExplainer (Luo et al., 2020) proposes learning a mask predictor for edge masks to provide explanations. XGNN (Yuan al., 2020) focuses on investigating graph patterns leading to specific classes. In contrast to these approaches, our work leverages causality to achieve faithful explanations, distinguishing it from existing methods. More related work about causal inference shown in Appendix A.3.
5 CONCLUSION
In conclusion, our work has addressed the critical challenges associated with interpretability in Dy- namic Graph Neural Networks (DyGNNss) Our research has pioneered the development of DyGNN explanation, a novel approach tailored to the unique characteristics of dynamic graphs. Our ex- perimental results, encompassing synthetic and real-world datasets, have demonstrated the superior performance of DyGNNExplainer in both explanation tasks and real predictions. Furthermore, we contribute to the field by generating synthetic dynamic datasets tailored for dynamic graph inter- pretability tasks, which lays the foundation for future developments in the field of dynamic graph analysis and interpretation.

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Published as a conference paper at ICLR 2024
ACKNOWLEDGEMENT
This work is supported by National Key R&D Program of China under Grant 2022YFA (1022Y0A1003000, Internal Project of Shenzhen Research Institute of Big Data under Grant J00220230001
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A APPENDIX
A.1 DATASET
Node classification datasets We process three benchmark synthetic datasets BA-Shapes, Tree- Cycles, and Tree-Grid (Ying et al., 2019), as dynamic graph datasets DBA-Shapes, D'rreeCycles, and DTree-Grid. Furthermore, we utilize a real-world dynamic graph dataset Elliptic 3. (I) BA- Shapes is single graph consisting of a base Airabasi-Alber (BA) graph with 300 nodes and 80 motifs. These motifs are attached to randomly selected nodes from the BA graph. After that, random edges are added to perturb the graph. Node features are not assigned in BA- Shapes. (2) In the Pree-Cycles dataset, an 8-level balanced binary tree is adopted as the base graph. A set of 80 six-node cycle motifs are attached to randomly selected nodes from the base graph. (3) Tree-Grid is constructed in the same way as the Tree-Cycles, except that 3-by-3 grid motifs are used to replace the cycle motif's. (4) Elliptic is Bitcoin transaction dataset. Nodes represent transactions and edges represent payment flows. We utilize this dataset for the node classification task.
Graph classification datasets We process a benchmark synthetic dataset BA-2motifss dataset (Luo et al., 2020) as dynamic graph dataset DBA-2motifs, And we utilize a real-word dataset Meme- Tracker (Leskovec al., 2009). (1) BA-2mosifs adopts the BA graphs as base graphs. Half graphs are attached with 'house' motifs and the rest are attached with five-node cycle motifs. Graphs are assigned to of classes according 27.6 million news articles and blog posts from 3.3 million online sources with time stamps over a one-year period. The time-stamp indicates the information arrival time of a node from its parent nodes. We treat each website as graph node, there is an edge between two nodes if a website forwards articles or blogs from another website. Thus, the propagation network forms a graph at a specific observation time stamp. All the graphs at different time stamps in a cascade have the same label.
the type of attached motifs. (2) MemeTrracker contains
Dynamic data generation process First, we randomly select root vertex with nonzero out- degree. The vertex then added to the initially empty list and all outgoing edges are added to the initially empty first-in-frst-ouu queue, where the first element added to the queue will be the first one to be removed. We choose an edge from the candidate set each time and calculate the time delay for the edge until the time delay exceeds a given time window (we use [0,1000] as the time window). When calculating the time delay of propagation, we follow a power-law distribution. Finally, we separate the graph with time delay of 100, 200, 300, 400, 500 (e.g., we form the first graph in a time-variant graph when the propagation time delay is 100). Thus, the average length in the synthetic data is since have 5 graphs in each time-variant graph. The whole data set is generated by repeating the above steps to generate 200 graph sequences. Then we relabel the nodes according to the diffusion direction of the motif nodes. For example, the BA-Shapes dataset, if the node connected to the base in the house appears first, then other nodes in the motif appear, the nodes located at the top/middle/bottomm of the 'house' are labeled with 1, 1,2.3, respectively. In contrast, other nodes in the motif appear first, the nodes located at the top/middleebootom of the 'house" are labeled with 4,5,6. The nodes in the base graph are labeled with O.
A.2 EXPERIMENTAL SETTINGS
Baselines Since we are the first to explain DyGNNs, we compare our approach against various powerful static interpretability frameworks for GNNs.
GNNExplainer (Ying et al., 2019) employs a technique called mask optimization to seek soft masks for edges and node features. These masks are instrumental in explaining the predictions made by GNNs.
PGExplainer (Luo et al., 2020) takes a different approach by proposing the learning of a mask predictor. This predictor is responsible for generating edge masks, enabling instance-specific explanations for GNN predictions.
Gem (Lin al., 2021) distinguishes itself by focusing on explaining graph-structured data. frames the explanation task for GNNs as causal learning problem, aiming to generate concise subgraphs that contribute to predictions.
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OrphicX (Lin et al., 2022) quantifies the causal attribution within the latent space without assum- ing the independence of explained features.
For all these static baselines, we input graphs without time attributes. That is, we treat all nodes and edges as occurring simultaneously.
Hyperparameter setting For the VGAE, we apply a two-layer GCN with output dimensions [32, 64, 128] and [16, 32, 64] in the encoder. The max time step T is set as 5. In the contrastive loss, the temperature coefficient т, weight parameters a and 02 are set from [0.2, 0.5, 0.8]. In the final optimization objects, the loss function weight parameters λ1 22. A3. and X4 are set from [0.2. 0.4, 0.6, 0.8, IJ. And the best performance is obtained where \ = 1, X = 0.4, A3 = 0.2, and X₂ = 0.2. We trained the explainers using the Adam optimizer (Kingma & Ba, 2014) with learning rate of [le-2, Ic-3, le-4] and batch size 64. When comparing to other baselines, we either utilize the same search range adopt the optimal settings recommended by the original authors of the baselines. We divide the dataset as training set and test set with a ratio 8:2, which is a common setring in previous works. All experiments are conducted on NVIDIA Tesla VI0OS GPU, and the reported results are the average of three replicate experiments.
A.3 MORE RELATED WORK ABOUT CAUSAL INFERENCE
The quest for DyGNN explanations often revolves around discerning the 'what if" and 'why' aspects, which inherently pertain to causality. Causal reasoning serves as potent framework for addressing such inquiries (O' S'haughnessy et al., 2020). Various formalisms causality have emerged, includ- ing structural causal models (SCM) (Pearl, 2009), Granger causality (Granger, 1969), and causal Bayesian networks (Pearl, 2009). While most explanation methods have been designed to elucidate conventional neural networks in image domains, Gem (Lin al., 2021) represents a departure in its focus on explaining graph-structured data. Specifically, Gem formulates the task of explaining Graph Neural Networks (GNNs) as causal learning problem. It proposes causal explanation model capable of generating concise subgraphs that contribute to predictions. This approach fun- damentally perturbs input aspects in the data space observe the target GNN's response, naturally leading to the assumption of independent explained features. However, the interdependence inher- ent in graph-structured structured data, coupled with the non-linear transformations performed by GNNs, can compromise the efficacy and optimality of this assumption. Subsequently, OrphicX (Lin et al., 2022) quantifies the causal attribution of data aspects in the latent space without relying on the assumption of independent explained features. However, both Gem and OrphicX do not account for dynamic causal factors in dynamic graphs (Wu et al., 2022: Xia et al., 2023), thereby missing the opportunity capture spatial-temporal correlations across dynamic graphs. In contrast, approach differen- tiates between trivial, static, and dynamic causal factors, employing two constraints to ensure both spatial and temporal interpretabilityy for DyGNNs.
A.4 MORE DETAILED PROOFS AND EXPLANATIONS
Backdoor adjustment In Equation 1, we merge the estimation of P()(do(C)) with that of P())do(D)),The detailed derivation process of backdoor adjustment can be shown as:
P()]do(D))
Σ P1)(aoD)),S)P(((a(())
= Σ (())))(C))P(SS)
(16)
-EP(S) Σ
= P(S) Σ P())S)P(T).
Complexity analysis VGAE-based encoder is the most time consuming component in method. In the dynamic VGAE-based encoder, we generate the causal soft mask matrix MC and the dynamic soft mask matric MP with ((d [ complexity for T unique time steps. where d is the embedding size. The contrastive learning part also costs lots of time and has time complexity O(V x d T2).
Then, the total time complexity is 2 d T + V d T2). Note that T << [V], then ignore the time of contrastive learning and obtain the total time complexity as 0( d T).
13


Reviews:
[{"review_id": "ILC64Glsq1", "reviewer": "Reviewer_8sLV", "summary": "This paper presents a causal approach to improving the interpretability of GNNs. The authors have integrated a contrastive learning module that distinguishes between non-causal and causal relationships, enhancing the clarity of the model's decision-making process. Additionally, a dynamic correlating component is employed to differentiate dynamic from static causal relationships, providing a nuanced understanding of changes over time. Furthermore, the authors utilize a VGAE-based model to generate causal-and-dynamic masks, which contribute to spatial interpretability. This model also captures dynamic relationships across temporal scales through causal inference, thereby boosting the model's ability to interpret temporal data.", "questions": "See weakness", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) The composition and articulation of the paper are logical and coherent. The use of a causality-driven approach to enhance the out-of-distribution generalization capabilities of dynamic GNNs is intriguing.\n\n(2) Introducing research on temporal distribution shift in sequential processes is important and may provide valuable insights for subsequent studies.", "weaknesses": "(1) The paper's presentation appears problematic, particularly in the description of the backdoor adjustment. While simplified results are provided in the main text, the specific derivation process is absent and should be relegated to the appendix. Additionally, the computational intensity of introducing temporal masks, which could be exacerbated by the incorporation of contrastive learning (VGAE is known to be computationally demanding), is not addressed. The authors should include complexity descriptions to inform the reader. However, these issues are not discussed in the paper.\n\n(2) The proposal of 4 loss functions can be unfriendly to network training. If even one parameter is improperly tuned, it could lead to significant instability or even failure in network training. The authors should systematically discuss parameter selection techniques or guidelines to aid those who follow in this line of work.\n\n(3) There is a lack of related experiments: although experiments are conducted, there is a shortage of benchmarks in this field. It is recommended that the authors refer to [1] to add more experiments to validate the effectiveness of their DyGNN, such as including the Ogbn-Arxiv dataset. Additionally, an ablation study replacing VGAE-like models is crucial to help others understand the contribution of each model component.\n\n(4) Related work is missing from the paper, especially concerning spatio-temporal related work [5], generalization/extrapolation on graphs, and causality learning [2-4]. The authors should consider these areas to provide a more comprehensive context for their research.\n\n[2] Sui, Yongduo, et al. \"Causal attention for interpretable and generalizable graph classification.\" Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2022.\n\n[3] Wu, Ying-Xin, et al. \"Discovering invariant rationales for graph neural networks.\" arXiv preprint arXiv:2201.12872 (2022).\n\n[4] Miao, Siqi, Mia Liu, and Pan Li. \"Interpretable and generalizable graph learning via stochastic attention mechanism.\" International Conference on Machine Learning. PMLR, 2022.\n\n[5] Xia, Yutong, et al. \"Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment.\" arXiv preprint arXiv:2309.13378 (2023).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WOT2WFINQc", "reviewer": "Reviewer_U7py", "summary": "This paper proposes a novel approach for interpretability in dynamic graph neural networks. The proposed framework is demonstrated on both synthetic and real-world datasets. The experimental results show that the proposed method outperforms the baselines (all baselines are for explaining static graph neural networks). Another contribution is that the paper constructs a new synthetic benchmark dataset for dynamic graph interpretability tasks.", "questions": "In table 2, the best performance for OrphicX is obtained by DTree-Grid?", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The proposed framework is the first work for interpretability in dynamic graph neural networks. This is a significant contribution. The paper is well organized and clearly described. The method is technically sound. The experiments are comprehensive and the results show the effectiveness of the proposed method. The new constructed benchmark dataset is a good addition to the research domain.", "weaknesses": "Minors: \nIn Figure 1, the text is too small.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "q90TUxGqx8", "reviewer": "Reviewer_fzQP", "summary": "This paper proposed a causality-inspired generative model to explain DyGNN predictions by identifying the trivial, static, and dynamic causal relationships. To experimentally evaluate the proposed approach, synthetic dynamic datasets are generated and provided. Evaluations on both synthetic datasets and real-world datasets demonstrate superior performance.", "questions": "In Table 2, for Node classification task, OrphicX performs better than DyGNNExplainer on DTree-Grid dataset but is not bolded?\n\nCan you compare your model on static graphs to state-of-the-art explainers?\n\nHow sensitive the model is to the hyper parameters in Equation 15? What’s the computational complexity of solving Equation 15?", "limitations": "", "rating": 5, "confidence": 2, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "Originality: this paper is aimed at explaining dynamic graphs by proposing a causal inspired framework. Existing works on the explanation of GNNs are on static graphs. This paper instead focuses on dynamic graphs. Disentangling spatial and temporal relationships can be very challenging. This paper explicitly constructs a structural causal model by considering trivial relationships and causal relationships (consisting of static relationships and dynamic relationships) to solve this problem, which is interesting.", "weaknesses": "The presentation can be improved. It is hard for me to follow the paper well. For example, in the Introduction section, it is hard to straightforwardly understand the spatial interpretability and temporal interpretability. Illustrations can help readers understand better. Besides, it is not easy for me to understand the challenges for implementing the SCM (third paragraph in the Intro). Correspondingly, I didn’t see how the proposed approach addresses the challenges in the fourth paragraph. \n\nThe significance of the proposed approach is not clear. It is hard to judge the performance improvement achieved by DyGNNExplainer since other baselines are all for static graphs.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KidnSLrJ44", "reviewer": "Reviewer_JCbW", "summary": "This work aims at interpreting the Dynamic Graph Neural Networks (DyGNNs), and proposes an innovative causality-inspired\ngenerative framework based on structural causal model (SCM), which explores the underlying philosophies of DyGNN predictions by identifying the trivial, static, and dynamic causal relationships. This work actually identifies the subgraph via a masking mechanism.", "questions": "1. In Equation 7, $e$ is not defined in this paper, and the implementation of  $s( \\cdot , \\cdot )$ is also not provided. \n\n2. Does $||A||$ operate by summing all elements of $A$ in Equation 14? Besides, does Equation 14 exist error? To satisying the sparsity requirement of causal and dynamic causal graph set, whether Equation 14 should be replaced by $\\frac{{||A_t^C|{|_1} + ||A_t^S|{|_1}}}{{||{A_t}|{|_1}}}$?\n\n3. In Table 2, OrphicX achieves the best performances on DTree-Grid (96.1). But, you bold your work DyGNNExplainer (94.2 < 96.1).\n\n4. $\\Theta $ should be replaced by $\\Psi $ in the last line of Section 2.\n\n5. How to interpret the 'dynamic' in DyGNNExplainer? Can the datasets in experiments support the augment raised in this paper, as it seems there are no dynamic graph in experiments?\n\n6. Distinguish the distinctions between this work and CaST.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "S1. The research motivation of this paper is clear. The existing studies on the interpretability of Dynamic Graph Neural Networks are still limited, thus it is meaningful to bridge such gap.\n \nS2. The description of the existing challenges to the interpretability of DyGNNs is interesting. The authors argue that the first challenge lies in the approach to disentangling the complex causal relationships as no explicit information is available for the identification of trivial, dynamic, and static relationships.", "weaknesses": "W1. I'm confused about this sentence, 'Hence, our ultimate objective is to define a generative model', in Section 2.1. Throughout the whole paper, DyGNNExplainer is a representational model.\n\nW2. Equation 1 should be described in detail. Since causal relationships ($C$) consist of dynamic ($D$) and static ($S$) relationships, there should exist $P(S) = P(C) - P(D)$. I guess this equation is derived from it, but I can't see the logical derivation.\n\nW3. This paper still has not well addressed the interpretability issue of DyGNNs. The authors only provide evidence in performance improvements and static interpretability ('house' motif in BA-Shapes). We can not observe specific causal relationships in dynamic graphs from provided results. Besides, the baselines are interpretability methods conducted on static graphs, and the datasets are not classic dynamic graph datasets, such as traffic and citation network datasets. Thus, this proposed solution does not satisfy the expectation that exploring the interpretability of dynamic graph.\n\nW4. Some important literature is missing, e.g., CauSTG for capturing invariant relations targets temporal shifts in ST graphs [1] and CaST for discovering via Structural Causal Model (SCM) with back-door and front-door adjustment [2]. The authors should distinguish the distinctions between the proposed DyGNNExplainer and  (CauSTG, CaST), especially the CaST.\n\n\n\n[1] Xia Y, Liang Y, Wen H, et, al. Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment[J]. arXiv preprint arXiv:2309.13378, 2023.\n\n[2] Zhou Z,  Huang Q,  Yang K, et, al. Maintaining the Status Quo: Capturing Invariant Relations for OOD Spatiotemporal Learning. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '23), 3603–3614.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)