SlowGuess/NeurIPS_2023_OCR huggingface dataset:
- RQ1: How effective is  $\pi$ -GNN when it is generalized to different graph datasets?
- RQ2: How effective is  $\pi$ -GNN when it is generalized to different graph tasks?
Table 1: Interpretation Performance (ROC-AUC) Comparison. The underlined results highlight the best baselines. The bold results mean the  $\pi$ -GNN or  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$  outperform the best baselines.
Model	BA-2Motifs	Mutag	MNIST-75sp	Spurious-Motif
b=0.5	b=0.7	b=0.9
GNNExplainer	67.35 ± 3.29	61.98 ± 5.45	59.01 ± 2.04	62.62 ± 1.35	62.25 ± 3.61	58.86 ± 1.93
PGExplainer	84.59 ± 9.09	60.91 ± 17.10	69.34 ± 4.32	69.54 ± 5.64	72.33 ± 9.18	72.34 ± 2.91
GraphMask	92.54 ± 8.07	62.23 ± 9.01	73.10 ± 6.41	72.06 ±5.58	73.06 ± 4.91	66.68 ± 6.96
IB-Subgraph	86.06 ± 28.37	91.04 ± 6.59	51.20 ± 5.12	57.29 ± 14.35	62.89 ± 15.59	47.29 ± 13.39
DIR	82.78 ± 10.97	64.44 ± 28.81	32.35 ± 9.39	78.15 ± 1.32	77.68 ± 1.22	49.08 ± 3.66
GIN-GSAT	98.74 ± 0.55	99.60 ± 0.51	83.36 ± 1.02	78.45 ± 3.12	74.07 ± 5.28	71.97 ± 4.41
PNA-GSAT	93.77 ± 3.90	99.07 ± 0.50	84.68 ± 1.06	83.34 ± 2.17	86.94 ± 4.05	88.66 ± 2.44
π-GNN	99.33 ± 0.63	99.81 ± 0.17	92.77 ± 0.80	93.24 ± 0.72	96.92 ± 0.85	96.39 ± 0.92
π-GNNDFT	93.19 ± 1.48	95.29 ± 0.67	85.18 ± 1.08	86.29 ± 2.22	87.43 ± 2.47	89.64 ± 2.26
In the experiment, we use two popular synthetic datasets [10, 11, 13, 14] and four real-world datasets of graph classification tasks. The details of dataset characteristics and statistics are summarized in Appendix B. A brief introduction to the datasets is as follows.
- Synthetic Datasets. BA-2Motifs [10] and Spurious-Motif [13] are two widely-used synthetic datasets to evaluate the interpretation performance of the GNN explanation methods.
- Real-world Datasets. We use four real-world datasets, the superpixel graph dataset MNIST-75sp [40], the sentiment analysis dataset Graph-SST2 [16], and two chemical molecule datasets Mutag [18] and Ogbg-Molhiv [47]. Note that, in the MNIST-75sp dataset, the subgraph with nonzero pixel values is regarded as the ground-truth explanation [14]; in the Mutag dataset,  $-\mathrm{NO}_2$  and  $-\mathrm{NH}_2$  functional groups in mutagen graphs are labelled as the ground-truth explanation [28]. Hence, we use the MNIST-75sp and Mutag datasets for both the interpretation and the prediction evaluations.
We extensively compare  $\pi$ -GNN with the following two types of baselines:
- Interpretation Baselines. We compare the interpretation performance with both the post-hoc explanation methods including GNNExplainer [10], PGExplainer [11], and GraphMask [39] and the intrinsic interpretable methods including DIR [13], IB-subgraph [12], GIN-GSAT, and PNA-GSAT [14]. Following the standard setting, the evaluation metric is the explanation ROC-AUC [13, 14].
- Prediction Baselines. We compare the perdition performance with the powerful GNN models including GIN [4] and PNA [32] and the intrinsic interpretable methods including DIR, IB-subgraph, GIN-GSAT, and PNA-GSAT. For the OGBG-Molhiv dataset, we use the classification ROC-AUC as the prediction metric [47]. For all the other dataset, we report the classification accuracy [13].
Additionally, we report the performance of  $\pi$ -GNN which directly fine-tunes on downstream datasets without pre-training (denoted as the  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$ ), to investigate the effectiveness of pre-training phase. All the results are averaged over 10-times evaluation with different random seeds. Architecture of the downstream GNN predictors used in  $\pi$ -GNN and  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$  are reported in Appendix C.
4.2 Main Results (RQ1)
To investigate the effectiveness of  $\pi$ -GNN, we compare the interpretation and the prediction performance with the SOTA interpretation and prediction baselines. See Appendix C for the pre-training and fine-tuning details. The overall interpretation performance and prediction performance are summarized in Table 1 and Table 2, respectively. We conclude the following observations:
-  $\pi$ -GNN significantly outperforms the leading GNN explanation methods. Specifically, for the Spurious-Motif dataset,  $\pi$ -GNN surpasses DIR by  $27.21\%$  on average and by  $47.31\%$  at most. Compared with the best baselines, i.e., the GSAT with a 4-layer PNA encoder,  $\pi$ -GNN improves the interpretation performance by  $9.20\%$  on average. However, we merely employ the combination of a truncated SVD embedding and a 2-layer MLP as the encoder, which convincingly demonstrates the effectiveness of our proposed pre-training phase. Moreover, as the degree of spurious correlation in
Table 2: Prediction Performance (Acc) Comparison. The underlined results highlight the best baselines. The bold results mean the  $\pi$ -GNN or  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$  outperform the best baselines.
Model	Molhiv(AUC)	Graph-SST2	MNIST-75sp	Spurious-Motif
b=0.5	b=0.7	b=0.9
GIN	76.69 ± 1.25	82.73 ± 0.77	95.74 ± 0.36	39.87 ± 1.30	39.04 ± 1.62	38.57 ± 2.31
PNA	78.91 ± 1.04	79.87 ± 1.02	87.20 ± 5.61	68.15 ± 2.39	66.35 ± 3.34	61.40 ± 3.56
IB-Subgraph	76.43 ± 2.65	82.99 ± 0.67	93.10 ± 1.32	54.36 ± 7.09	48.51 ± 5.76	46.19 ± 5.63
DIR	76.34 ± 1.01	82.32 ± 0.85	88.51 ± 2.57	45.49 ± 3.81	41.13 ± 2.62	37.61 ± 2.02
GIN-GSAT	76.47 ± 1.53	82.95 ± 0.58	96.24 ± 0.17	52.74 ± 4.08	49.12 ± 3.29	44.22 ± 5.57
PNA-GSAT	80.24 ± 0.73	80.92 ± 0.66	93.96 ± 0.92	68.74 ± 2.24	64.38 ± 3.20	57.01 ± 2.95
π-GNN	80.86 ± 0.61	88.05 ± 0.43	96.89 ± 0.20	74.67 ± 0.63	77.52 ± 0.77	77.46 ± 0.96
π-GNNDFT	79.71 ± 1.08	83.48 ± 1.20	92.89 ± 0.95	70.78 ± 1.63	71.02 ± 1.43	72.61 ± 1.75
Spurious-Motif (i.e., the parameter  $b$ ) increasing, the performance of  $\pi$ -GNN does not decrease as most of the baselines. The post-hoc explainers, including GNNExplainer, PGExplainer, and GraphMask seems to be robust in terms of the spurious correlation, but their interpretability is limited by the fixed prediction model. Although DIR and GSAT introduce complex mechanism for mitigating the spurious correlation,  $\pi$ -GNN still performs better. We ascribe this superiority to the generalizable knowledge which is distilled from the pre-training phase over large dataset with ground-truth explanations. For the BA-2Motifs and the Mutag datasets,  $\pi$ -GNN using a more simpler encoder architecture also achieves comparable performance. For the MNIST-75sp dataset,  $\pi$ -GNN surpasses the best baseline PNA-GSAT by  $4.50\%$ . Such top-tier performance strongly validates the effectiveness of  $\pi$ -GNN explainer.
-  $\pi$ -GNN also achieves better prediction performance than the baselines. Overall,  $\pi$ -GNN outperforms all the prediction baselines consistently by a significant margin. Specifically, for the Spurious-Motif dataset,  $\pi$ -GNN outperforms the best baselines by  $11.05\%$  on average, which is a significant improvement. If we restrict the baselines into interpretable GNNs, the performance boost is much more significant (by  $13.17\%$  on average and up to  $20.45\%$ ). For the Graph-SST2 dataset,  $\pi$ -GNN outperforms the black-box predictor (i.e., GIN and PNA), as well as the SOTA interpretable methods IB-Subgraph, which optimizes the explanatory subgraph based on the information bottleneck principle. Note that, we only implement a 2-layer GCN with global mean pooling function as the Graph-SST2 predictor. We credit such outperformance to the pre-training phase, from which the universal patterns of the graphs are potentially distilled. For the MNIST-75sp dataset,  $\pi$ -GNN achieves comparable prediction accuracy with the GSAT methods, but our interpretation ROC-AUC exceeds GSAT by  $8.09\%$ . Additionally, one can notice that the black-box predictors are insensitive to the spurious correlation while the interpretable baselines deteriorate obviously. This phenomena may indicate that insufficient interpretability conflicts with the chase of prediction accuracy, but a powerful interpreter is quite helpful to the subsequent predictor.
- The pre-training phase advances the interpreter in terms of both interpretation and verdict performance. As shown in Table 1 and Table 2, the  $\pi$ -GNN with pre-training phase significantly improves both the interpretation and the prediction performance, compared with the reduced variant  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$ . For the interpretation ROC-AUC,  $\pi$ -GNN outperforms the reduced variant by  $6.91\%$  on average. This suggests that the universal structural patterns distilled in the pre-training phase can indeed generalize to various downstream tasks and improve the interpretability. Compared with the reduced variant,  $\pi$ -GNN consistently provides much stabler interpretation with smaller variance. Additionally, one can observe that the reduced variant  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$  still surpasses the best baselines on some real-world datasets, such as the interpretation performance on MNIST-75sp dataset and the prediction performance on Graph-SST2 dataset. This may imply that the edge interaction captured by  $\pi$ - $\mathrm{GNN}_{\mathrm{DFT}}$  is able to identify the influential subgraphs more accurately.
Moreover, we present the explanatory visualization, the investigate of different pre-training datasets and the hyper-parameter analysis in Appendix D, E and F, respectively.
4.3 Inter-Task Generalization Performance (RQ2)
To further investigate whether the universal structural patterns behind different tasks is common, we next study the generalization ability across different tasks. Specifically, we evaluate the  $\pi$ -GNN model that is pre-trained over graph classification dataset PT-Motifs on the explanation task of node
Table 3: Inter-Task Interpretation Performance (ROC-AUC) Comparison. The **bold font highlights the best results and the **underlined results highlight the second best method.
Model	BA-Shapes	BA-Community	Tree-Cycles	Tree-Grid
GRAD	88.20	75.00	90.50	61.20
Attention	81.50	73.90	82.40	66.70
GNNExplainer	92.50	83.60	94.80	87.50
PGExplainer	96.30 ± 1.10	94.50 ± 1.90	98.70 ± 0.70	90.70 ± 1.40
π-GNN	94.78 ± 0.32	94.67 ± 1.50	95.19 ± 0.88	90.11 ± 1.10
π-GNNDFT	93.17 ± 0.40	92.15 ± 1.61	92.53 ± 1.81	88.62 ± 1.87
classification datasets. The pre-trained  $\pi$ -GNN model and the reduced variant are both equipped with a node classifier. Following existing works, we use four widely-used synthetic node classification datasets [10], namely BA-Shapes, BA-Community, Tree-Cycles and Tree-Grid, whose detailed statistics are presented in Appendix B. The main result of inter-task explanation in Table 3 shows that  $\pi$ -GNN achieves comparable performance with SOTA node classification explainers. This evidence is accordant with our basic premise that the universal structural patterns can generalize across datasets of different tasks. For the BA-Community dataset,  $\pi$ -GNN even supposes PGExplainer with smaller variance. This may be because the community structure in the BA-Community graph conforms more to the universal patterns embedded in  $\pi$ -GNN.
As shown in Figure 3, we conduct ablation study on  $\pi$ -GNN, by evaluate the performance of its three variants. First,  $\pi$ -GNN-SPL substitutes the structural pattern learning module with  $N$ -thread GNN encoders. Second,  $\pi$ -GNN-HPR removes the hypergraph refining module and directly calculates the edge contribution score. Third, we simultaneously conduct the two ablations above and denote it as  $\pi$ -GNN-ALL. Additionally, we report the performance of the variant without pre-training phase.
Specifically, when removing the structural pattern learning module, the interpretation performance on Mutag decreases by  $3.85\%$  on average and the prediction performance on Graph-SST2 decreases by  $1.08\%$  on average. For the variant  $\pi$ -GNN-HPR, the interpretation and prediction performance decreases by  $6.56\%$  and  $1.84\%$ , respectively. When we remove the two modules simultaneously, the interpretation and prediction performance decreases by  $7.56\%$  and  $2.16\%$ , respectively. The ablation study on the two modules demonstrates their effectiveness in capturing universal structural patterns and identifying the explanatory subgraphs. Moreover, for all the variants,  $\pi$ -GNN consistently outperforms the variant without pre-training phase by  $5.59\%$  in terms of ROC-AUC on Mutag and  $2.84\%$  in terms of accuracy on Graph-SST2.
Intrinsic interpretable GNNs. The leading interpretable GNNs [12, 13, 14] usually consist of an explainer module and a predictor module. The prepositional explainer takes the raw graph as input and outputs the explanation subgraph. The subsequent predictor calculates the prediction strictly relying on the explanation. Graph neural networks with attention mechanism are regarded as the initial interpretable GNNs [13, 14], such as graph attention network [3], self-attention graph pooling [40], where the learned weights can be interpreted as the importance of certain features. Recently, invariant learning is introduced to construct intrinsic interpretable GNNs [48, 49], such as DIR [13]. It argues that augmenting training data with causal intervention may assist explainer to distinguish the causal and non-causal parts. Besides, interpretable GNNs based on the information bottleneck principle [50], such as IB-Subgraph [12] and GSAT [14], are proposed to constraint the information flow from the input graph to the prediction, where the label-relevant graph components will be kept while the label-irrelevant ones are reduced.
Pre-training on Graphs. The research focus of current graph pre-training is the graph representation learning problem, whose objective is to learn a generic encoder  $f(\mathbf{A}, \mathbf{X})$  for various downstream tasks [51, 52]. The development of graph pre-training can be broadly divided into pre-trained graph embeddings [41, 53, 42] and pre-trained graph encoders [23, 22, 24, 21]. Pre-trained graph embedding models aim to provide good graph embeddings for various tasks, while the models themselves are no
(a) Interpretation performance on Mutag
(b) Interpretation performance on Spurious-Motif
(c) Prediction performance on Graph-SST2
(d) Prediction performance on Spurious-Motif
Figure 3: The ablation study of  $\pi$ -GNN on Mutag, Graph-SST2, and Spurious-Motif datasets.
longer needed to the tasks. DeepWalk [41] explores the graph embeddings by conducting random walks over graphs to generate node sequences which contain the co-occurrence relationship. Further, Node2vec [42] defines a flexible node neighborhood and proposes a biasd random walk process. The goal of pre-trained graph encoder models is a generic encoder model which can deal with different tasks. Gpt-GNN [23] pre-trains a 5-layer GIN encoder across the graph-level and node-level tasks. GCC [22] introduces the contrastive learning framework to pre-train the encoder over subgraph discrimination task. However, the precursor graph pre-training works are not designed to the graph explanation problem and can not be directly applied to the pre-training interpretable GNNs.
In this work, we for the first time investigated the universal interpretation problem in graph data and proposed the Pre-training Interpretable Graph Neural Network named  $\pi$ -GNN.  $\pi$ -GNN is able to work well on different types of graphs and downstream tasks.  $\pi$ -GNN was pre-trained over a constructed large synthetic graph dataset with ground-truth explanations to distill the generalizable interpretability. Then,  $\pi$ -GNN was fine-tuned on downstream tasks. Technically, we proposed an intergrated embedding module to capture and integrate multiple graph structural patterns for more generalizable representations. A hypergraph refining module was aslo proposed to incorporate the universal patterns with local interaction for more faithful explanatory subgraphs identification. Extensive experiments on different datasets and tasks demonstrated the promising generalizable interpretability as well as prediction performance of  $\pi$ -GNN.
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In Table 4, we give the mathematical symbols and their descriptions used in this paper for clarity.
Table 4: Symbols and their descriptions.
Symbol	Description
G, V, E	Graph instance, node set, edge set
X	Node feature matrix
XE	Edge feature matrix
A, Aij	Adjacency matrix, element at the i-th row, j-th column of A
v, vi; e, ei	Node instance; edge instance
N(v)	Neighborhood of node v
W	Trainable parameter matrix
F(·), σ(·)	Non-linear activation function, Sigmoid function
h	Edge contribution function
ρ, ρ	Ground-truth explanation, predicted explanation
S	Selection module
g	Explanatory subgraph
B, Bi	Set of basic pattern-learners, basic pattern-learner
N	Number of basic pattern-learners
Zi, Z	Pattern matrix, pattern tensor
Φ	Integrated pattern-learner
ZInt	Integrated pattern representation
ZE	Edge structural representation
S	Subset of node
f(2)	Node to edge transition function
Gh, VH, Eh	Hypergraph instance, hypernode set, hyperedge set
EP, EN	Positive (Negative) edge set
b	Degree of spurious correlation in Spurious-Motif dataset
We introduce the datasets used in the main experiment as follows.
- BA-2Motifs [10] is a synthetic dataset with binary graph classes for evaluating the interpretation performance. House motifs and cycle motifs decide the graph labels and serve as the ground-truth explanations of the two classes, respectively.
- Spurious-Motif [13] is a synthetic dataset with three graph classes for evaluating both the interpretation and the prediction performance. Each class corresponds to a particular motif which is regarded as the ground-truth explanation. During the synthesis process, spurious correlations, including the unbalanced base sampling and the scale drift, are injected into the training dataset. A hyper-parameter  $b$  controls the degree of spurious correlation, usually set as  $\{0.5, 0.7, 0.9\}$ .
- Mutag [18] is a chemical molecule dataset with binary graph classes which represents mutagenic property. Benefiting from domain knowledge,  $-\mathrm{NO}_2$  and  $-\mathrm{NH}_2$  functional groups in mutagen graphs are labelled as the ground-truth explanation. Therefore, we employ the Mutag dataset for the evaluation of interpretation and prediction performance.
- MNIST-75sp [40] converts the MNIST image dataset into a superpixel graph dataset with ten graph classes. The nodes are superpixels, while edges are the spatial distance between the related endpoints. The subgraph with nonzero pixel values is regarded as the ground-truth explanation. Hence, the Mnist-75sp is used for both the interpretation and the prediction evaluations.
- Graph-SST2 [16] is a sentiment analysis dataset with binary graph labels, where each sequence in SST2 dataset is transformed to a graph. Since no ground-truth explanations are available, we evaluate the prediction performance only.