Towards Prototype-Based Self-Explainable Graph Neural Network Enyan Dai

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Towards Prototype-Based Self-Explainable Graph Neural

Network

Enyan Dai

The Pennsylvania State University

emd5759@psu.edu

Suhang Wang

The Pennsylvania State University

szw494@psu.edu

ABSTRACT

Graph Neural Networks (GNNs) have shown great ability in mod-

eling graph-structured data for various domains. However, GNNs

are known as black-box models that lack interpretability. Without

understanding their inner working, we cannot fully trust them,

which largely limits their adoption in high-stake scenarios. Though

some initial eorts have been taken to interpret the predictions

of GNNs, they mainly focus on providing post-hoc explanations

using an additional explainer, which could misrepresent the true

inner working mechanism of the target GNN. The works on self-

explainable GNNs are rather limited. Therefore, we study a novel

problem of learning prototype-based self-explainable GNNs that

can simultaneously give accurate predictions and prototype-based

explanations on predictions. We design a framework which can

learn prototype graphs that capture representative patterns of each

class as class-level explanations. The learned prototypes are also

used to simultaneously make prediction for for a test instance and

provide instance-level explanation. Extensive experiments on real-

world and synthetic datasets show the eectiveness of the proposed

framework for both prediction accuracy and explanation quality.

ACM Reference Format:

Enyan Dai and Suhang Wang. 2022. Towards Prototype-Based Self-Explainable

Graph Neural Network. In Proceedings of ACM Conference (Conference’17).

ACM, New York, NY, USA, 9 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn

1 INTRODUCTION

Graph structured data such as trac networks, social networks,

and molecular graphs are very pervasive in real world. To model

the graph structured data for various applications such as drug

discovery [

], nancial analysis [

], and recommendation sys-

tem [

], various graph neural networks (GNNs) [

] have

been proposed and made remarkable achievements. The success

of GNNs relies on the message-passing mechanism, i.e., the node

representations in GNNs will aggregate the information from the

neighbors to capture the attribute and topology information. Many

message-passing mechanisms have been investigated to learn pow-

erful representations from graphs, facilitating various tasks such

as node classication [8, 17] and graph classication [35].

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https://doi.org/10.1145/nnnnnnn.nnnnnnn

Figure 1: An illustration of self-explanation with prototypes

on classifying whether the test graph is cyclic.

Despite the great success of GNNs in modeling graphs, GNNs

have the same issue of lacking explainability as other deep learn-

ing models due to the high non-linearity in the model. In addi-

tion, the message-passing mechanism of GNNs that aggregates

neighborhood features to capture topology information makes it

more challenging to understand the predictions. The lacking of

explainability in GNNs will largely limit their adoption in critical

applications pertaining to fairness, privacy and safety. For instance,

a GNN model may be trained to explore the proprieties of various

drugs. However, due to the black-box characteristic of GNNs, it is

unknown whether the rules learned by GNN model is consistent

with the chemical rules in the real-world, which raises the concern

of applying predictions that may threaten the drug safety.

Extensive approaches [

] have been investigated to explain

trained neural networks or give self-explainable predictions on

independent and identically distributed (i.i.d) data such as images.

However, they fail to generalize to GNNs due to the utilization of

message-passing mechanism designed for relational information

preservation. Recently, some initial eorts [

] have

been taken to address the explainability issue of GNNs. For example,

GNNExplainer [

] explains the prediction of an instance by identi-

fying the crucial subgraph of the instance’s local graph. Model-level

explanation is also investigated by generating graph patterns that

maximize the prediction of each class by the target model [

However, most of existing GNN explainers focus on the post-hoc

explanations, i.e., learning an additional explainer to explain the

predictions of a trained GNN. Since the learned explainer cannot

have perfect delity to the original model, the post-hoc explana-

tions may misrepresent the true explanations of the GNNs [

Therefore, it is crucial to develop a self-explainable GNN, which

can simultaneously give predictions and explanations.

One promising direction of self-explainable GNN is to learn

prototype graphs of each class to present the key patterns of each

class and simultaneously conduct prediction and give explanations

with the learned prototypes. The prototypes can provide class-level

and instance-level self-explanations. Figure 1 gives an illustration

of the prototype-based self-explanations on a toy classication

problem. As shown in the gure, the problem is to predict whether

a graph is cyclic or not. Taking the class cyclic as an example, the

learned prototype graphs are typical patterns of cyclic graphs of

arXiv:2210.01974v1 [cs.LG] 5 Oct 2022

various sizes. Therefore, the learned prototype graphs of class cyclic

can provide class-level explanation to show representative graphs of

class cyclic. For a test graph

G𝑡

, we will match it with the prototype

graphs of each class to give the prediction. Specically, the instance-

level explanation for predicting

G𝑡

can be: “Graph

G𝑡

is classied

as cyclic, because it is most similar to the second prototype graph

of class cyclic." Though promising, learning representative graphs

for self-explainable classication remains an open problem.

Therefore, in this work,we investigate a novel problem of learn-

ing prototype-based self-explainable graph neural network. How-

ever, this is a non-trivial task. There are two main challenges: (

)

how to eciently learn high-quality prototypes that are representa-

tives of each class for class-level explanation. Though some existing

works [

] have studied prototype learning for self-explanations,

they are mainly proposed for i.i.d data. Recently, ProtGNN [

]

applies a Monte Carlo tree search to identify subgraphs from raw

graph as prototypes. However, the search algorithm is very time

consuming. And the prototypes are limited to the subgraphs in

the dataset, which might not be that representative; and (

) how

to simultaneously give an accurate prediction and provide correct

prototype-based instance-level explanation. Dierent from images,

the matching process between the test graph and prototype graphs

cannot directly use simple metric such as Euclidean distance. More-

over, the supervision of the matching result is not available. How

to eectively leverage the classication supervision for prototype

learning and correct explanations needs further investigation.

In an attempt to address the above challenges, we develop a

novel

rototype-Based Self-E

plainable

GNN

(PxGNN)

. To e-

ciently obtain the prototype graphs, PxGNN adopts a prototype

graph generator to attain the prototype graphs from the learnable

prototype embeddings. A constraint on the learnable prototype

embeddings and self-supervision from graph reconstruction are

utilized to guarantee the quality of learned prototype embeddings

and generated prototype graphs, respectively. An encoder is de-

ployed to match the test graph with the generated prototype graphs

for self-explainable classication. Since representative prototype

graphs of a certain class is supposed to be similar to the test graphs

in the same class, the labels can provide implicit supervision to

ensure the representativeness of the prototype graphs and guide

the matching process. More specically, a novel classication loss is

proposed to simultaneously ensure the accuracy of prediction and

the quality of prototype-based instance-level explanation. And the

classication loss is utilized to jointly train the model and prototype

embeddings to learn prototypes well represent their corresponding

classes. In summary, our main contributions are:

•

We investigate a novel problem of learning prototype graphs for

self-explainable classication on graph-structured data;

•

We develop a new framework PxGNN, which learns an eective

prototype generator with self-supervision to obtain high-quality

prototype graphs for accurate predictions and explanations;

•

We construct a synthetic dataset which can quantitatively evalu-

ate the prototype-base explanation; and

•

Extensive experiments on both real-world and synthetic datasets

demonstrate the eectiveness of our PxGNN in learning repre-

sentative prototypes for accurate self-explainable classication.

1Code and datasets will be released upon acceptance

2 RELATED WORK

2.1 Graph Neural Networks

Graph Neural Networks (GNNs) [

] have shown great

ability for representation learning on graphs, which facilitate var-

ious applications such as trac analysis [

], recommendation

system [

], and drug generation [

]. Generally, existing GNNs [

–

] utilize a message-passing mechanism that a

node’s representation is updated by aggregating and combining the

features from its neighbors. For example, GCN [

] averages the

representations of neighbors and the target node followed by an

non-linear transformation. GAT [

] adopts an attention mecha-

nism to better aggregate the representations of the nodes from the

neighbors. Recently, various GNN models are proposed to further

improve the performance of GNNs [

]. For in-

stance, FastGCN [

] is proposed to alleviate the scalability issue of

GCN. In addition, some methods [

] focus on overcoming the

oversmoothing issue of GCN and design deep GNNs to incorporate

more hops of neighbors. Moreover, to facilitate the downstream

tasks that are short of labels, self-supervised GNNs [

]

are investigated to learn better representations.

2.2 Explainability of Graph Neural Networks

Despite the great success of graph neural networks, the problem

of lacking explainability hinders the adoption of GNNs to various

high-stake domains such as credit estimation. Though extensive

methods [

] have been proposed to explain neural

networks, they are overwhelmingly developed for i.i.d data such

as images and texts and cannot be directly applied to explain GNN

models. Recently, some works in explainability of GNNs are emerg-

ing [

]. The majority of these GNN explainers

give the explanations by extracting the crucial nodes, edges, and/or

node features. For instance, GNNExplainer [

] learns soft masks

for edges and node features to explain the predictions with the

identied subgraphs and features. PGExplainer [

] proposes to

combine the global view of GNNs to facilitate the extraction of im-

portant graphs by applying a parameterized explainer. XGNN [

]

generates representative graphs for a class as model-level explana-

tions for graph classication.

However, the aforementioned methods focus on post-hoc ex-

planations for a trained GNN, i.e., they usually require additional

explainer to explain the target GNN, which might misrepresent the

decision reasons of the model. There are very few initial eorts

for self-explainable GNNs [

], which aims to simultaneously

give predictions and explanations on the predictions. SE-GNN [

]

simultaneously give the predictions and explanations of a target

node by identifying the K-nearest labeled nodes. ProtGNN [

] is

the most similar work to ours, which nds subgraphs from the raw

graphs as prototypes to give self-explanations. However, ProtGNN

only focuses on graph classication and the computational cost

is very large due to the searching phase in nding the prototype

subgraphs. Our proposed method is inherently dierent from this

work: (

) we propose a novel prototype-based self-explainable GNN

that is eective in both node and graph-level classication tasks;

(

) a prototype generator is deployed to eciently learn more

representative prototypes for self-explainable classication.

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TowardsPrototype-BasedSelf-ExplainableGraphNeuralNetworkEnyanDaiThePennsylvaniaStateUniversityemd5759@psu.eduSuhangWangThePennsylvaniaStateUniversityszw494@psu.eduABSTRACTGraphNeuralNetworks(GNNs)haveshowngreatabilityinmod-elinggraph-structureddataforvariousdomains.However,GNNsareknownasblack-boxmod...

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Towards Prototype-Based Self-Explainable Graph Neural Network Enyan Dai

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