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PAGE: Prototype-Based Model-Level Explanations for Graph Neural Networks

Yong-Min Shin, Sun-Woo Kim, Won-Yong Shin

TL;DR

PAGE tackles the problem of model-level explainability for graph neural networks by introducing a two-phase prototype-based approach. It first clusters graph-level embeddings with a Gaussian mixture model to select representative graphs, then discovers class-specific prototype subgraphs using a novel node-tuple scoring function across multiple search sessions. The method leverages both graph- and node-level embeddings and yields human-interpretable prototypes that reflect the learned decision rules, with theoretical ties to the Weisfeiler-Lehman kernel and strong empirical performance against the state-of-the-art XGNN across six datasets. PAGE demonstrates robustness to data scarcity and improved computational efficiency, offering a practical pathway to concise, generalizable explanations for GNN-based graph classification in diverse domains.

Abstract

Aside from graph neural networks (GNNs) attracting significant attention as a powerful framework revolutionizing graph representation learning, there has been an increasing demand for explaining GNN models. Although various explanation methods for GNNs have been developed, most studies have focused on instance-level explanations, which produce explanations tailored to a given graph instance. In our study, we propose Prototype-bAsed GNN-Explainer (PAGE), a novel model-level GNN explanation method that explains what the underlying GNN model has learned for graph classification by discovering human-interpretable prototype graphs. Our method produces explanations for a given class, thus being capable of offering more concise and comprehensive explanations than those of instance-level explanations. First, PAGE selects embeddings of class-discriminative input graphs on the graph-level embedding space after clustering them. Then, PAGE discovers a common subgraph pattern by iteratively searching for high matching node tuples using node-level embeddings via a prototype scoring function, thereby yielding a prototype graph as our explanation. Using six graph classification datasets, we demonstrate that PAGE qualitatively and quantitatively outperforms the state-of-the-art model-level explanation method. We also carry out systematic experimental studies by demonstrating the relationship between PAGE and instance-level explanation methods, the robustness of PAGE to input data scarce environments, and the computational efficiency of the proposed prototype scoring function in PAGE.

PAGE: Prototype-Based Model-Level Explanations for Graph Neural Networks

TL;DR

PAGE tackles the problem of model-level explainability for graph neural networks by introducing a two-phase prototype-based approach. It first clusters graph-level embeddings with a Gaussian mixture model to select representative graphs, then discovers class-specific prototype subgraphs using a novel node-tuple scoring function across multiple search sessions. The method leverages both graph- and node-level embeddings and yields human-interpretable prototypes that reflect the learned decision rules, with theoretical ties to the Weisfeiler-Lehman kernel and strong empirical performance against the state-of-the-art XGNN across six datasets. PAGE demonstrates robustness to data scarcity and improved computational efficiency, offering a practical pathway to concise, generalizable explanations for GNN-based graph classification in diverse domains.

Abstract

Aside from graph neural networks (GNNs) attracting significant attention as a powerful framework revolutionizing graph representation learning, there has been an increasing demand for explaining GNN models. Although various explanation methods for GNNs have been developed, most studies have focused on instance-level explanations, which produce explanations tailored to a given graph instance. In our study, we propose Prototype-bAsed GNN-Explainer (PAGE), a novel model-level GNN explanation method that explains what the underlying GNN model has learned for graph classification by discovering human-interpretable prototype graphs. Our method produces explanations for a given class, thus being capable of offering more concise and comprehensive explanations than those of instance-level explanations. First, PAGE selects embeddings of class-discriminative input graphs on the graph-level embedding space after clustering them. Then, PAGE discovers a common subgraph pattern by iteratively searching for high matching node tuples using node-level embeddings via a prototype scoring function, thereby yielding a prototype graph as our explanation. Using six graph classification datasets, we demonstrate that PAGE qualitatively and quantitatively outperforms the state-of-the-art model-level explanation method. We also carry out systematic experimental studies by demonstrating the relationship between PAGE and instance-level explanation methods, the robustness of PAGE to input data scarce environments, and the computational efficiency of the proposed prototype scoring function in PAGE.
Paper Structure (36 sections, 2 theorems, 7 equations, 11 figures, 5 tables)

This paper contains 36 sections, 2 theorems, 7 equations, 11 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Main Contributions
  4. Organization and Notations
  5. Related work
  6. Explanation Methods for Deep Learning
  7. Explanation Methods for GNNs
  8. Discussion
  9. METHODOLOGY
  10. Settings and Basic Assumptions
  11. GNN Models for Graph Classification
  12. Problem Formulation
  13. Overview of Our PAGE Method
  14. PAGE: Proposed Method
  15. Clustering and Selection of Graph-Level Embeddings (Phase 1)
  16. ...and 21 more sections

Key Result

Theorem 4.1.1

Let $f_\text{GNN}^{(p)}$ denote the function that returns node-level vector representations at the $p$-th GNN layer in $f_\text{GNN}$. Then for all $p \geq 0$, there exists a GNN model equivalent to a node coloring such that $f_\text{GNN}^{(p)}(u)=f_\text{GNN}^{(p)}(v)$ if and only if $c^{(p)}(u)=c

Figures (11)

  • Figure 1: A comparison between instance-level and model-level explanation methods to capture the general behavior of GNNs.
  • Figure 2: A schematic overview overview and an illustrative example of our PAGE method.
  • Figure 3: Visualization of graph-level embeddings for the BA-house dataset.
  • Figure 4: An example that illustrates the mechanism of the core prototype search module for a certain search session when $k=3$.
  • Figure 5: Qualitative comparison of PAGE and XGNN for five datasets (excluding MNIST-sp, which is separately presented in Fig. \ref{['fig:MNIST_sp_results']}), where each node is colored differently according to the types of nodes.
  • ...and 6 more figures

Theorems & Definitions (11)

  • Theorem 4.1.1: Morris et al., 2019
  • Corollary 4.1.2
  • proof
  • Example 1
  • Remark 1
  • Definition 1: Prototype scoring function
  • Remark 2
  • Remark 3
  • Example 2
  • Definition 2: Concentration score
  • ...and 1 more