Factorized Explainer for Graph Neural Networks

TL;DR

This work identifies a fundamental flaw in GIB-based post-hoc explanations for graph neural networks: the original objective can yield trivial, input-insensitive explanations. It introduces a modified GIB objective that compares the model's predictions on the subgraph to the ground-truth label via cross-entropy, tying explanations to the actual model behavior. To overcome locality and aggregation losses in existing parametric explainers, the authors propose K-FactExplainer, a factorized framework that combines multiple local explainers with a global selector, and they provide a bootstrapping method to bound the number of components. Through extensive experiments on synthetic and real datasets, the method shows consistent improvements in explanation faithfulness (AUC) over baselines and demonstrates robustness to multi-motif scenarios and lossy aggregation, offering practical impact for trustworthy GNN deployments.

Abstract

Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. To open the black-box of these deep learning models, post-hoc instance-level explanation methods have been proposed to understand GNN predictions. These methods seek to discover substructures that explain the prediction behavior of a trained GNN. In this paper, we show analytically that for a large class of explanation tasks, conventional approaches, which are based on the principle of graph information bottleneck (GIB), admit trivial solutions that do not align with the notion of explainability. Instead, we argue that a modified GIB principle may be used to avoid the aforementioned trivial solutions. We further introduce a novel factorized explanation model with theoretical performance guarantees. The modified GIB is used to analyze the structural properties of the proposed factorized explainer. We conduct extensive experiments on both synthetic and real-world datasets to validate the effectiveness of our proposed factorized explainer.

Figures (2)

• Figure 1: Illustration of K-FactExplainer method. Starting from the left, the node embeddings for graph G are produced using the original GNN. The edge embeddings and graph embedding are produced by concatenating the node embeddings. The MLP $\Psi_0$ assigns weight to the outputs of PGExplainer MLPs $\Psi_{t}, t\in[k]$. The resulting vector of edge probabilities $\overline{\Omega}\triangleq (\sum_{t=1}^kp_t\omega^t_{i,j})_{i,j\in [n]}$ is used to produce the sampled explanation graph $G^*$. The explanation is fed to the original GNN and the output label is compared with the original prediction. The training proceeds by minimizing the cross-entropy term $CE(Y',\widehat{Y})$, where $\widehat{Y}$ is GNN prediction for the original input graph $G$.
• Figure 2: Visualization of BA-4motifs dataset. A BA-graph is used as the base graph. Each label is associated with two motifs.

Theorems & Definitions (14)

• Definition 1: Statistically Degraded Classification
• Remark 1
• Remark 2
• Remark 3
• Theorem 1
• Lemma 1: Modified Data Processing Inequality
• Definition 2: Geodisc Restricted Graph
• Definition 3: Local Explanation Methods
• Proposition 1: Locality of PGExplainer
• Remark 4