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GnnXemplar: Exemplars to Explanations -- Natural Language Rules for Global GNN Interpretability

Burouj Armgaan, Eshan Jain, Harsh Pandey, Mahesh Chandran, Sayan Ranu

TL;DR

GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science, is proposed, which significantly outperforms existing methods in fidelity, scalability, and human interpretability.

Abstract

Graph Neural Networks (GNNs) are widely used for node classification, yet their opaque decision-making limits trust and adoption. While local explanations offer insights into individual predictions, global explanation methods, those that characterize an entire class, remain underdeveloped. Existing global explainers rely on motif discovery in small graphs, an approach that breaks down in large, real-world settings where subgraph repetition is rare, node attributes are high-dimensional, and predictions arise from complex structure-attribute interactions. We propose GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science. GnnXemplar identifies representative nodes in the GNN embedding space, exemplars, and explains predictions using natural language rules derived from their neighborhoods. Exemplar selection is framed as a coverage maximization problem over reverse k-nearest neighbors, for which we provide an efficient greedy approximation. To derive interpretable rules, we employ a self-refining prompt strategy using large language models (LLMs). Experiments across diverse benchmarks show that GnnXemplar significantly outperforms existing methods in fidelity, scalability, and human interpretability, as validated by a user study with 60 participants.

GnnXemplar: Exemplars to Explanations -- Natural Language Rules for Global GNN Interpretability

TL;DR

GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science, is proposed, which significantly outperforms existing methods in fidelity, scalability, and human interpretability.

Abstract

Graph Neural Networks (GNNs) are widely used for node classification, yet their opaque decision-making limits trust and adoption. While local explanations offer insights into individual predictions, global explanation methods, those that characterize an entire class, remain underdeveloped. Existing global explainers rely on motif discovery in small graphs, an approach that breaks down in large, real-world settings where subgraph repetition is rare, node attributes are high-dimensional, and predictions arise from complex structure-attribute interactions. We propose GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science. GnnXemplar identifies representative nodes in the GNN embedding space, exemplars, and explains predictions using natural language rules derived from their neighborhoods. Exemplar selection is framed as a coverage maximization problem over reverse k-nearest neighbors, for which we provide an efficient greedy approximation. To derive interpretable rules, we employ a self-refining prompt strategy using large language models (LLMs). Experiments across diverse benchmarks show that GnnXemplar significantly outperforms existing methods in fidelity, scalability, and human interpretability, as validated by a user study with 60 participants.

Paper Structure

This paper contains 41 sections, 5 theorems, 29 equations, 19 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction and Related Works
  2. Existing Works and Open Challenges
  3. Contributions
  4. Preliminaries and Problem Formulation
  5. Methodology
  6. Exemplar Identification.
  7. Quantifying Representativeness through Reverse k-NN
  8. Sampling for Scalable Computation of Reverse k-NN
  9. Coverage Maximization
  10. Discovery of Exemplar Signatures
  11. Experiments
  12. Experimental Setup
  13. Fidelity
  14. Ablation Study
  15. Impact of Parameters and Gnn architectures
  16. ...and 26 more sections

Key Result

Lemma 1

Given an error threshold $\theta$ and confidence level $1 - \delta$, it suffices to sample $z \geq \frac{\ln{\left(\frac{2}{\delta}\right)}(2+\theta)}{\theta^2}$ nodes to ensure that for any $v \in \mathcal{V}\xspace_{tr},\;P\left( \left| \widetilde{\Pi}(v) - \Pi(v) \right| \leq \theta \right) \geq

Figures (19)

  • Figure 1: The pipeline of GnnXemplar.
  • Figure 2: Pipeline of signature discovery through iterative self-refinement of LLM output.
  • Figure 3: Ablation study on GnnXemplar. Left: Impact of Rev-$k$-NN based exemplar selection. Right: Impact of self-refinement strategy vs. zero-shot rule discovery.
  • Figure 4: Taxonomy of factual GNN explainers. Generation: RGExplainer rgexplainer, GFlowExplainer gflowexplainer, GEM gem; Gradient: SA guided-bp, Guided-BP guided-bp, Grad-CAM Excitation-BP; Decomposition: CAM Excitation-BP, Excitation-BP Excitation-BP, DEGREE degree, GNN-LRP GNN-LRP, GOAT goat; Perturbation: GNNExplainer gnnexplainer, PGExplainer pgexplainer, CF$^2$cff, GraphMask Graph-mask, ReFine ReFine, Zorro zorro, SubgraphX subgraphx, GstarX gstarx, TAGExplainer xie2022task; Surrogate: GraphLime graphlime, ReLex RELex, PGM-Explainer pgm-ex, DnX dnx, GraphSVX graphsvx; Subgraph sets: XGNN xgnn, GCNeuron xuanyuan2023global, GNNInterpreter gnninterpreter, DAGExplainer dagexplainer, MAGE mage; Subgraph formulae: GLGExplainer glgexplainer, GraphTrail armgaan2024graphtrail.
  • Figure 5: Subgraphs from the Questions dataset. Notice how active nodes 1, 2, and 3 surrounded by inactive nodes are predicted as inactive. This misclassification pattern is the signal that GnnXemplar picks up when learning the signature for the inactive class.
  • ...and 14 more figures

Theorems & Definitions (13)

  • Definition 1: Graph
  • Definition 2: Node Classification
  • Definition 3: Exemplars
  • Definition 4: Exemplar Signature
  • Definition 5: Reverse $k$-NN and Representative Power
  • Lemma 1
  • Definition 6: Exemplar Set
  • Theorem 1
  • Theorem 2
  • Definition 7: Set Cover
  • ...and 3 more