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EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time

Shengyao Lu, Bang Liu, Keith G. Mills, Jiao He, Di Niu

TL;DR

EiG-Search tackles the efficiency gap in subgraph-level GNN explanations by advocating edge-induced subgraphs and per-instance size selection. It introduces a training-free, linear-time framework that ranks edges with Linear Gradients and exhaustively evaluates subgraphs formed by top-$k$ edges to optimize fidelity for each graph instance. Across seven datasets, EiG-Search achieves superior subgraph fidelity and markedly faster explanations than baselines, while maintaining determinism. The work highlights the interpretability and practicality gains from edge-centric explanations and per-instance sparsity, offering a scalable path for trustworthy GNN explanations.

Abstract

Understanding and explaining the predictions of Graph Neural Networks (GNNs), is crucial for enhancing their safety and trustworthiness. Subgraph-level explanations are gaining attention for their intuitive appeal. However, most existing subgraph-level explainers face efficiency challenges in explaining GNNs due to complex search processes. The key challenge is to find a balance between intuitiveness and efficiency while ensuring transparency. Additionally, these explainers usually induce subgraphs by nodes, which may introduce less-intuitive disconnected nodes in the subgraph-level explanations or omit many important subgraph structures. In this paper, we reveal that inducing subgraph explanations by edges is more comprehensive than other subgraph inducing techniques. We also emphasize the need of determining the subgraph explanation size for each data instance, as different data instances may involve different important substructures. Building upon these considerations, we introduce a training-free approach, named EiG-Search. We employ an efficient linear-time search algorithm over the edge-induced subgraphs, where the edges are ranked by an enhanced gradient-based importance. We conduct extensive experiments on a total of seven datasets, demonstrating its superior performance and efficiency both quantitatively and qualitatively over the leading baselines.

EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time

TL;DR

EiG-Search tackles the efficiency gap in subgraph-level GNN explanations by advocating edge-induced subgraphs and per-instance size selection. It introduces a training-free, linear-time framework that ranks edges with Linear Gradients and exhaustively evaluates subgraphs formed by top- edges to optimize fidelity for each graph instance. Across seven datasets, EiG-Search achieves superior subgraph fidelity and markedly faster explanations than baselines, while maintaining determinism. The work highlights the interpretability and practicality gains from edge-centric explanations and per-instance sparsity, offering a scalable path for trustworthy GNN explanations.

Abstract

Understanding and explaining the predictions of Graph Neural Networks (GNNs), is crucial for enhancing their safety and trustworthiness. Subgraph-level explanations are gaining attention for their intuitive appeal. However, most existing subgraph-level explainers face efficiency challenges in explaining GNNs due to complex search processes. The key challenge is to find a balance between intuitiveness and efficiency while ensuring transparency. Additionally, these explainers usually induce subgraphs by nodes, which may introduce less-intuitive disconnected nodes in the subgraph-level explanations or omit many important subgraph structures. In this paper, we reveal that inducing subgraph explanations by edges is more comprehensive than other subgraph inducing techniques. We also emphasize the need of determining the subgraph explanation size for each data instance, as different data instances may involve different important substructures. Building upon these considerations, we introduce a training-free approach, named EiG-Search. We employ an efficient linear-time search algorithm over the edge-induced subgraphs, where the edges are ranked by an enhanced gradient-based importance. We conduct extensive experiments on a total of seven datasets, demonstrating its superior performance and efficiency both quantitatively and qualitatively over the leading baselines.
Paper Structure (28 sections, 3 theorems, 14 equations, 11 figures, 5 tables, 1 algorithm)

This paper contains 28 sections, 3 theorems, 14 equations, 11 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Notations.
  4. Graph neural networks.
  5. Problem setup.
  6. Investigating Subgraph-level Explanations via Inducing Technique and Size
  7. Subgraph Inducing Technique
  8. Size of the Subgraph Explanations
  9. Linear-Complexity Search over Edge-induced Subgraphs
  10. Experiments
  11. Faithfulness of the entire framework.
  12. Effectiveness of each phase.
  13. Efficiency.
  14. Other tasks.
  15. Conclusion
  16. ...and 13 more sections

Key Result

Theorem 3.6

Given a graph $G=(V,E)$, an edge-induced subgraph-level explanation $G[E_S]$, a node-induced subgraph-level explanation $G[V_S]$, and a node-and-edge-induced subgraph-level explanation $G[V_S, E_S]$. The following inequalities on the intuitiveness of these explanations always hold, for any $V_S\subs

Figures (11)

  • Figure 1: Illustration of subgraph explanations. (a): If nodes that are not directly neighboring each other are selected, determining the important subgraph structure becomes non-trivial. If edges are selected, the corresponding endpoints are naturally selected, which naturally gives a subgraph explanation. (b): Node-selection-based methods are not able to discover the angle-shape structure as an explanation, whereas edge-selection can be helpful. (c): The orange nodes stand for "C", blue nodes stand for "N", and red nodes stand for "O". Picking a single subgraph for explanations cannot properly find the disconnected "NO2" groups as we highlighted. (d): The size of the critical subgraph is the size of highlighted "NO2", which is different from (c).
  • Figure 2: An example illustrating edge score approximation, where $w_{e1}$ and $w_{e2}$ are the edge weights, $c$ is a class of the GNN.
  • Figure 3: Overall Fidelity at different levels of average sparsity using EiG-Search and a number of baselines. Higher is better.
  • Figure 4: Comparsion between the baselines and EiG-Search after applying Linear-Complexity search.
  • Figure 5: Comparsion between SA and EiG-Search after applying Linear-Complexity search.
  • ...and 6 more figures

Theorems & Definitions (12)

  • Definition 3.1: Intuitiveness of Subgraph-Level Explanations
  • Definition 3.2: Exhaustiveness of Subgraph-Level Explanation Inducing Techiniques
  • Definition 3.3: Node-Induced Subgraph-Level Explanations
  • Definition 3.4: Edge-Induced Subgraph-Level Explanations
  • Definition 3.5: Node-and-Edge-Induced Subgraph-Level Explanations
  • Theorem 3.6
  • Theorem 3.7
  • Definition 3.8: Sparsity
  • Definition 3.9: Subgraph-Level Fidelity
  • Proposition 3.10
  • ...and 2 more