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LogicXGNN: Grounded Logical Rules for Explaining Graph Neural Networks

Chuqin Geng, Ziyu Zhao, Zhaoyue Wang, Haolin Ye, Yuhe Jiang, Xujie Si

TL;DR

This work tackles the misalignment between fidelity in abstract concept spaces and practical grounding of GNN explanations. It introduces LogicXGNN, a post-hoc framework that learns logical rules over predicates reflecting GNN message-passing and grounds these rules via orbit-based subgraph representations, accompanied by a data-grounded fidelity Fid_D metric. Empirically, LogicXGNN achieves substantial improvements in Fid_D (over 20% on average) and dramatic speedups (10–100x) over state-of-the-art baselines, while maintaining strong coverage, stability, and validity across architectures and datasets. The approach provides scalable, interpretable, and trustworthy GNN explanations with direct grounding in observable data.

Abstract

Existing rule-based explanations for Graph Neural Networks (GNNs) provide global interpretability but often optimize and assess fidelity in an intermediate, uninterpretable concept space, overlooking grounding quality for end users in the final subgraph explanations. This gap yields explanations that may appear faithful yet be unreliable in practice. To this end, we propose LogicXGNN, a post-hoc framework that constructs logical rules over reliable predicates explicitly designed to capture the GNN's message-passing structure, thereby ensuring effective grounding. We further introduce data-grounded fidelity ($\textit{Fid}_{\mathcal{D}}$), a realistic metric that evaluates explanations in their final-graph form, along with complementary utility metrics such as coverage and validity. Across extensive experiments, LogicXGNN improves $\textit{Fid}_{\mathcal{D}}$ by over 20% on average relative to state-of-the-art methods while being 10-100 $\times$ faster. With strong scalability and utility performance, LogicXGNN produces explanations that are faithful to the model's logic and reliably grounded in observable data. Our code is available at https://github.com/allengeng123/LogicXGNN/.

LogicXGNN: Grounded Logical Rules for Explaining Graph Neural Networks

TL;DR

This work tackles the misalignment between fidelity in abstract concept spaces and practical grounding of GNN explanations. It introduces LogicXGNN, a post-hoc framework that learns logical rules over predicates reflecting GNN message-passing and grounds these rules via orbit-based subgraph representations, accompanied by a data-grounded fidelity Fid_D metric. Empirically, LogicXGNN achieves substantial improvements in Fid_D (over 20% on average) and dramatic speedups (10–100x) over state-of-the-art baselines, while maintaining strong coverage, stability, and validity across architectures and datasets. The approach provides scalable, interpretable, and trustworthy GNN explanations with direct grounding in observable data.

Abstract

Existing rule-based explanations for Graph Neural Networks (GNNs) provide global interpretability but often optimize and assess fidelity in an intermediate, uninterpretable concept space, overlooking grounding quality for end users in the final subgraph explanations. This gap yields explanations that may appear faithful yet be unreliable in practice. To this end, we propose LogicXGNN, a post-hoc framework that constructs logical rules over reliable predicates explicitly designed to capture the GNN's message-passing structure, thereby ensuring effective grounding. We further introduce data-grounded fidelity (), a realistic metric that evaluates explanations in their final-graph form, along with complementary utility metrics such as coverage and validity. Across extensive experiments, LogicXGNN improves by over 20% on average relative to state-of-the-art methods while being 10-100 faster. With strong scalability and utility performance, LogicXGNN produces explanations that are faithful to the model's logic and reliably grounded in observable data. Our code is available at https://github.com/allengeng123/LogicXGNN/.

Paper Structure

This paper contains 45 sections, 1 theorem, 19 equations, 15 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Graph neural networks for graph classification
  4. First-order logical rules for GNN interpretability
  5. The LogicXGNN Framework ($\phi_M$)
  6. Identifying hidden predicates $P$ for $\phi_M$
  7. Determining the logical structure of $\phi_M$
  8. Grounding $\phi_M$ into the input feature space
  9. Inference and Data-Grounded Fidelity.
  10. Analysis
  11. Computational complexity.
  12. Generalization across different GNN architectures.
  13. Evaluation
  14. Baselines.
  15. How effective is $\phi_M$ as a logical rule-based explanation tool?
  16. ...and 30 more sections

Key Result

Theorem D.1

The multi-criteria orbit sorting scheme employed in Algorithm alg:stable_orbits produces a deterministic total ordering for any graph with fixed structure and anchor node.

Figures (15)

  • Figure 1: Existing methods such as GraphTrail compute fidelity in an uninterpretable concept space while overlooking the grounding quality of final subgraph explanations presented to end users.
  • Figure 2: An overview of the LogicXGNN framework, which involves identifying hidden predicates, extracting rules, and grounding these rules in the input space for interpretability.
  • Figure 3: Impact of tree depth on $\textit{Fid}_{\mathcal{D}}$.
  • Figure 4: Baselines' explanations exhibit conflicting rules and chemically invalid subgraphs.
  • Figure 5: Besides representative subgraphs, our approach $\phi_M$ also provides general grounding rules for each predicate, effectively capturing more of the model's behavior, thereby achieving high fidelity.
  • ...and 10 more figures

Theorems & Definitions (4)

  • Definition 3.1: Subgraph Input Feature $\mathbf{Z}$
  • Theorem D.1: Orbit Sorting Consistency
  • proof
  • Remark D.2