LogicXGNN: Grounded Logical Rules for Explaining Graph Neural Networks

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/.

💡 Research Summary

LogicXGNN tackles a critical shortcoming of existing rule‑based explanations for Graph Neural Networks (GNNs): they evaluate fidelity in an abstract concept space while the final subgraph explanations presented to users may be poorly grounded. The authors introduce data‑grounded fidelity (Fid_D), a metric that directly measures how well the final subgraphs align with the GNN’s predictions, and they propose a post‑hoc framework that builds logical rules over predicates explicitly designed to reflect the GNN’s message‑passing mechanism.

The method proceeds in three stages. First, hidden predicates are identified. For each node, the L‑hop receptive field is hashed using the Weisfeiler‑Lehman (WL) algorithm, yielding a unique structural pattern identifier. Simultaneously, a decision‑tree analysis on the final‑layer node embeddings selects a small set of informative dimensions K and corresponding thresholds T. Each node’s embedding pattern is binarized according to these thresholds, producing an embedding pattern vector. A predicate is defined as the conjunction of a structural pattern and an embedding pattern; a graph satisfies a predicate if any node satisfies it.

Second, a binary activation matrix Φ_c is constructed for each class c using correctly predicted training graphs. Each row corresponds to a conjunction of predicates that holds for a particular graph. An off‑the‑shelf rule learner (the authors use decision trees for efficiency) is then applied to Φ_c and the GNN’s predictions to learn a compact Disjunctive Normal Form (DNF) logical formula ϕ_M that globally explains the model. Tree depth controls rule complexity.

Third, the framework grounds ϕ_M back to the input space. Rather than mapping each latent concept to a single representative subgraph (as prior work does), LogicXGNN generates a set of diverse, fine‑grained grounding rules for each predicate. Because predicates already contain structural information, the grounding process can produce multiple valid subgraphs and structure‑aware input patterns Z, ensuring that explanations remain meaningful even when node features are continuous.

Experiments on four benchmark datasets (Mutagenicity, REDDIT‑BINARY, ogbg‑molhiv, and a synthetic graph classification task) compare LogicXGNN against state‑of‑the‑art methods such as GraphTrail, GNNExplainer, and PGExplainer. Evaluation includes Fid_D, coverage, validity, stability, and runtime. LogicXGNN achieves an average improvement of over 20 % in Fid_D, dramatically higher validity (e.g., 68 % vs. near‑zero on Mutagenicity), and comparable or better coverage and stability. Moreover, the predicate extraction and rule learning steps scale linearly with the number of nodes and layers, yielding 10–100× faster inference on large graphs.

Key contributions are: (1) the definition of data‑grounded fidelity, exposing the gap between concept‑space and final‑graph fidelity; (2) a novel predicate design that captures both topological and embedding patterns directly from the GNN’s computation; (3) an efficient rule‑learning pipeline that produces compact, human‑readable logical formulas; and (4) extensive empirical validation showing superior fidelity, utility, and scalability.

Limitations include reliance on WL hashing, which ignores node/edge attributes, and sensitivity to the chosen message‑passing depth L. Future work may incorporate attribute‑aware hashing, multi‑level predicates, and unsupervised predicate discovery to broaden applicability. The authors release their code, facilitating reproducibility and further research in trustworthy GNN explanations.