Relevant Walk Search for Explaining Graph Neural Networks

2026-05-22

AI Summary

This work addresses the exponential computational complexity of existing high-order explainability methods for graph neural networks (GNNs), such as GNN-LRP, which becomes intractable on large-scale graphs due to exhaustive path enumeration. To overcome this limitation, the authors introduce a polynomial-time algorithm that efficiently identifies the top-K most influential paths for a given prediction by adapting the max-product algorithm from probabilistic graphical models to the GNN interpretability domain. The proposed approach synergistically combines techniques from GNNs and graphical models, achieving neuron-level exactness while enabling scalable node-level approximations with substantially reduced computational overhead. Extensive experiments across diverse benchmarks—including epidemiology, molecular property prediction, and natural language processing—demonstrate the method’s efficiency, scalability, and practical applicability to large-scale GNN explanation tasks.

Abstract

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of \emph{walks} to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires {\em exponential} computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose {\em polynomial-time} algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the \emph{max-product} algorithm -- a common tool for finding the maximum likelihood configurations in probabilistic graphical models -- and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under \href{https://github.com/xiong-ping/rel_walk_gnnlrp}{github.com/xiong-ping/rel\_walk\_gnnlrp}.

Problem

• Graph Neural Networks
• Explainability
• Relevance Propagation
• Computational Complexity
• Walk Search

Innovation

• Graph Neural Networks
• Explainability
• Relevant Walks
• Polynomial-time Algorithm
• Max-product Algorithm