Efficient Higher-order Subgraph Attribution via Message Passing

2026-05-21

AI Summary

Existing higher-order subgraph attribution methods, such as GNN-LRP, suffer from exponential computational complexity, which hinders their scalability to deep graph neural networks. This work proposes an efficient algorithm grounded in the message-passing mechanism and the distributive property, achieving—for the first time—linear-time complexity for higher-order subgraph attribution, with computational overhead scaling linearly with network depth. The proposed method not only substantially accelerates the attribution process but also naturally incorporates neighborhood graph structural information, thereby establishing a generalized subgraph attribution framework. Experimental results demonstrate that the approach significantly enhances scalability and computational efficiency while preserving attribution fidelity.

Abstract

Explaining graph neural networks (GNNs) has become more and more important recently. Higher-order interpretation schemes, such as GNN-LRP (layer-wise relevance propagation for GNN), emerged as powerful tools for unraveling how different features interact thereby contributing to explaining GNNs. GNN-LRP gives a relevance attribution of walks between nodes at each layer, and the subgraph attribution is expressed as a sum over exponentially many such walks. In this work, we demonstrate that such exponential complexity can be avoided. In particular, we propose novel algorithms that enable to attribute subgraphs with GNN-LRP in linear-time (w.r.t. the network depth). Our algorithms are derived via message passing techniques that make use of the distributive property, thereby directly computing quantities for higher-order explanations. We further adapt our efficient algorithms to compute a generalization of subgraph attributions that also takes into account the neighboring graph features. Experimental results show the significant acceleration of the proposed algorithms and demonstrate the high usefulness and scalability of our novel generalized subgraph attribution method.

Problem

• subgraph attribution
• graph neural networks
• higher-order interpretation
• computational complexity
• explainability

Innovation

• message passing
• subgraph attribution
• GNN-LRP
• linear-time algorithm
• higher-order explanation