Local Geometry Improves Explanation Robustness for Graph Neural Networks

Abstract

Graph Neural Networks (GNNs) are widely used in high-stakes decision-making, where explanation robustness is crucial. Yet, even minor structural perturbations can drastically change explanations without changing predictions. Existing methods primarily characterize structural perturbations by their edit distance or budget, and enforce robustness through uniform constraints or averaging mechanisms over this perturbation set, which fail to capture the inherently direction-dependent effects of structural changes.

In this paper, we propose GeoXGNN (Local Geometry Improves Explanation Robustness for Graph Neural Networks), a robust explanation framework that explicitly models the directional sensitivity of structural perturbations from a geometric perspective. GeoXGNN introduces local, direction-aware metrics in the node representation space to characterize how perturbations along different directions affect node embeddings and explanation outcomes. Based on the learned local metrics, GeoXGNN further enforces directional constraints, encouraging explanations to remain robust along high-sensitivity directions while preserving explanatory fidelity.

Extensive experiments on multiple node-level and graph-level benchmark datasets demonstrate that GeoXGNN significantly improves explanation robustness over existing methods.