Explaining Graph Neural Networks for Node Similarity on Graphs

TL;DR

The paper addresses explainability for node similarity predicted by graph neural networks on graphs, formalizing similarity via cosine on node embeddings $y(i,j) = \frac{\mathbf{z}_i^{\top}\mathbf{z}_j}{\|\mathbf{z}_i\|\|\mathbf{z}_j\|}$ learned in an unsupervised manner. It compares two explanation paradigms—mutual-information-based perturbation explanations and gradient-based explanations—finding that gradient-based explanations offer actionable, consistent, and sparse insights for similarity tasks. Through extensive experiments on six datasets using multiple unsupervised GNNs (GAE, VGAE, DGI, GRACE), the authors show that gradient-based explanations yield stable fidelity and low effect overlap, while MI explanations lack such consistency. The findings provide practical guidance for building explainable similarity systems and demonstrate that sparse gradient-based explanations can ground edge-level interventions without sacrificing explanatory power.

Abstract

Similarity search is a fundamental task for exploiting information in various applications dealing with graph data, such as citation networks or knowledge graphs. While this task has been intensively approached from heuristics to graph embeddings and graph neural networks (GNNs), providing explanations for similarity has received less attention. In this work we are concerned with explainable similarity search over graphs, by investigating how GNN-based methods for computing node similarities can be augmented with explanations. Specifically, we evaluate the performance of two prominent approaches towards explanations in GNNs, based on the concepts of mutual information (MI), and gradient-based explanations (GB). We discuss their suitability and empirically validate the properties of their explanations over different popular graph benchmarks. We find that unlike MI explanations, gradient-based explanations have three desirable properties. First, they are actionable: selecting inputs depending on them results in predictable changes in similarity scores. Second, they are consistent: the effect of selecting certain inputs overlaps very little with the effect of discarding them. Third, they can be pruned significantly to obtain sparse explanations that retain the effect on similarity scores.

Figures (3)

• Figure 1: Illustration of the problem we investigate in our work. Given nodes $1$ and $2$ in a graph, unsupervised learning methods can be used to train a GNN to learn node embeddings, where a score of similarity can be estimated by cosine similarity. We are interested in computing explanations for such scores, that assign values of attributions to edges in the graph. In this example, we show with blue a positive influence in the similarity score, and with red a negative influence.
• Figure 2: Influence of sparse explanations on fidelity metrics (Fid$_a$ and Fid$_b$) and effect overlap (EO), evaluated with GAE embeddings across different datasets. At zero sparsity, all edges above (or below) the explanation threshold are kept and used to compute the change in similarity scores Fid$_a$ (or F$_b$), as well as the effect overlap (EO). Larger values of sparsity indicate the fraction of edges discarded before computing the change in similarity scores. Confidence intervals are shown indicating two standard deviations over 10 runs.
• Figure 3: Example of explanations provided by GNNExplainer (\ref{['fig:gnnexplainer_case']}) and Integrated Gradients (\ref{['fig:gradient_case']}) for the similarity computed between two entities in the DBpedia50k knowledge graph: Lilium and Dendrobium, two genera of flowering plants. Edge thickness indicate magnitude, and blue indicates edges that result in an increase of the score, red edges result in a decrease, and gray edges have little effect.