Explaining Graph Neural Networks via Structure-aware Interaction Index

TL;DR

The paper addresses explainability for graph neural networks by introducing the Myerson-Taylor interaction index, which internalizes graph structure into node and motif attributions. Building on this, the authors present MAGE, a structure-aware explainer that uses second-order MTI to compute pairwise node interactions and optimizes for multiple explanatory motifs that can be positive or negative. They provide an axiomatic justification showing MTI is unique under five natural axioms and demonstrate through extensive experiments on ten datasets that MAGE consistently outperforms state-of-the-art baselines, achieving significant improvements in explanation accuracy and motif fidelity with favorable query efficiency. The work advances graph explainability by jointly accounting for connectivity and high-order interactions, enabling concise, human-interpretable subgraph explanations with potential impact across molecular, visual, and text domains.

Abstract

The Shapley value is a prominent tool for interpreting black-box machine learning models thanks to its strong theoretical foundation. However, for models with structured inputs, such as graph neural networks, existing Shapley-based explainability approaches either focus solely on node-wise importance or neglect the graph structure when perturbing the input instance. This paper introduces the Myerson-Taylor interaction index that internalizes the graph structure into attributing the node values and the interaction values among nodes. Unlike the Shapley-based methods, the Myerson-Taylor index decomposes coalitions into components satisfying a pre-chosen connectivity criterion. We prove that the Myerson-Taylor index is the unique one that satisfies a system of five natural axioms accounting for graph structure and high-order interaction among nodes. Leveraging these properties, we propose Myerson-Taylor Structure-Aware Graph Explainer (MAGE), a novel explainer that uses the second-order Myerson-Taylor index to identify the most important motifs influencing the model prediction, both positively and negatively. Extensive experiments on various graph datasets and models demonstrate that our method consistently provides superior subgraph explanations compared to state-of-the-art methods.

Figures (14)

• Figure 1: MAGE operates in two distinct phases: First, MAGE employs the second-order Myerson-Taylor index to calculate pairwise interactions among graph nodes, represented by an interaction matrix $\mathbf{B}$. This matrix $\mathbf{B}$ serves as the input for the motif optimization. This optimization module searches for the $m$ most influential motifs contributing to the model's prediction.
• Figure 2: (a) Examples of how Shapley and Myerson values evaluate a disconnected coalition. The set $T$ is not connected, and in the Myerson value, the function $f|_{E}(T)$ becomes the sum of output over two connected sets $R_1$ and $R_2$. (b) The relations between the four allocation methods in this paper: solid arrows indicate the generalization direction, and dashed arrows indicate the recovery direction. Conditions for recovery are written on the dashed arrows.
• Figure 3: (a) An example in the Mutagenic dataset. Only MAGE correctly highlights the two -NO2 groups. (b) An example in the SPMotif dataset. Only MAGE can identify the house motif in the input graph. (c) An example in BA-HouseGrid shows MAGE's ability to highlight negative motifs. Green indicates positive motifs, and red indicates negative motifs. (model prediction: grid)
• Figure 4: An example in the Graph-SST2 dataset. MAGE's explanation is more concise and correctly captures the main verb 'deserves', crucial to determining a sentence's sentiment, while other baselines fail to identify it.
• Figure 5: This example visualizes the explanation for the GCN model of MAGE against competing baselines on MNIST75SP. Despite achieving high fidelity ($\mathrm{Fid}^+$) scores, the explanations of baselines are not meaningful. Meanwhile, only MAGE can generate an explanation that aligns with pixels that describe number '8'

Theorems & Definitions (28)

• Definition 3.1: Shapley value shapley1953value
• Definition 3.2: Shapley-Taylor index sundararajan2020shapley
• Definition 3.3: Myerson value myerson1977graphs
• Definition 4.1: Myerson-Taylor index
• Theorem 5.1: Uniqueness
• Theorem 1.1: Shapley-Taylor uniqueness sundararajan2020shapley
• Definition 2.1: Myerson-Taylor index
• Proposition 2.2
• proof : Proof of Proposition \ref{['prop:myti-l']}
• Proposition 2.3