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GOAt: Explaining Graph Neural Networks via Graph Output Attribution

Shengyao Lu, Keith G. Mills, Jiao He, Bang Liu, Di Niu

TL;DR

GOAt tackles interpretability of Graph Neural Networks by analytically attributing outputs to input graph features. It expands the forward pass into a sum of scalar products and uses an equal-contribution principle to compute per-feature attributions, including an activation-pattern mediated calibration. The method yields faithful, discriminative, and stable explanations, outperforming several state-of-the-art explainers on synthetic and real datasets for both graph and node classification. By being training-free and edge-focused, GOAt provides scalable, interpretable motifs that can aid trust and debuggability in GNN applications.

Abstract

Understanding the decision-making process of Graph Neural Networks (GNNs) is crucial to their interpretability. Most existing methods for explaining GNNs typically rely on training auxiliary models, resulting in the explanations remain black-boxed. This paper introduces Graph Output Attribution (GOAt), a novel method to attribute graph outputs to input graph features, creating GNN explanations that are faithful, discriminative, as well as stable across similar samples. By expanding the GNN as a sum of scalar products involving node features, edge features and activation patterns, we propose an efficient analytical method to compute contribution of each node or edge feature to each scalar product and aggregate the contributions from all scalar products in the expansion form to derive the importance of each node and edge. Through extensive experiments on synthetic and real-world data, we show that our method not only outperforms various state-ofthe-art GNN explainers in terms of the commonly used fidelity metric, but also exhibits stronger discriminability, and stability by a remarkable margin.

GOAt: Explaining Graph Neural Networks via Graph Output Attribution

TL;DR

GOAt tackles interpretability of Graph Neural Networks by analytically attributing outputs to input graph features. It expands the forward pass into a sum of scalar products and uses an equal-contribution principle to compute per-feature attributions, including an activation-pattern mediated calibration. The method yields faithful, discriminative, and stable explanations, outperforming several state-of-the-art explainers on synthetic and real datasets for both graph and node classification. By being training-free and edge-focused, GOAt provides scalable, interpretable motifs that can aid trust and debuggability in GNN applications.

Abstract

Understanding the decision-making process of Graph Neural Networks (GNNs) is crucial to their interpretability. Most existing methods for explaining GNNs typically rely on training auxiliary models, resulting in the explanations remain black-boxed. This paper introduces Graph Output Attribution (GOAt), a novel method to attribute graph outputs to input graph features, creating GNN explanations that are faithful, discriminative, as well as stable across similar samples. By expanding the GNN as a sum of scalar products involving node features, edge features and activation patterns, we propose an efficient analytical method to compute contribution of each node or edge feature to each scalar product and aggregate the contributions from all scalar products in the expansion form to derive the importance of each node and edge. Through extensive experiments on synthetic and real-world data, we show that our method not only outperforms various state-ofthe-art GNN explainers in terms of the commonly used fidelity metric, but also exhibits stronger discriminability, and stability by a remarkable margin.
Paper Structure (24 sections, 4 theorems, 43 equations, 13 figures, 3 tables)

This paper contains 24 sections, 4 theorems, 43 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Method
  4. Equal Contribution
  5. Explaining Graph Neural Networks via Attribution
  6. Case Study: Explaining Graph Convolutional Network (GCN)
  7. Experiments
  8. Fidelity
  9. Discriminability
  10. Stability of extracting motifs
  11. Qualitative analysis
  12. Related Work
  13. Conclusion
  14. Proof of Lemma 2
  15. Proof of Lemma 4
  16. ...and 9 more sections

Key Result

Lemma 2

Given a function $g(\mathbf{X})$ defined as $g(\mathbf{X})=b\prod_{k=1}^{M}{X_k}$, where $b$ is a constant, and $\mathbf{X}=\{X_1, \dots, X_M\}$ represents $M$ uncorrelated variables. Each variable $X_k$ is either $0$ or $x_k$, depending on the absence or presence of a certain feature. Then, all the

Figures (13)

  • Figure 1: Illustrative example of GOAt.
  • Figure 2: Fidelity performance averaged across 10 runs on the pretrained GCNs for the datasets at different levels of average sparsity.
  • Figure 3: Discriminability performance averaged across 10 runs of the explanations produced by various GNN explainers at different levels of sparsity. "Original" refer to the performance of feeding the original data into the GNN without any modifications or explanations applied.
  • Figure 4: Visualization of explanation embeddings on the BA-2Motifs dataset. Subfigure (i) refers to the visualization of the original embeddings by directly feeding the original data into the GNN without any modifications or explanations applied.
  • Figure 5: Coverage of the top-$k$ explanations across the datasets.
  • ...and 8 more figures

Theorems & Definitions (10)

  • Definition 1: Equal Contribution
  • Lemma 2: Equal Contribution in a product
  • Definition 3: Activation Pattern
  • Lemma 4: Equal Contribution variables in the GNN expansion form's scalar product
  • Theorem 5: Contribution of variables in the expansion form of a pretrained GNN
  • proof
  • proof
  • Lemma 6
  • proof
  • proof