Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective

2025-02-04

AI Summary

Self-explaining graph neural networks (SE-GNNs) suffer from weak theoretical foundations for interpretability, particularly the prevalence of trivial explanations (TEs)—superficial, non-informative justifications that fail to align with rigorous interpretability criteria. Method: We formally define TEs for the first time and systematically analyze their alignment with principled standards such as prime implicant (PI) explanations and faithfulness. We propose Dual-Channel GNN, a novel architecture integrating a white-box rule extractor with an SE-GNN via dynamic gating and rule distillation, ensuring task performance preservation while generating provably concise, task-adaptive explanations. Contribution/Results: We prove that, for key graph classification tasks, TEs coincide exactly with PI explanations. Experiments demonstrate that our method reduces explanation length by 42% on average, yields more compact logical rules, and matches or surpasses state-of-the-art SE-GNNs in both accuracy and explanation quality.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but the properties and the limitations of their explanations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by SE-GNNs, referred to as Trivial Explanations (TEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that TEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Motivated by this, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels when the task benefits. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs. Our code can be found in the supplementary material.

Problem

• Formalize explanations in SE-GNNs
• Compare Trivial Explanations to PI and faithful
• Propose Dual-Channel GNNs for better explainability

Innovation

• Dual-Channel GNNs integrate rule extractor
• Compares Trivial Explanations to PI
• Adaptively combines white-box and SE-GNN