Generating Robust Counterfactual Witnesses for Graph Neural Networks

TL;DR

This work defines robust counterfactual witnesses (RCWs) as subgraphs that yield factual, counterfactual, and robust explanations for graph neural networks under up to $k$ edge disturbances, addressing the need for invariant explanations in sensitive domains. It proves that verifying a $k$-RCW is NP-hard in general, but identifies a tractable APPNP-specific regime under $(k,b)$-disturbances and provides a practical verification method. The authors introduce RoboGExp, a sequential expand-verify algorithm, and its parallel variant paraRoboGExp, with concrete time bounds that enable scalable RCW generation on large graphs. Empirical results on multiple benchmarks show RoboGExp produces concise, robust RCWs with superior fidelity metrics and better efficiency than baselines, while the parallel version demonstrates strong scalability. Overall, the paper advances trustworthy, robust explanations for GNNs with actionable, domain-relevant subgraph structures and practical algorithms for large-scale deployment.$

Abstract

This paper introduces a new class of explanation structures, called robust counterfactual witnesses (RCWs), to provide robust, both counterfactual and factual explanations for graph neural networks. Given a graph neural network M, a robust counterfactual witness refers to the fraction of a graph G that are counterfactual and factual explanation of the results of M over G, but also remains so for any "disturbed" G by flipping up to k of its node pairs. We establish the hardness results, from tractable results to co-NP-hardness, for verifying and generating robust counterfactual witnesses. We study such structures for GNN-based node classification, and present efficient algorithms to verify and generate RCWs. We also provide a parallel algorithm to verify and generate RCWs for large graphs with scalability guarantees. We experimentally verify our explanation generation process for benchmark datasets, and showcase their applications.

Figures (6)

• Figure 1: $G_1$:Left-Bold nodes and edges indicate a counterfactual. Middle-Red bold nodes and edges indicate a new counterfactual after deleting dotted edges. Right-A counterfactual robust to graph edits. $G_2$: The shaded area is a robust counterfactual, also "vulnerable zone" in cyber networks.
• Figure 2: Generating robust witness for $G_1$ with expansion and verification.
• Figure 3: Effectiveness with Impact Factors
• Figure 4: Scalability and Efficiency
• Figure 5: Case Study: Left: a small $$RCW that capture an invariant structure for three variants of a drug structure; Right: an $$RCW that explains topic change with matching new citations.