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.

翻译：本文提出了一类新型解释结构,称为稳健反事实见证(Robust Counterfactual Witnesses, RCWs),旨在为图神经网络提供兼具反事实与事实性质的稳健解释。给定图神经网络M,稳健反事实见证是指图G中构成M在G上结果之反事实与事实解释的子图部分,且该性质在G通过翻转最多k对节点而受到的任意"扰动"下仍然成立。我们验证与生成稳健反事实见证的难度结果进行了刻画,范围从可处理结果到co-NP完全问题。针对基于GNN的节点分类任务,我们研究了此类结构,并提出了验证与生成RCW的高效算法。我们还设计了一种可扩展的并行算法,用于验证与生成大规模图上的RCW。通过基准数据集上的实验验证了所提解释生成过程,并展示了其应用场景。