Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.

翻译：可解释性方法的价值仅在于其解释能忠实描述被解释模型。本文考虑预测结果在特定对称群下保持不变的神经网络，包括从卷积神经网络到图神经网络等常见架构。任何能忠实解释此类模型的解释方法，都需与此不变性保持一致。我们通过几何深度学习的形式化框架，将这一直觉转化为解释不变性和等变性的概念。通过这一严谨的形式化体系，我们推导出：(1) 两个评估任意可解释性方法在模型对称群下鲁棒性的指标；(2) 若干主流可解释性方法的理论鲁棒性保证；(3) 提升任意可解释性方法关于对称群不变性的系统化方法。通过实证测量与多种模态和对称群关联的模型解释的指标，我们总结出5条指导原则，帮助可解释性方法的用户和开发者生成鲁棒的解释。