  For neural models to garner widespread public trust and ensure fairness, we
must have human-intelligible explanations for their predictions. Recently, an
increasing number of works focus on explaining the predictions of neural models
in terms of the relevance of the input features. In this work, we show that
feature-based explanations pose problems even for explaining trivial models. We
show that, in certain cases, there exist at least two ground-truth
feature-based explanations, and that, sometimes, neither of them is enough to
provide a complete view of the decision-making process of the model. Moreover,
we show that two popular classes of explainers, Shapley explainers and minimal
sufficient subsets explainers, target fundamentally different types of
ground-truth explanations, despite the apparently implicit assumption that
explainers should look for one specific feature-based explanation. These
findings bring an additional dimension to consider in both developing and
choosing explainers.
