The problem of counterfactual visual explanations is considered. A new family of discriminant explanations is introduced. These produce heatmaps that attribute high scores to image regions informative of a classifier prediction but not of a counter class. They connect attributive explanations, which are based on a single heat map, to counterfactual explanations, which account for both predicted class and counter class. The latter are shown to be computable by combination of two discriminant explanations, with reversed class pairs. It is argued that self-awareness, namely the ability to produce classification confidence scores, is important for the computation of discriminant explanations, which seek to identify regions where it is easy to discriminate between prediction and counter class. This suggests the computation of discriminant explanations by the combination of three attribution maps. The resulting counterfactual explanations are optimization free and thus much faster than previous methods. To address the difficulty of their evaluation, a proxy task and set of quantitative metrics are also proposed. Experiments under this protocol show that the proposed counterfactual explanations outperform the state of the art while achieving much higher speeds, for popular networks. In a human-learning machine teaching experiment, they are also shown to improve mean student accuracy from chance level to 95\%.
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