We regard explanations as a blending of the input sample and the models output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these properties and between explanation-generating functions and intermediate representations of learned models and are able to show, for example, that if the activations of a given layer are consistent with an explanation, then so do all other subsequent layers. In addition, we study the intersection and union of explanations as a way to construct new explanations.
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