Semantics and explanation: why counterfactual explanations produce adversarial examples in deep neural networks

Recent papers in explainable AI have made a compelling case for counterfactual modes of explanation. While counterfactual explanations appear to be extremely effective in some instances, they are formally equivalent to adversarial examples. This presents an apparent paradox for explainability researchers: if these two procedures are formally equivalent, what accounts for the explanatory divide apparent between counterfactual explanations and adversarial examples? We resolve this paradox by placing emphasis back on the semantics of counterfactual expressions. Producing satisfactory explanations for deep learning systems will require that we find ways to interpret the semantics of hidden layer representations in deep neural networks.