  Attribution methods aim to explain a neural network's prediction by
highlighting the most relevant image areas. A popular approach is to
backpropagate (BP) a custom relevance score using modified rules, rather than
the gradient. We analyze an extensive set of modified BP methods: Deep Taylor
Decomposition, Layer-wise Relevance Propagation (LRP), Excitation BP,
PatternAttribution, DeepLIFT, Deconv, RectGrad, and Guided BP. We find
empirically that the explanations of all mentioned methods, except for
DeepLIFT, are independent of the parameters of later layers. We provide
theoretical insights for this surprising behavior and also analyze why DeepLIFT
does not suffer from this limitation. Empirically, we measure how information
of later layers is ignored by using our new metric, cosine similarity
convergence (CSC). The paper provides a framework to assess the faithfulness of
new and existing modified BP methods theoretically and empirically. For code
see: https://github.com/berleon/when-explanations-lie
