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There is great interest in "saliency methods" (also called "attributionmethods"), which give "explanations" for a deep net's decision, by assigning a"score" to each feature/pixel in the input. Their design usually involvescredit-assignment via the gradient of the output with respect to input.Recently Adebayo et al. [arXiv:1810.03292] questioned the validity of many ofthese methods since they do not pass simple *sanity checks* which test whetherthe scores shift/vanish when layers of the trained net are randomized, or whenthe net is retrained using random labels for inputs.  We propose a simple fix to existing saliency methods that helps them passsanity checks, which we call "competition for pixels". This involves computingsaliency maps for all possible labels in the classification task, and using asimple competition among them to identify and remove less relevant pixels fromthe map. The simplest variant of this is "Competitive Gradient $\odot$ Input(CGI)": it is efficient, requires no additional training, and uses only theinput and gradient. Some theoretical justification is provided for it(especially for ReLU networks) and its performance is empirically demonstrated.

A Simple Saliency Method That Passes the Sanity Checks