  SmoothGrad and VarGrad are techniques that enhance the empirical quality of
standard saliency maps by adding noise to input. However, there were few works
that provide a rigorous theoretical interpretation of those methods. We
analytically formalize the result of these noise-adding methods. As a result,
we observe two interesting results from the existing noise-adding methods.
First, SmoothGrad does not make the gradient of the score function smooth.
Second, VarGrad is independent of the gradient of the score function. We
believe that our findings provide a clue to reveal the relationship between
local explanation methods of deep neural networks and higher-order partial
derivatives of the score function.
