vainaijr:

what is the intuition behind using this technique, and how does one understand this formula in a better way?


So the goal of the attribution exercise we are doing is to attribute the difference between F(x) and F(x’) to the inidividual components of the input difference (x-x’).
What happens is that we are following the line form x’ to x. If we integrate the derivative in the direction of this line that, we get the difference between F(x) and F(x’), this is the fundamental theorem of calculus.
But now, the “derivative in the direction of this line” can be written as a scalar product of the gradient of F with the direction vector ((x-x’) / |x-x’|). The integrated gradient now collects the gradient of F parts separately (before the scalar product).
This and a change of variables leads to the formula you cite above.
Inherent in the construction is sum_i IntegratedGrads_i(x) = F(x) - F(x’), so we are indeed decomposing the difference.
Best regards
Thomas