  Saliency methods can make deep neural network predictions more interpretable
by identifying a set of critical features in an input sample, such as pixels
that contribute most strongly to a prediction made by an image classifier.
Unfortunately, recent evidence suggests that many saliency methods poorly
perform, especially in situations where gradients are saturated, inputs contain
adversarial perturbations, or predictions rely upon inter-feature dependence.
To address these issues, we propose a framework that improves the robustness of
saliency methods by following a two-step procedure. First, we introduce a
perturbation mechanism that subtly varies the input sample without changing its
intermediate representations. Using this approach, we can gather a corpus of
perturbed data samples while ensuring that the perturbed and original input
samples follow the same distribution. Second, we compute saliency maps for the
perturbed samples and propose a new method to aggregate saliency maps. With
this design, we offset the gradient saturation influence upon interpretation.
From a theoretical perspective, we show the aggregated saliency map could not
only capture inter-feature dependence but, more importantly, robustify
interpretation against previously described adversarial perturbation methods.
Following our theoretical analysis, we present experimental results suggesting
that, both qualitatively and quantitatively, our saliency method outperforms
existing methods.
