  Feature attributions are a popular tool for explaining the behavior of Deep
Neural Networks (DNNs), but have recently been shown to be vulnerable to
attacks that produce divergent explanations for nearby inputs. This lack of
robustness is especially problematic in high-stakes applications where
adversarially-manipulated explanations could impair safety and trustworthiness.
Building on a geometric understanding of these attacks presented in recent
work, we identify Lipschitz continuity conditions on models' gradient that lead
to robust gradient-based attributions, and observe that smoothness may also be
related to the ability of an attack to transfer across multiple attribution
methods. To mitigate these attacks in practice, we propose an inexpensive
regularization method that promotes these conditions in DNNs, as well as a
stochastic smoothing technique that does not require re-training. Our
experiments on a range of image models demonstrate that both of these
mitigations consistently improve attribution robustness, and confirm the role
that smooth geometry plays in these attacks on real, large-scale models.
