  Adversarially robust classifiers possess a trait that non-robust models do
not -- Perceptually Aligned Gradients (PAG). Their gradients with respect to
the input align well with human perception. Several works have identified PAG
as a byproduct of robust training, but none have considered it as a standalone
phenomenon nor studied its own implications. In this work, we focus on this
trait and test whether \emph{Perceptually Aligned Gradients imply Robustness}.
To this end, we develop a novel objective to directly promote PAG in training
classifiers and examine whether models with such gradients are more robust to
adversarial attacks. Extensive experiments on multiple datasets and
architectures validate that models with aligned gradients exhibit significant
robustness, exposing the surprising bidirectional connection between PAG and
robustness. Lastly, we show that better gradient alignment leads to increased
robustness and harness this observation to boost the robustness of existing
adversarial training techniques.
