  The maximum mean discrepancy (MMD) test could in principle detect any
distributional discrepancy between two datasets. However, it has been shown
that the MMD test is unaware of adversarial attacks -- the MMD test failed to
detect the discrepancy between natural and adversarial data. Given this
phenomenon, we raise a question: are natural and adversarial data really from
different distributions? The answer is affirmative -- the previous use of the
MMD test on the purpose missed three key factors, and accordingly, we propose
three components. Firstly, the Gaussian kernel has limited representation
power, and we replace it with an effective deep kernel. Secondly, the test
power of the MMD test was neglected, and we maximize it following asymptotic
statistics. Finally, adversarial data may be non-independent, and we overcome
this issue with the wild bootstrap. By taking care of the three factors, we
verify that the MMD test is aware of adversarial attacks, which lights up a
novel road for adversarial data detection based on two-sample tests.
