What happens when you add random noise to the inputs to the neural net?
While it is difficult to locate the adversarial examples by random permutation, they do not appear to be extremely specific. The paper even suggests that they exist within specific areas of the input space. So depending on the size of said area, adding noise will just lead you to a similarly adversarial image.
Regardless they propose a better way of fixing the problem by just modifying the training algorithm to penalize networks that have a structure allowing this kind of error.
Neural networks can still perform arbitrary computations, despite this result, so there is no reason to try and manually fix up bad inputs when you can train the network to do it.
http://www.iro.umontreal.ca/~lisa/publications2/index.php/pu...
To the GP, noise is often added to training datasets for exactly the reason you're suggesting it. One of the novel things the paper cited discusses, however, is even if you feed the adversarial perturbations into additional training data, there are yet new ways to subtly perturb the inputs to get incorrect results.
Misclassification is a pretty fundamental consequence of dimensionality reduction, of course, but the surprise is how close those misclassifications are in input-space. This isn't mistaking a box for a square because it's looked at head on, it's mistaking a bus for an ostrich because some of the pixels in the image changed to a slightly different shade of yellow.