> If this model can provide an explanation for the small noises impacting NN performance on images (from karpathy.github.io, posted to HN earlier today) then that would be rocking

This paper [0] does a pretty good job of giving an explanation for that.

[0] http://arxiv.org/abs/1412.6572

Honestly, that abstract makes me more upset. If these are due to NN's nature as linear classifers, then we are all in trouble, given that almost everything useful is based off linear models. Given the title of the paper though, I should probably be more hopeful :)

The adversarial noise issue is not so hard to understand, it's just costly to correct.

That link provides the explanation: if your classifier is not very regularized, then the classification regions are going to be close and irregular, s.t. a small vector may lead you from one to another. It's more of a geometrical fact f you think of classification regions in those spaces (of high dimension).

Guaranteeing a large minimum distance is hard (essentially why error correcting codes are pretty hard to encode/decode)

the fact that random noise can be classified as strongly belonging to some class, and the fact that classification results can be unstable, is simply a result of the fact the input space is very high dimensional, and the output space is very small (say a few isolated points). That is, if you are discriminatively training a mapping from images in R^(224 x 224 x 3) to 1000 points (class labels), there is going to be a tremendous amount of instability in the inverse direction.