  Neural network based classifiers are still prone to manipulation through
adversarial perturbations. State of the art attacks can overcome most of the
defense or detection mechanisms suggested so far, and adversaries have the
upper hand in this arms race. Adversarial examples are designed to resemble the
normal input from which they were constructed, while triggering an incorrect
classification. This basic design goal leads to a characteristic spatial
behavior within the context of Activation Spaces, a term coined by the authors
to refer to the hyperspaces formed by the activation values of the network's
layers. Within the output of the first layers of the network, an adversarial
example is likely to resemble normal instances of the source class, while in
the final layers such examples will diverge towards the adversary's target
class. The steps below enable us to leverage this inherent shift from one class
to another in order to form a novel adversarial example detector. We construct
Euclidian spaces out of the activation values of each of the deep neural
network layers. Then, we induce a set of k-nearest neighbor classifiers (k-NN),
one per activation space of each neural network layer, using the
non-adversarial examples. We leverage those classifiers to produce a sequence
of class labels for each nonperturbed input sample and estimate the a priori
probability for a class label change between one activation space and another.
During the detection phase we compute a sequence of classification labels for
each input using the trained classifiers. We then estimate the likelihood of
those classification sequences and show that adversarial sequences are far less
likely than normal ones. We evaluated our detection method against the state of
the art C&W attack method, using two image classification datasets (MNIST,
CIFAR-10) reaching an AUC 0f 0.95 for the CIFAR-10 dataset.
