  Deep neural networks (DNN) trained in a supervised way suffer from two known
problems. First, the minima of the objective function used in learning
correspond to data points (also known as rubbish examples or fooling images)
that lack semantic similarity with the training data. Second, a clean input can
be changed by a small, and often imperceptible for human vision, perturbation,
so that the resulting deformed input is misclassified by the network. These
findings emphasize the differences between the ways DNN and humans classify
patterns, and raise a question of designing learning algorithms that more
accurately mimic human perception compared to the existing methods.
  Our paper examines these questions within the framework of Dense Associative
Memory (DAM) models. These models are defined by the energy function, with
higher order (higher than quadratic) interactions between the neurons. We show
that in the limit when the power of the interaction vertex in the energy
function is sufficiently large, these models have the following three
properties. First, the minima of the objective function are free from rubbish
images, so that each minimum is a semantically meaningful pattern. Second,
artificial patterns poised precisely at the decision boundary look ambiguous to
human subjects and share aspects of both classes that are separated by that
decision boundary. Third, adversarial images constructed by models with small
power of the interaction vertex, which are equivalent to DNN with rectified
linear units (ReLU), fail to transfer to and fool the models with higher order
interactions. This opens up a possibility to use higher order models for
detecting and stopping malicious adversarial attacks. The presented results
suggest that DAM with higher order energy functions are closer to human visual
perception than DNN with ReLUs.
