  Convolutional Neural Networks (CNNs) are build specifically for computer
vision tasks for which it is known that the input data is a hierarchical
structure based on locally correlated elements. The question that naturally
arises is what happens with the performance of CNNs if one of the basic
properties of the data is removed, e.g. what happens if the image pixels are
randomly permuted? Intuitively one expects that the convolutional network
performs poorly in these circumstances in contrast to a multilayer perceptron
(MLPs) whose classification accuracy should not be affected by the pixel
randomization. This work shows that by randomizing image pixels the
hierarchical structure of the data is destroyed and long range correlations are
introduced which standard CNNs are not able to capture. We show that their
classification accuracy is heavily dependent on the class similarities as well
as the pixel randomization process. We also indicate that dilated convolutions
are able to recover some of the pixel correlations and improve the performance.
