  Deep convolutional neural networks are generally regarded as robust function
approximators. So far, this intuition is based on perturbations to external
stimuli such as the images to be classified. Here we explore the robustness of
convolutional neural networks to perturbations to the internal weights and
architecture of the network itself. We show that convolutional networks are
surprisingly robust to a number of internal perturbations in the higher
convolutional layers but the bottom convolutional layers are much more fragile.
For instance, Alexnet shows less than a 30% decrease in classification
performance when randomly removing over 70% of weight connections in the top
convolutional or dense layers but performance is almost at chance with the same
perturbation in the first convolutional layer. Finally, we suggest further
investigations which could continue to inform the robustness of convolutional
networks to internal perturbations.
