Noise Sensitivity and Stability of Deep Neural Networks for Binary
  Classification
Johan Jonasson Jeffrey E. Steif Olof Zetterqvist
A first step is taken towards understanding often observed non-robustness
phenomena of deep neural net (DNN) classifiers. This is done from the
perspective of Boolean functions by asking if certain sequences of Boolean
functions represented by common DNN models are noise sensitive or noise stable,
concepts defined in the Boolean function literature. Due to the natural
randomness in DNN models, these concepts are extended to annealed and quenched
versions. Here we sort out the relation between these definitions and
investigate the properties of two standard DNN architectures, the fully
connected and convolutional models, when initiated with Gaussian weights.