  We consider a neural network architecture with randomized features, a
sign-splitter, followed by rectified linear units (ReLU). We prove that our
architecture exhibits robustness to the input perturbation: the output feature
of the neural network exhibits a Lipschitz continuity in terms of the input
perturbation. We further show that the network output exhibits a discrimination
ability that inputs that are not arbitrarily close generate output vectors
which maintain distance between each other obeying a certain lower bound. This
ensures that two different inputs remain discriminable while contracting the
distance in the output feature space.
