  We show that the Rademacher complexity-based approach can generate
non-vacuous generalisation bounds on Convolutional Neural Networks (CNNs) for
classifying a small number of classes of images. The development of new
Talagrand's contraction lemmas for high-dimensional mappings between function
spaces and CNNs for general Lipschitz activation functions is a key technical
contribution. Our results show that the Rademacher complexity does not depend
on the network length for CNNs with some special types of activation functions
such as ReLU, Leaky ReLU, Parametric Rectifier Linear Unit, Sigmoid, and Tanh.
