  In this paper we cast the well-known convolutional neural network in a
Gaussian process perspective. In this way we hope to gain additional insights
into the performance of convolutional networks, in particular understand under
what circumstances they tend to perform well and what assumptions are
implicitly made in the network. While for fully-connected networks the
properties of convergence to Gaussian processes have been studied extensively,
little is known about situations in which the output from a convolutional
network approaches a multivariate normal distribution.
