  The projected belief network (PBN) is a layered generative network with
tractable likelihood function, and is based on a feed-forward neural network
(FF-NN). It can therefore share an embodiment with a discriminative classifier
and can inherit the best qualities of both types of network. In this paper, a
convolutional PBN is constructed that is both fully discriminative and fully
generative and is tested on spectrograms of spoken commands. It is shown that
the network displays excellent qualities from either the discriminative or
generative viewpoint. Random data synthesis and visible data reconstruction
from low-dimensional hidden variables are shown, while classifier performance
approaches that of a regularized discriminative network. Combination with a
conventional discriminative CNN is also demonstrated.
