  The convolutional neural networks (CNNs) have proven to be a powerful tool
for discriminative learning. Recently researchers have also started to show
interest in the generative aspects of CNNs in order to gain a deeper
understanding of what they have learned and how to further improve them. This
paper investigates generative modeling of CNNs. The main contributions include:
(1) We construct a generative model for the CNN in the form of exponential
tilting of a reference distribution. (2) We propose a generative gradient for
pre-training CNNs by a non-parametric importance sampling scheme, which is
fundamentally different from the commonly used discriminative gradient, and yet
has the same computational architecture and cost as the latter. (3) We propose
a generative visualization method for the CNNs by sampling from an explicit
parametric image distribution. The proposed visualization method can directly
draw synthetic samples for any given node in a trained CNN by the Hamiltonian
Monte Carlo (HMC) algorithm, without resorting to any extra hold-out images.
Experiments on the challenging ImageNet benchmark show that the proposed
generative gradient pre-training consistently helps improve the performances of
CNNs, and the proposed generative visualization method generates meaningful and
varied samples of synthetic images from a large-scale deep CNN.
