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