Learning Multi-grid Generative ConvNets by Minimal Contrastive Divergence

This paper proposes a minimal contrastive divergence method for learning energy-based generative ConvNet models of images at multiple grids (or scales) simultaneously. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized examples from the model. Within each iteration of our learning algorithm, for each observed training image, we generate synthesized images at multiple grids by initializing the finite-step MCMC sampling from a minimal 1× 1 version of the training image. The synthesized image at each subsequent grid is obtained by a finite-step MCMC initialized from the synthesized image generated at the previous coarser grid. After obtaining the synthesized examples, the parameters of the models at multiple grids are updated separately and simultaneously based on the differences between synthesized and observed examples. We call this learning method the multi-grid minimal contrastive divergence. We show that this method can learn realistic energy-based generative ConvNet models, and it outperforms the original contrastive divergence (CD) and persistent CD.