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This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. 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 x 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 show that this multi-grid method can learn realistic energy-based generative ConvNet models, and it outperforms the original contrastive divergence (CD) and persistent CD.
Energy-Based Models (EBMs) assign unnormalized log-probability to data samples. This functionality has a variety of applications, such as sample synthesis, data denoising, sample restoration, outlier detection, Bayesian reasoning, and many more. But
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized models log-density. We estimate the Stein discrepancy between the data density $p(x)$ and the model
Learning how to model complex scenes in a modular way with recombinable components is a pre-requisite for higher-order reasoning and acting in the physical world. However, current generative models lack the ability to capture the inherently compositi
Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of
This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits.