Yang Lu

Ruiqi Gao, Yang Lu, Junpei Zhou et al.

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.

Jianwen Xie, Yang Lu, Ruiqi Gao et al.

This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy function is defined by a bottom-up ConvNet, which maps the observed image to the energy. We call it the descriptor network. The second model is a generator network, which is a non-linear version of factor analysis. It is defined by a top-down ConvNet, which maps the latent factors to the observed image. The maximum likelihood learning algorithms of both models involve MCMC sampling such as Langevin dynamics. We observe that the two learning algorithms can be seamlessly interwoven into a cooperative learning algorithm that can train both models simultaneously. Specifically, within each iteration of the cooperative learning algorithm, the generator model generates initial synthesized examples to initialize a finite-step MCMC that samples and trains the energy-based descriptor model. After that, the generator model learns from how the MCMC changes its synthesized examples. That is, the descriptor model teaches the generator model by MCMC, so that the generator model accumulates the MCMC transitions and reproduces them by direct ancestral sampling. We call this scheme MCMC teaching. We show that the cooperative algorithm can learn highly realistic generative models.

Tian Han, Yang Lu, Song-Chun Zhu et al.

This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating back-propagation algorithm iterates the following two steps: (1) Inferential back-propagation, which infers the latent factors by Langevin dynamics or gradient descent. (2) Learning back-propagation, which updates the parameters given the inferred latent factors by gradient descent. The gradient computations in both steps are powered by back-propagation, and they share most of their code in common. We show that the alternating back-propagation algorithm can learn realistic generator models of natural images, video sequences, and sounds. Moreover, it can also be used to learn from incomplete or indirect training data.

Jianwen Xie, Yang Lu, Song-Chun Zhu et al.

We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns.

Yang Lu, Song-Chun Zhu, Ying Nian Wu

The convolutional neural network (ConvNet or CNN) has proven to be very successful in many tasks such as those in computer vision. In this conceptual paper, we study the generative perspective of the discriminative CNN. In particular, we propose to learn the generative FRAME (Filters, Random field, And Maximum Entropy) model using the highly expressive filters pre-learned by the CNN at the convolutional layers. We show that the learning algorithm can generate realistic and rich object and texture patterns in natural scenes. We explain that each learned model corresponds to a new CNN unit at a layer above the layer of filters employed by the model. We further show that it is possible to learn a new layer of CNN units using a generative CNN model, which is a product of experts model, and the learning algorithm admits an EM interpretation with binary latent variables.

Jifeng Dai, Yang Lu, Ying-Nian Wu

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.