A new form of variational autoencoder (VAE) is developed, in which the joint distribution of data and codes is considered in two (symmetric) forms: ( @math ) from observed data fed through the encoder to yield codes, and ( @math ) from latent codes drawn from a simple prior and propagated through the decoder to manifest data. Lower bounds are learned for marginal log-likelihood fits observed data and latent codes. When learning with the variational bound, one seeks to minimize the symmetric Kullback-Leibler divergence of joint density functions from ( @math ) and ( @math ), while simultaneously seeking to maximize the two marginal log-likelihoods. To facilitate learning, a new form of adversarial training is developed. An extensive set of experiments is performed, in which we demonstrate state-of-the-art data reconstruction and generation on several image benchmark datasets.
GANs @cite_10 constitute another recent framework for learning a generative model. Recent extensions of GAN have focused on boosting the performance of image generation by improving the generator @cite_33 , discriminator @cite_28 or the training algorithm @cite_42 @cite_5 @cite_38 . More recently, some researchers @cite_7 @cite_8 @cite_32 have employed a bidirectional network structure within the adversarial learning framework, which in theory guarantees the matching of joint distributions over two domains. However, non-identifiability issues are raised in @cite_29 . For example, they have difficulties in providing good reconstruction in latent variable models, or discovering the correct pairing relationship in domain transformation tasks. It was shown that these problems are alleviated in DiscoGAN @cite_31 , CycleGAN @cite_19 and ALICE @cite_29 via additional @math , @math or adversarial losses. However, these methods lack of explicit probabilistic modeling of observations, thus could not directly evaluate the likelihood of given data samples.
@cite_38 @cite_33 @cite_7 @cite_8 @cite_28 @cite_29 @cite_42 @cite_32 @cite_19 @cite_5 @cite_31 @cite_10
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We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. As a new way of training generative models, Generative Adversarial Net (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is nontrivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines. As a new way of training generative models, Generative Adversarial Nets (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is non-trivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines. We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. We focus on two applications of GANs: semi-supervised learning, and the generation of images that humans find visually realistic. Unlike most work on generative models, our primary goal is not to train a model that assigns high likelihood to test data, nor do we require the model to be able to learn well without using any labels. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3 . We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Frechet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the Frechet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. We introduce an adversarial learning framework, which we named KBGAN, to improve the performances of a wide range of existing knowledge graph embedding models. Because knowledge graph datasets typically only contain positive facts, sampling useful negative training examples is a non-trivial task. Replacing the head or tail entity of a fact with a uniformly randomly selected entity is a conventional method for generating negative facts used by many previous works, but the majority of negative facts generated in this way can be easily discriminated from positive facts, and will contribute little towards the training. Inspired by generative adversarial networks (GANs), we use one knowledge graph embedding model as a negative sample generator to assist the training of our desired model, which acts as the discriminator in GANs. The objective of the generator is to generate difficult negative samples that can maximize their likeliness determined by the discriminator, while the discriminator minimizes its training loss. This framework is independent of the concrete form of generator and discriminator, and therefore can utilize a wide variety of knowledge graph embedding models as its building blocks. In experiments, we adversarially train two translation-based models, TransE and TransD, each with assistance from one of the two probability-based models, DistMult and ComplEx. We evaluate the performances of KBGAN on the link prediction task, using three knowledge base completion datasets: FB15k-237, WN18 and WN18RR. Experimental results show that adversarial training substantially improves the performances of target embedding models under various settings. Generative adversarial networks (GANs) learn a deep generative model that is able to synthesize novel, high-dimensional data samples. New data samples are synthesized by passing latent samples, drawn from a chosen prior distribution, through the generative model. Once trained, the latent space exhibits interesting properties that may be useful for downstream tasks such as classification or retrieval. Unfortunately, GANs do not offer an “inverse model,” a mapping from data space back to latent space, making it difficult to infer a latent representation for a given data sample. In this paper, we introduce a technique, inversion , to project data samples, specifically images, to the latent space using a pretrained GAN. Using our proposed inversion technique, we are able to identify which attributes of a data set a trained GAN is able to model and quantify GAN performance, based on a reconstruction loss. We demonstrate how our proposed inversion technique may be used to quantitatively compare the performance of various GAN models trained on three image data sets. We provide codes for all of our experiments in the website ( https: github.com ToniCreswell InvertingGAN ). Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models over discrete data. We also achieve high quality generations on CIFAR-10 and LSUN bedrooms. A Triangle Generative Adversarial Network ( @math -GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. @math -GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach. A Triangle Generative Adversarial Network ( @math -GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. @math -GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach. Generative adversarial networks (GANs) are highly effective unsupervised learning frameworks that can generate very sharp data, even for data such as images with complex, highly multimodal distributions. However GANs are known to be very hard to train, suffering from problems such as mode collapse and disturbing visual artifacts. Batch normalization (BN) techniques have been introduced to address the training. Though BN accelerates the training in the beginning, our experiments show that the use of BN can be unstable and negatively impact the quality of the trained model. The evaluation of BN and numerous other recent schemes for improving GAN training is hindered by the lack of an effective objective quality measure for GAN models. To address these issues, we first introduce a weight normalization (WN) approach for GAN training that significantly improves the stability, efficiency and the quality of the generated samples. To allow a methodical evaluation, we introduce squared Euclidean reconstruction error on a test set as a new objective measure, to assess training performance in terms of speed, stability, and quality of generated samples. Our experiments with a standard DCGAN architecture on commonly used datasets (CelebA, LSUN bedroom, and CIFAR-10) indicate that training using WN is generally superior to BN for GANs, achieving 10 lower mean squared loss for reconstruction and significantly better qualitative results than BN. We further demonstrate the stability of WN on a 21-layer ResNet trained with the CelebA data set. The code for this paper is available at this https URL