When optimizing against the mean loss over a distribution of predictions in the context of a regression task, then even if there is a distribution of targets the optimal prediction distribution is always a delta function at a single value. Methods of constructing generative models need to overcome this tendency. We consider a simple method of summarizing the prediction error, such that the optimal strategy corresponds to outputting a distribution of predictions with a support that matches the support of the distribution of targets --- optimizing against the minimal value of the loss given a set of samples from the prediction distribution, rather than the mean. We show that models trained against this loss learn to capture the support of the target distribution and, when combined with an auxiliary classifier-like prediction task, can be projected via rejection sampling to reproduce the full distribution of targets. The resulting method works well compared to other generative modeling approaches particularly in low dimensional spaces with highly non-trivial distributions, due to mode collapse solutions being globally suboptimal with respect to the extreme value loss. However, the method is less suited to high-dimensional spaces such as images due to the scaling of the number of samples needed in order to accurately estimate the extreme value loss when the dimension of the data manifold becomes large.
: Generative adversarial networks use a pair of networks in order to effectively estimate, then minimize, the difference between two data distributions. The discriminator network tries to classify samples as belonging to either the true or fake distribution, while the generator network uses the gradients propagated through the discriminator to try to fool it. The Nash equilibrium of this game is the point at which the fake and true distributions are identical. Due to training instability and phenomena such as mode collapse, there have been a number of refinements on the basic GAN idea such as LSGAN @cite_12 , Unrolled GANs @cite_8 , WGAN @cite_26 , WGAN-GP @cite_33 , Relativistic GANs @cite_17 , as well as fusing GANs with other techniques such as in VAEGAN @cite_19 , BEGAN @cite_5 , etc. Very high resolution outputs have been achieved by progressively stacking generators at a sequence of scales (Progressive GANs @cite_22 ).
@cite_26 @cite_33 @cite_22 @cite_8 @cite_19 @cite_5 @cite_12 @cite_17
2739748921 2605135824 2766527293 2953246223 2202109488 2605195953 2593414223 2810518847
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. We describe a new training methodology for generative adversarial networks. The key idea is to grow both the generator and discriminator progressively: starting from a low resolution, we add new layers that model increasingly fine details as training progresses. This both speeds the training up and greatly stabilizes it, allowing us to produce images of unprecedented quality, e.g., CelebA images at 1024^2. We also propose a simple way to increase the variation in generated images, and achieve a record inception score of 8.80 in unsupervised CIFAR10. Additionally, we describe several implementation details that are important for discouraging unhealthy competition between the generator and discriminator. Finally, we suggest a new metric for evaluating GAN results, both in terms of image quality and variation. As an additional contribution, we construct a higher-quality version of the CelebA dataset. We introduce a method to stabilize Generative Adversarial Networks (GANs) by defining the generator objective with respect to an unrolled optimization of the discriminator. This allows training to be adjusted between using the optimal discriminator in the generator's objective, which is ideal but infeasible in practice, and using the current value of the discriminator, which is often unstable and leads to poor solutions. We show how this technique solves the common problem of mode collapse, stabilizes training of GANs with complex recurrent generators, and increases diversity and coverage of the data distribution by the generator. We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic. We propose a new equilibrium enforcing method paired with a loss derived from the Wasserstein distance for training auto-encoder based Generative Adversarial Networks. This method balances the generator and discriminator during training. Additionally, it provides a new approximate convergence measure, fast and stable training and high visual quality. We also derive a way of controlling the trade-off between image diversity and visual quality. We focus on the image generation task, setting a new milestone in visual quality, even at higher resolutions. This is achieved while using a relatively simple model architecture and a standard training procedure. Unsupervised learning with generative adversarial networks (GANs) has proven hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss function for the discriminator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson X2 divergence. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stable during the learning process. We evaluate LSGANs on LSUN and CIFAR-10 datasets and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by regular GANs. We also conduct two comparison experiments between LSGANs and regular GANs to illustrate the stability of LSGANs. In standard generative adversarial network (SGAN), the discriminator estimates the probability that the input data is real. The generator is trained to increase the probability that fake data is real. We argue that it should also simultaneously decrease the probability that real data is real because 1) this would account for a priori knowledge that half of the data in the mini-batch is fake, 2) this would be observed with divergence minimization, and 3) in optimal settings, SGAN would be equivalent to integral probability metric (IPM) GANs. We show that this property can be induced by using a relativistic discriminator which estimate the probability that the given real data is more realistic than a randomly sampled fake data. We also present a variant in which the discriminator estimate the probability that the given real data is more realistic than fake data, on average. We generalize both approaches to non-standard GAN loss functions and we refer to them respectively as Relativistic GANs (RGANs) and Relativistic average GANs (RaGANs). We show that IPM-based GANs are a subset of RGANs which use the identity function. Empirically, we observe that 1) RGANs and RaGANs are significantly more stable and generate higher quality data samples than their non-relativistic counterparts, 2) Standard RaGAN with gradient penalty generate data of better quality than WGAN-GP while only requiring a single discriminator update per generator update (reducing the time taken for reaching the state-of-the-art by 400 ), and 3) RaGANs are able to generate plausible high resolutions images (256x256) from a very small sample (N=2011), while GAN and LSGAN cannot; these images are of significantly better quality than the ones generated by WGAN-GP and SGAN with spectral normalization.