In this paper, we present a novel localized Generative Adversarial Net (GAN) to learn on the manifold of real data. Compared with the classic GAN that globally parameterizes a manifold, the Localized GAN (LGAN) uses local coordinate charts to parameterize distinct local geometry of how data points can transform at different locations on the manifold. Specifically, around each point there exists a local generator that can produce data following diverse patterns of transformations on the manifold. The locality nature of LGAN enables local generators to adapt to and directly access the local geometry without need to invert the generator in a global GAN. Furthermore, it can prevent the manifold from being locally collapsed to a dimensionally deficient tangent subspace by imposing an orthonormality prior between tangents. This provides a geometric approach to alleviating mode collapse at least locally on the manifold by imposing independence between data transformations in different tangent directions. We will also demonstrate the LGAN can be applied to train a robust classifier that prefers locally consistent classification decisions on the manifold, and the resultant regularizer is closely related with the Laplace-Beltrami operator. Our experiments show that the proposed LGANs can not only produce diverse image transformations, but also deliver superior classification performances.
The distinction between global and local coordinate systems results in conceptual and algorithmic differences between global and local GANs. Conceptually, the global GANs assume that the manifolds formed by their generators could be globally parameterized in a way that the manifolds are topologically similar to an Euclidean coordinate space. In contrast, the localized paradigm abandons the global parameterizability assumption, allowing us to use multiple local coordinate charts to cover an entire manifold. Algorithmically, if a global GAN needs to access local geometric information underlying its generated manifold, it has to invert the generator function in order to find the global coordinates corresponding to a given data point. This is usually performed by learning an auto-encoder network along with the GAN models, e.g., BiGAN @cite_16 and ALI @cite_4 . On the contrary, the localized GAN enables direct access to local geometry without having to invert a global generator, since the local geometry around a point is directly available from the corresponding local generator. Moreover, the orthormornality between local tangents could also maximize the capability of a local GAN in exploring independent local transformations along different coordinate directions, thereby preventing the manifold of generated data from being locally collapsed with deficient dimensions.
@cite_16 @cite_4
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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. Real images often lie on a union of disjoint manifolds rather than one globally connected manifold, and this can cause several difficulties for the training of common Generative Adversarial Networks (GANs). In this work, we first show that single generator GANs are unable to correctly model a distribution supported on a disconnected manifold, and investigate how sample quality, mode collapse and local convergence are affected by this. Next, we show how using a collection of generators can address this problem, providing new insights into the success of such multi-generator GANs. Finally, we explain the serious issues caused by considering a fixed prior over the collection of generators and propose a novel approach for learning the prior and inferring the necessary number of generators without any supervision. Our proposed modifications can be applied on top of any other GAN model to enable learning of distributions supported on disconnected manifolds. We conduct several experiments to illustrate the aforementioned shortcoming of GANs, its consequences in practice, and the effectiveness of our proposed modifications in alleviating these issues. The Generative Adversarial Networks (GANs) have demonstrated impressive performance for data synthesis, and are now used in a wide range of computer vision tasks. In spite of this success, they gained a reputation for being difficult to train, what results in a time-consuming and human-involved development process to use them. We consider an alternative training process, named SGAN, in which several adversarial "local" pairs of networks are trained independently so that a "global" supervising pair of networks can be trained against them. The goal is to train the global pair with the corresponding ensemble opponent for improved performances in terms of mode coverage. This approach aims at increasing the chances that learning will not stop for the global pair, preventing both to be trapped in an unsatisfactory local minimum, or to face oscillations often observed in practice. To guarantee the latter, the global pair never affects the local ones. The rules of SGAN training are thus as follows: the global generator and discriminator are trained using the local discriminators and generators, respectively, whereas the local networks are trained with their fixed local opponent. Experimental results on both toy and real-world problems demonstrate that this approach outperforms standard training in terms of better mitigating mode collapse, stability while converging and that it surprisingly, increases the convergence speed as well. In this paper, we propose the Self-Attention Generative Adversarial Network (SAGAN) which allows attention-driven, long-range dependency modeling for image generation tasks. Traditional convolutional GANs generate high-resolution details as a function of only spatially local points in lower-resolution feature maps. In SAGAN, details can be generated using cues from all feature locations. Moreover, the discriminator can check that highly detailed features in distant portions of the image are consistent with each other. Furthermore, recent work has shown that generator conditioning affects GAN performance. Leveraging this insight, we apply spectral normalization to the GAN generator and find that this improves training dynamics. The proposed SAGAN achieves the state-of-the-art results, boosting the best published Inception score from 36.8 to 52.52 and reducing Frechet Inception distance from 27.62 to 18.65 on the challenging ImageNet dataset. Visualization of the attention layers shows that the generator leverages neighborhoods that correspond to object shapes rather than local regions of fixed shape.