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 performs better than prior work, boosting the best published Inception score from 36.8 to 52.52 and reducing Fr\'echet 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.

A broad range of cross-multi-domain generation researches boils down to matching a joint distribution by deep generative models (DGMs). Hitherto methods excel in pairwise domains whereas as the number of domains increases, remain struggling to scale themselves to fit a joint distribution. In this paper, we propose a domain-scalable DGM, \emph{i.e.}, MMI-ALI for multi-domain joint distribution matching. As an multi-domain ensemble model of ALIs \cite{dumoulin2016adversarially}, MMI-ALI is adversarially trained with maximizing \emph{Multivariate Mutual Information} (MMI) \emph{w.r.t.} joint variables of each pair of domains and their shared feature. The negative MMIs are upper bounded by a series of feasible losses that provably lead to matching multi-domain joint distributions. MMI-ALI linearly scales as the number of domains increases and may share parameters across domains and thus, strikes a right balance between efficacy and scalability. We evaluate MMI-ALI in diverse challenging multi-domain scenarios and verify the superiority of our DGM.

Deep generative models are becoming a cornerstone of modern machine learning. Recent work on conditional generative adversarial networks has shown that learning complex, high-dimensional distributions over natural images is within reach. While the latest models are able to generate high-fidelity, diverse natural images at high resolution, they rely on a vast quantity of labeled data. In this work we demonstrate how one can benefit from recent work on self- and semi-supervised learning to outperform state-of-the-art on both unsupervised ImageNet synthesis, as well as in the conditional setting. In particular, the proposed approach is able to match the sample quality (as measured by FID) of the current state-of-the art conditional model BigGAN on ImageNet using only 10% of the labels and outperform it using 20% of the labels.

In this article we revisit the definition of Precision-Recall (PR) curves for generative models proposed by (Sajjadi et al., 2018). Rather than providing a scalar for generative quality, PR curves distinguish mode-collapse (poor recall) and bad quality (poor precision). We first generalize their formulation to arbitrary measures hence removing any restriction to finite support. We also expose a bridge between PR curves and type I and type II error (a.k.a. false detection and rejection) rates of likelihood ratio classifiers on the task of discriminating between samples of the two distributions. Building upon this new perspective, we propose a novel algorithm to approximate precision-recall curves, that shares some interesting methodological properties with the hypothesis testing technique from (Lopez-Paz & Oquab, 2017). We demonstrate the interest of the proposed formulation over the original approach on controlled multi-modal datasets.

The Wasserstein distance serves as a loss function for unsupervised learning which depends on the choice of a ground metric on sample space. We propose to use the Wasserstein distance itself as the ground metric on the sample space of images. This ground metric is known as an effective distance for image retrieval, that correlates with human perception. We derive the Wasserstein ground metric on pixel space and define a Riemannian Wasserstein gradient penalty to be used in the Wasserstein Generative Adversarial Network (WGAN) framework. The new gradient penalty is computed efficiently via convolutions on the $L^2$ gradients with negligible additional computational cost. The new formulation is more robust to the natural variability of the data and provides for a more continuous discriminator in sample space.

We take the novel perspective to view data not merely as a probability distribution but as a current. Primarily studied in the field of geometric measure theory, k-currents are continuous linear functionals acting on compactly supported smooth differential forms and can be understood as a generalized notion of oriented k-dimensional manifold. By moving from distributions (which are 0-currents) to k-currents, we can explicitly orient the data by attaching a k-dimensional tangent plane to each sample point. Based on the flat metric which is a fundamental distance between currents, we derive FlatGAN, a formulation in the spirit of generative adversarial networks but generalized to k-currents. In our theoretical contribution we prove that the flat metric between a parametrized current and a reference current is continuous in the parameters. In experiments, we show that the proposed shift to k>0 leads to interpretable and disentangled latent representations which behave equivariantly to the specified oriented tangent planes.

Building on the success of deep learning, two modern approaches to learn a probability model from the data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we resolve this issue by constructing an explicit probability model that can be used to compute sample likelihood statistics in GANs. In particular, we prove that under this probability model, a family of Wasserstein GANs with an entropy regularization can be viewed as a generative model that maximizes a variational lower-bound on average sample log likelihoods, an approach that VAEs are based on. This result makes a principled connection between two modern generative models, namely GANs and VAEs. In addition to the aforementioned theoretical results, we compute likelihood statistics for GANs trained on Gaussian, MNIST, SVHN, CIFAR-10 and LSUN datasets. Our numerical results match consistently with the proposed theory.

The advent of generative adversarial networks (GAN) has enabled new capabilities in synthesis, interpolation, and data augmentation heretofore considered very challenging. However, one of the common assumptions in most GAN architectures is the assumption of simple parametric latent-space distributions. While easy to implement, a simple latent-space distribution can be problematic for uses such as interpolation, as the samples drawn often lead to distributional mismatches when interpolated in the latent-space. We present a rather simple formalization of this problem; using basic results from probability theory and off-the-shelf-optimization tools, we develop ways to arrive at appropriate non-parametric priors. The obtained prior exhibits unusual qualitative properties in terms of its shape, and quantitative benefits in terms of lower divergence with its mid-point distribution. We demonstrate that our designed prior helps to improve the quality of image generation along any Euclidean straight line during interpolation, both qualitatively and quantitatively, without any additional training or architectural modifications. The proposed formulation is quite flexible, paving the way to impose newer constraints on the latent-space statistics.

In this paper we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by the discriminator is uninformative to guide the generator. By contrast, Wasserstein GAN (WGAN), where the discriminative function is restricted to 1-Lipschitz, does not suffer from such a gradient uninformativeness problem. We further show in the paper that the model with a compact dual form of Wasserstein distance, where the Lipschitz condition is relaxed, also suffers from this issue. This implies the importance of Lipschitz condition and motivates us to study the general formulation of GANs with Lipschitz constraint, which leads to a new family of GANs that we call Lipschitz GANs (LGANs). We show that LGANs guarantee the existence and uniqueness of the optimal discriminative function as well as the existence of a unique Nash equilibrium. We prove that LGANs are generally capable of eliminating the gradient uninformativeness problem. According to our empirical analysis, LGANs are more stable and generate consistently higher quality samples compared with WGAN.

Most deep learning classification studies assume clean data. However, when dealing with the real world data, we encounter three problems such as 1) missing data, 2) class imbalance, and 3) missing label problems. These problems undermine the performance of a classifier. Various preprocessing techniques have been proposed to mitigate one of these problems, but an algorithm that assumes and resolves all three problems together has not been proposed yet. In this paper, we propose HexaGAN, a generative adversarial network framework that shows promising classification performance for all three problems. We interpret the three problems from a single perspective to solve them jointly. To enable this, the framework consists of six components, which interact with each other. We also devise novel loss functions corresponding to the architecture. The designed loss functions allow us to achieve state-of-the-art imputation performance, with up to a 14% improvement, and to generate high-quality class-conditional data. We evaluate the classification performance (F1-score) of the proposed method with 20% missingness and confirm up to a 5% improvement in comparison with the performance of combinations of state-of-the-art methods.