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Register a new userSpectral Regularization for Combating Mode Collapse in GANs
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Despite excellent progress in recent years, mode collapse remains a major unsolved problem in generative adversarial networks (GANs).In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. Theoretical analysis shows that the optimal solution to the discriminator has a strong relationship to the spectral distributions of the weight matrix.Therefore, we monitor the spectral distribution in the discriminator of spectral normalized GANs (SN-GANs), and discover a phenomenon which we refer to as spectral collapse, where a large number of singular values of the weight matrices drop dramatically when mode collapse occurs. We show that there are strong evidence linking mode collapse to spectral collapse; and based on this link, we set out to tackle spectral collapse as a surrogate of mode collapse. We have developed a spectral regularization method where we compensate the spectral distributions of the weight matrices to prevent them from collapsing, which in turn successfully prevents mode collapse in GANs. We provide theoretical explanations for why SR-GANs are more stable and can provide better performances than SN-GANs. We also present extensive experimental results and analysis to show that SR-GANs not only always outperform SN-GANs but also always succeed in combating mode collapse where SN-GANs fail. The code is available at https://github.com/max-liu-112/SRGANs-Spectral-Regularization-GANs-.
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Generative adversarial networks (GANs) are a class of deep generative models which aim to learn a target distribution in an unsupervised fashion. While they were successfully applied to many problems, training a GAN is a notoriously challenging task and requires a significant number of hyperparameter tuning, neural architecture engineering, and a non-trivial amount of tricks. The success in many practical applications coupled with the lack of a measure to quantify the failure modes of GANs resulted in a plethora of proposed losses, regularization and normalization schemes, as well as neural architectures. In this work we take a sober view of the current state of GANs from a practical perspective. We discuss and evaluate common pitfalls and reproducibility issues, open-source our code on Github, and provide pre-trained models on TensorFlow Hub.
This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. According to the regularity theory of Monge-Amp`{e}re equation, if the support of the target measure is disconnected or just non-convex, the optimal transportation mapping is discontinuous. General DNNs can only approximate continuous mappings. This intrinsic conflict leads to the convergence difficulty and mode collapse in GANs. We test our hypothesis that the supports of real data distribution are in general non-convex, therefore the discontinuity is unavoidable using an Autoencoder combined with discrete optimal transportation map (AE-OT framework) on the CelebA data set. The testing result is positive. Furthermore, we propose to approximate the continuous Brenier potential directly based on discrete Brenier theory to tackle mode collapse. Comparing with existing method, this method is more accurate and effective.
We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a family of generator objectives that target arbitrary $f$-divergences without minimizing a lower bound, and use them to train generative image models that target either improved sample quality or greater sample diversity.
Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images. But many of these methods, including generative adversarial networks (GANs), can be difficult to train, in part because they are prone to mode collapse, which means that they characterize only a few modes of the true distribution. To address this, we introduce VEEGAN, which features a reconstructor network, reversing the action of the generator by mapping from data to noise. Our training objective retains the original asymptotic consistency guarantee of GANs, and can be interpreted as a novel autoencoder loss over the noise. In sharp contrast to a traditional autoencoder over data points, VEEGAN does not require specifying a loss function over the data, but rather only over the representations, which are standard normal by assumption. On an extensive set of synthetic and real world image datasets, VEEGAN indeed resists mode collapsing to a far greater extent than other recent GAN variants, and produces more realistic samples.
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative model minimizing a divergence measure, e.g. the Jensen-Shannon (JS) divergence, to the data distribution. However, in practice the discriminator is constrained to be in a smaller class $mathcal{F}$ such as neural nets. Then, a natural question is how the divergence minimization interpretation changes as we constrain $mathcal{F}$. In this work, we address this question by developing a convex duality framework for analyzing GANs. For a convex set $mathcal{F}$, this duality framework interprets the original GAN formulation as finding the generative model with minimum JS-divergence to the distributions penalized to match the moments of the data distribution, with the moments specified by the discriminators in $mathcal{F}$. We show that this interpretation more generally holds for f-GAN and Wasserstein GAN. As a byproduct, we apply the duality framework to a hybrid of f-divergence and Wasserstein distance. Unlike the f-divergence, we prove that the proposed hybrid divergence changes continuously with the generative model, which suggests regularizing the discriminators Lipschitz constant in f-GAN and vanilla GAN. We numerically evaluate the power of the suggested regularization schemes for improving GANs training performance.
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