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Register a new userTowards Efficient and Unbiased Implementation of Lipschitz Continuity in GANs
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Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In this paper, we demonstrate that gradient penalty introduces undesired bias, while spectral normalization might be over restrictive. We accordingly propose a new method which is efficient and unbiased. Our experiments verify our analysis and show that the proposed method is able to achieve successful training in various situations where gradient penalty and spectral normalization fail.
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Wasserstein GANs (WGANs), built upon the Kantorovich-Rubinstein (KR) duality of Wasserstein distance, is one of the most theoretically sound GAN models. However, in practice it does not always outperform other variants of GANs. This is mostly due to the imperfect implementation of the Lipschitz condition required by the KR duality. Extensive work has been done in the community with different implementations of the Lipschitz constraint, which, however, is still hard to satisfy the restriction perfectly in practice. In this paper, we argue that the strong Lipschitz constraint might be unnecessary for optimization. Instead, we take a step back and try to relax the Lipschitz constraint. Theoretically, we first demonstrate a more general dual form of the Wasserstein distance called the Sobolev duality, which relaxes the Lipschitz constraint but still maintains the favorable gradient property of the Wasserstein distance. Moreover, we show that the KR duality is actually a special case of the Sobolev duality. Based on the relaxed duality, we further propose a generalized WGAN training scheme named Sobolev Wasserstein GAN (SWGAN), and empirically demonstrate the improvement of SWGAN over existing methods with extensive experiments.
Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the generator of GANs have been reported. This paper will first theoretically analyze GANs approximation property. Similar to the universal approximation property of the fully connected neural networks with one hidden layer, we prove that the generator with the input latent variable in GANs can universally approximate the potential data distribution given the increasing hidden neurons. Furthermore, we propose an approach named stochastic data generation (SDG) to enhance GANsapproximation ability. Our approach is based on the simple idea of imposing randomness through data generation in GANs by a prior distribution on the conditional probability between the layers. SDG approach can be easily implemented by using the reparameterization trick. The experimental results on synthetic dataset verify the improved approximation ability obtained by this SDG approach. In the practical dataset, four GANs using SDG can also outperform the corresponding traditional GANs when the model architectures are smaller.
Knowledge distillation has become one of the most important model compression techniques by distilling knowledge from larger teacher networks to smaller student ones. Although great success has been achieved by prior distillation methods via delicately designing various types of knowledge, they overlook the functional properties of neural networks, which makes the process of applying those techniques to new tasks unreliable and non-trivial. To alleviate such problem, in this paper, we initially leverage Lipschitz continuity to better represent the functional characteristic of neural networks and guide the knowledge distillation process. In particular, we propose a novel Lipschitz Continuity Guided Knowledge Distillation framework to faithfully distill knowledge by minimizing the distance between two neural networks Lipschitz constants, which enables teacher networks to better regularize student networks and improve the corresponding performance. We derive an explainable approximation algorithm with an explicit theoretical derivation to address the NP-hard problem of calculating the Lipschitz constant. Experimental results have shown that our method outperforms other benchmarks over several knowledge distillation tasks (e.g., classification, segmentation and object detection) on CIFAR-100, ImageNet, and PASCAL VOC datasets.
In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs. We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal discriminative function is not reliable, which turns out to be the fundamental cause of failure in training of GANs. We further demonstrate that a well-defined distance metric does not necessarily guarantee the convergence of GANs. Finally, we prove in this paper that Lipschitz-continuity condition is a general solution to make the gradient of the optimal discriminative function reliable, and characterized the necessary condition where Lipschitz-continuity ensures the convergence, which leads to a broad family of valid GAN objectives under Lipschitz-continuity condition, where Wasserstein distance is one special case. We experiment with several new objectives, which are sound according to our theorems, and we found that, compared with Wasserstein distance, the outputs of the discriminator with new objectives are more stable and the final qualities of generated samples are also consistently higher than those produced by Wasserstein distance.
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free and scale-free algorithms for a simplified setting with hints. We present t
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