Generative adversarial networks (GANs) have been enjoying considerable success in recent years. However, mode collapse remains a major unsolved problem in training GANs and is one of the main obstacles hindering progress. In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. We first perform theoretical analysis to show that the spectral distributions of the weight matrix in the discriminator affect how the equality of Lipschitz constraint can be fulfilled, thus will have an impact on the performance of the discriminator. Prompted by these analysis, we set out to monitor the spectral distributions in the discriminators 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 evidences 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 introduce two schemes, one static and one dynamic, to compensate the spectral distributions of the weight matrices to prevent them from collapsing, which in turn successfully prevents mode collapse in GANs. Through gradient analysis, 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-

近年来，生成对抗网络（GAN）取得了相当大的成功。但是，模式崩溃仍然是训练GAN时尚未解决的主要问题，并且是阻碍进步的主要障碍之一。在本文中，我们提出了GAN的频谱正则化（SR-GAN），这是一种解决GAN中模式崩溃问题的新方法。我们首先进行理论分析，以表明鉴别器中权重矩阵的频谱分布会影响如何实现Lipschitz约束的等式，从而对鉴别器的性能产生影响。在这些分析的提示下，我们着手监测光谱归一化GAN（SN-GAN）的鉴别器中的光谱分布，并发现一种现象，我们称之为光谱崩溃，当模式崩溃发生时，权重矩阵的大量奇异值会急剧下降。我们表明，有很强的证据将模式崩溃与频谱崩溃联系起来。基于此链接，我们着手解决频谱崩溃问题，这是模式崩溃的替代品。我们开发了一种频谱正则化方法，其中引入了两种方案，一种是静态的，另一种是动态的，以补偿权重矩阵的频谱分布以防止其崩溃，从而成功地防止了GAN中的模式崩溃。通过梯度分析，我们为SR-GAN为什么比SN-GAN更稳定并提供更好的性能提供了理论解释。我们还提供了广泛的实验结果和分析结果，表明SR-GAN不仅总是胜过SN-GAN，而且在对抗SN-GAN失效的模式崩溃中也总是成功的。该代码位于https://github.com/max-liu-112/SRGANs-Spectral-Regularization-GANs-