This article presents a new perspective from control theory to interpret and solve the instability and mode collapse problems of generative adversarial networks (GANs). The dynamics of GANs are parameterized in the function space and control directed methods are applied to investigate GANs. First, the linear control theory is utilized to analyze and understand GANs. It is proved that the stability depends only on control parameters. Second, a proportional–integral–derivative (PID) controller is designed to improve its stability. GANs can be controlled to adaptively generate images by an overshoot rate that is only related to the PID control parameters. Third, a new PIDGAN is derived with a theoretical guarantee of stability. Fourth, to exploit the nonlinear characteristics of GANs, the nonlinear control theory is applied to further analyze GANs and develop a feedback linearization control-based PIDGAN named NPIDGAN. Both PIDGAN and NPIDGAN not only improve stability but also prevent mode collapse. With five datasets covering a wide variety of image domains, the proposed models achieve superior performance with 1024×10241024\times 1024 resolution compared with the state-of-the-art GANs, even when data are limited.

中文翻译：

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参数化生成对抗网络的自动控制视角


本文提出了控制理论的新视角来解释和解决生成对抗网络（GAN）的不稳定性和模式崩溃问题。 GAN 的动力学在函数空间中进行参数化，并应用控制导向方法来研究 GAN。首先，利用线性控制理论来分析和理解 GAN。证明了稳定性仅取决于控制参数。其次，设计了比例积分微分（PID）控制器来提高其稳定性。可以通过仅与 P​​ID 控制参数相关的超调率来控制 GAN 自适应地生成图像。第三，推导了一种新的PIDGAN，并在理论上保证了稳定性。第四，为了利用GAN的非线性特性，应用非线性控制理论来进一步分析GAN并开发一种基于反馈线性化控制的PIDGAN，称为NPIDGAN。 PIDGAN 和 NPIDGAN 不仅可以提高稳定性，还可以防止模式崩溃。凭借涵盖各种图像领域的五个数据集，即使在数据有限的情况下，与最先进的 GAN 相比，所提出的模型也能以 1024×10241024×1024 分辨率实现卓越的性能。