Generative adversarial networks (GANs) are among the most successful models for learning high-complexity, real-world distributions. However, in theory, due to the highly non-convex, non-concave landscape of the minmax training objective, GAN remains one of the least understood deep learning models. In this work, we formally study how GANs can efficiently learn certain hierarchically generated distributions that are close to the distribution of real-life images. We prove that when a distribution has a structure that we refer to as Forward Super-Resolution, then simply training generative adversarial networks using stochastic gradient descent ascent (SGDA) can learn this distribution efficiently, both in sample and time complexities. We also provide empirical evidence that our assumption "forward super-resolution" is very natural in practice, and the underlying learning mechanisms that we study in this paper (to allow us efficiently train GAN via SGDA in theory) simulates the actual learning process of GANs on real-world problems.

翻译：生成对抗网络（GAN）是学习高复杂度真实世界分布最成功的模型之一。然而在理论上，由于极小极大训练目标的高度非凸、非凹景观，GAN仍是理解最不充分的深度学习模型之一。本文正式研究了GAN如何高效学习与真实图像分布相近的特定层次生成分布。我们证明，当分布具有我们称之为“前向超分辨率”的结构时，仅需使用随机梯度下降上升法（SGDA）训练生成对抗网络，即可在样本复杂度和时间复杂度上高效学习该分布。我们还提供实证证据表明，我们的假设“前向超分辨率”在实践中非常自然，并且本文研究的底层学习机制（理论上使我们能够通过SGDA高效训练GAN）模拟了真实问题上GAN的实际学习过程。