CIF: Small: Collaborative Research: Generative Adversarial Networks: From Art to Science

在现代大数据时代，尽管标记和分析单个数据样本的成本一直在快速下降，但数据集大小的无与伦比的快速增长通常会超过这一成本，这使得设计能够在不需要大量人力的情况下发现有意义的数据结构的无监督学习算法尤为及时。近年来，生成性对抗性网络(GANS)作为一种蓬勃发展的无监督机器学习技术已经在计算机视觉、自然语言处理等各个领域取得了重大进展。Gans可以基于未标记的自然图像生成高质量的逼真图像，并执行复杂的任务，如从草图合成照片和为图像上色。然而，也存在需要及时解决的挑战。据报道，甘斯的训练被认为是具有挑战性的、不稳定的，而且不易复制。本项目旨在通过基本公式、泛化和优化问题对GANS进行系统的研究。该项目的变革潜力在于通过最优运输、信息论、凸几何学和经验过程理论的新组合来开发基本工具和实用指南。这个项目的目标有四个方面：(1)建立一个分析高维GAN泛化特性的理论框架；(2)提出设计GAN以获得最佳统计特性的原则性方法；(3)当出现模式崩溃或鉴别器获胜等问题时诊断GAN；(4)开发计算高效的算法，以达到设计良好的GAN的统计极限。在这个项目中开发的理论和算法将对各种工程和科学应用产生影响，并为在现实世界中正确使用GANS提供见解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In the modern era of big data, although the cost of labeling and analyzing a single data sample has been decreasing rapidly, it is usually outpaced by the unrivaled fast growth of dataset size, which makes it particularly timely to design unsupervised learning algorithms that are able to discover meaningful structures of data without extensive human efforts. Recently, Generative Adversarial Networks (GANs) have emerged as a thriving unsupervised machine learning technique that has led to significant advances in various fields such as computer vision, natural language processing, and others. GANs can generate high-quality realistic images based on unlabeled natural images and perform sophisticated tasks such as synthesizing photos from sketches and coloring images. However, there also exist challenges that need timely solutions. The training of GANs has been reportedly observed to be challenging, unstable, and not easily reproducible. This project seeks to conduct a systematic study of GANs through the fundamental formulation, generalization and optimization issues. The transformative potential of the project is in the development of foundational tools and practical guidelines through novel combinations of optimal transport, information theory, convex geometry, and empirical process theory. The goal of this project is four-fold: (1) develop a theoretical framework for analyzing the generalization properties of GANs in high-dimensions; (2) suggest principled approaches to design GANs to achieve optimal statistical properties; (3) diagnose GANs when issues such as mode collapse or discriminator winning occur; (4) develop computationally efficient algorithms that can attain the statistical limits of well-designed GANs. The theory and algorithms developed within this projection will have impact on various engineering and scientific applications and provide insights for the proper usage of GANs in the real world.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.