RI: Small: Optimal Transport Generative Adversarial Networks: Theory, Algorithms, and Applications

随着传感技术的快速发展，未标记的高维复杂互连数据已经在各个应用领域变得无处不在，从科学和工程到社会和行为科学。生成模型已经成为一种非常有效的方法，用于从这种未标记的数据中建模和表示学习。因此，它们在当前的人工智能（AI）和机器学习研究中发挥了核心作用，扩大了AI应用的前沿。最著名的生成模型之一是生成对抗网络（GAN），这是一种基于深度神经网络的模型，旨在学习未知的数据分布。自推出以来，GAN模型已被证明是非常高效和有效的，特别是在生成高质量样本方面。然而，在使用GAN方面存在一些重大挑战，其中训练困难是一个值得注意的挑战。该项目的目标是推进GANs的理论和训练算法，并通过两个应用程序证明其有效性：一个是在人机协作焊接系统中产生的，另一个是从倾斜的类分布中采样的不平衡数据。通过应对这些挑战和研究现实世界的应用，该项目旨在促进生成模型在不同领域的更广泛应用。虽然GAN在许多现实世界的应用中取得了巨大的成功，但GAN的成功训练仍然难以捉摸。训练算法的不稳定性，模式崩溃和不收敛是主要问题，它们可以归因于当前的模型和依赖于极小极大优化的精确解的理论，当在实现中引入各种近似时，这些模型和理论适应性很差。在这个项目中，研究人员将系统地研究在近似的各个阶段出现的挑战，通过开发一个新的理论框架，更适合近似，因此，新的算法，具有更好的收敛性和稳定性。他们还将开发两种新的基于最优传输的GAN模型，分别用于学习离散数据分布和图形结构数据。他们将在两个无法通过现有GAN模型充分解决的应用中测试他们的能力。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

With the rapid advancements of sensing technologies, unlabeled high dimensional complex interconnected data have become ubiquitous across various application fields, spanning from science and engineering to social and behavioral sciences. Generative models have emerged as a highly effective approach for modeling and representation learning from such unlabeled data. As a result, they have taken a central role in current research of artificial intelligence (AI) and machine learning, expanding frontiers of AI applications. One of the most prominent generative models is the Generative Adversarial Network (GAN), which is a deep neural network-based model designed to learn unknown data distributions. Since its introduction, GAN models have proven to be exceptionally efficient and effective, particularly in generating high quality samples. However, there are some significant challenges in using GANs, with training difficulties being a notable one. The objective of this project is to advance theory and training algorithms for GANs and to demonstrate their effectiveness through two applications: one arising in a human-robot collaborative welding system and the other in imbalanced data sampled from skewed class distributions. By tackling these challenges and studying real-world applications, this project aims to contribute to the broader utilization of generative models across diverse domains.While GANs have enjoyed tremendous success in many real-world applications, successful training of GANs remains elusive. Instability, mode collapse, and non-convergence of training algorithms are the main issues and they can be attributed to the current models and the theory that rely on exact solutions of a minimax optimization, which adapt poorly when various approximations are introduced in implementations. In this project, the investigators will systematically study the challenges arising in various stages of approximations by developing a new theoretical framework that is more amenable to approximations and, consequently, new algorithms that have better convergence property and stability. They will also develop two novel optimal transport based GAN models for learning discrete data distributions and for graph structured data respectively. They will test their capabilities in two applications that cannot be adequately solved through the existing GAN models.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.