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

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

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.