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

Grants and Contracts Details


Overview: Generative adversarial network (GAN) is a deep neural network based generative model for learning data distributions. It is considered a game-changer to unsupervised learning through its design of a generator function with very few restrictions combined with a powerful discriminator model for learning. While it has enjoyed tremendous success in many real-world applications, successful training of GANs remains elusive. A major challenge arises in its formulation as a minimax problem that has many limitations and pitfalls in numerical implementations. We propose to address these challenges by proposing a maximin based theory and developing new losses and algorithms. We propose two novel optimal transport based GAN models for learning discrete distributions and graph structured data and we will test their capabilities through two unique applications that cannot be adequately solved through existing GAN models. Key Words: Neural network, generative network, optimal transport GAN, learning algorithm, welding system, skewed class distribution. Intellectual Merit: Many of the training difficulties associated with GANs can be attributed to the current models and theory that rely on exact solutions and adapt poorly when various approximations are introduced in implementations. This project aims to establish a new paradigm for GAN training by systematically addressing the challenges arising in various stages of approximations. Our proposed theory with a maximin formulation holds great promise to fundamentally resolve the convergence problem of GANs, leading to new research directions. Our proposed algorithms facilitate numerically stable gradient ascent descent optimizations for optimal transport based GAN models. Our proposed models for discrete distributions and graph structured data represent novel uses of the optimal transport theory to address some problems of significant interests to applications. Overall, our proposed works will advance mathematical theory for GANs and more generally adversarial learning, improve robustness and efficiency of their training algorithms, enrich their model versatility, and broaden GAN applications. Broader Impacts: GAN has become an essential machine learning method for representing and manipulating high-dimensional data. With rapid advances in sensing technologies, there are ubiquitous high- dimensional complex inter-connected data in almost all fields, ranging from chemistry to biology and from engineering to social and behavioral sciences. For such data with complex interrelationships, GANs have proved to be a powerful deep learning method to perform modeling and representation learning. This project will improve robustness of the training algorithms for GANs and demonstrate their effectiveness through examples in two representative fields: one arising in a human-robot collaborative welding system and the other in unbalanced data sampled from skewed class distributions. They will potentially impact on biomedical research, complex manufacturing, and workforce developments. The proposed research lies at the interface between mathematics, statistics, computer science, and engineering, and provides an ideal setting for research cross- fertilization and collaboration as well as interdisciplinary training. This project will train both graduate and undergraduate students in deep learning, who will gain valuable experiences in deep learning research and practices. We will share computer codes and data derived in this project in open source platforms, which will accelerate dissemination of the research results to the user communities and promote real world applications.
Effective start/end date10/1/239/30/26


  • National Science Foundation: $351,877.00


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