TITLE: A Geometric View to Generative Model in Deep Learning[Talk Link]
ABSTRACT: Generative Adversarial Net (GAN) is a powerful machine learning model, and becomes extremely successful recently. The generator and the discriminator in a GAN model competes each other and reaches the Nash equilibrium. GAN can generate samples automatically, therefore reduce the requirements for large amount of training data. It can also model distributions from data samples. In spite of its popularity, GAN model lacks theoretic foundation.In this talk, we give a geometric interpretation to optimal mass transportation theory, and applied for the GAN model.
We try to answer the following fundamental questions: 1. Does a GAN model learn a function, a mapping or a probability distribution ? Is the solution unique or infinite ? What is the dimension of the solution space ? What is the structure of the solution space? 2. Does a GAN model really learn or just memorize ? 3. Is the competition between the generator and discriminator really necessary ? Can we simplify the neural networks and avoid the competition ? 4. Why sometimes a ML model can be fooled easily? 5. Can we replace the black-box in the GAN model by a transparent model ?
BIO: Dr. Xianfeng David Gu （顾险峰）got his bachelor degree from Tsinghua university and PhD from Harvard University, supervised by the Fields medalist Prof. Shing-Tung Yau （丘成桐）. Currently, David is a tenured professor in Computer Science Department and Applied Mathematics Department in the State University of New York at Stony Brook. David is affiliated with Center of Mathematical Science and Applications at Harvard University. Prof. Yau and David founded a novel inter-disciplinary field - Computational Conformal Geometry, which applies modern geometry and topology in engineering and medical fields. David has published hundreds of academic papers in computer graphics, vision, networking and medical imaging, and several patents liscensed by Simens and GE. David won Morningside Gold Medal in applied mathematics for his fundamental contribution to combing geometry and computer science.