A0333
Title: Learning manifold-structured data using deep neural networks: Theory and applications
Authors: Rongjie Lai - Purdue University (United States) [presenting]
Abstract: Deep artificial neural networks have succeeded greatly in many problems in science and engineering. Our recent efforts are discussed to develop DNNs capable of learning non-trivial geometry information hidden in data. The first part discusses work on advocating using a multi-chart latent space for better data representation. Inspired by differential geometry, a Chart Auto-Encoder (CAE) is proposed, and a universal approximation theorem on its representation capability is proved. CAE admits desirable manifold properties that conventional auto-encoders with a flat latent space fail to obey. Statistical guarantees on the generalization error are further established for trained CAE models, and their robustness is shown to be noise. The numerical experiments also demonstrate satisfactory performance on synthetical and real-world data.
