题目：Multi-Grade Deep Learning

内容简介：The remarkable success of deep learning is widely recognized, yet its training process remains a black box. Standard deep learning relies on a single-grade approach, where a deep neural network (DNN) is trained end-to-end by solving a large, nonconvex optimization problem. As the depth of the network increases, this approach becomes computationally challenging due to the complexity of learning all weight matrices and bias vectors simultaneously. Inspired by the human education system, we propose a multi-grade deep learning (MGDL) model that structures learning into successive grades. Instead of solving a single large-scale optimization problem, MGDL decomposes the learning process into a sequence of smaller optimization problems, each corresponding to a grade. At each grade, a shallow neural network is learned to approximate the residual left from previous grades, and its parameters remain fixed in subsequent training. This hierarchical learning strategy mitigates the severity of nonconvexity in the original optimization problem, making training more efficient and stable. The final learned model takes a stair-shaped architecture, formed by the superposition of networks learned across all grades. MGDL naturally enables adaptive learning, allowing for the addition of new grades if the approximation error remains above a given tolerance. We establish theoretical guarantees in the context of function approximation, proving that if the newly learned network at a given grade is nontrivial, the optimal error is strictly reduced from the previous grade. Furthermore, we present numerical experiments demonstrating that MGDL significantly outperforms the conventional single-grade model in both efficiency and robustness to noise.

报告人：许跃生

报告人简介：Yuesheng Xu received his B.S. and M.S. degrees from Sun Yat-sen University, Guangdong, China, in 1982 and 1985, respectively, and his Ph.D. from Old Dominion University, Norfolk, VA, USA, in 1989. From 1996 to 1997, he was a Humboldt Research Fellow at RWTH Aachen University, Germany. He has held several distinguished academic positions, including Eberly Chair Professor of Mathematics at West Virginia University (2001–2003), Professor of Mathematics at Syracuse University (2003–2013), and Guohua Chair Professor of Mathematics at Sun Yat-sen University (2009–2017). He is currently a Professor of Data Science and Mathematics at Old Dominion University. His research, supported by NSF, NASA, DoD, and NIH, spans numerical analysis, applied harmonic analysis, image and signal processing, medical imaging, and machine learning. He has served as an editor or associate editor for various mathematical journals, including as Managing Editor of Advances in Computational Mathematics (Springer) from 1999 to 2012.

时  间：2025年5月9日19: 00开始

地  点：石牌校区南海楼338会议室

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2025年5月6日