Some recent results will be reported in this talk on the study of deep learning for its mathematical understanding in view of its relationship with traditional algorithms in scientific computing. The talk will begin with elementary introduction to basic algorithms from different fields, including logistic regression, support vector machine, finite element, and multigrid methods. The mathematical properties and connections of these algorithms will be used to understand and improve deep neural networks for their model structures, loss functions and relevant training algorithms. In particular a new class of convolutional neural networks (CNN), known as MgNet, will be introduced by combing the most effective multigrid methods used in scientific computing with CNN used in machine learning.
About the Speaker
Professor Xu, a Verne M. Willaman professor at The Pennsylvania State University, director of the PSU-PKU Joint Research Center for Computational Mathematics and Applications, has been authorized the position of professor fellowship of Changjiang Scholar Program of Peking University and Distinguished Youth (Class B) before. Professor Xu won the first Fung Kang Scientific Computing Award in 1995, the German ‘Humboldt’ Senior Scientist Award in 2005, the China Outstanding Youth Fund (Type B) in 2006, and the 6th International Industrial and Applied Mathematics in 2007, he was also invited to give a special report at the conference. In 2010, he was invited to give a 45-minute report at the World Congress of Mathematicians. In 2011, he was elected as a Fellow of the American Society of Industrial and Applied Mathematics. In 2012, he was elected as a Fellow of the American Mathematical Society. In 2011, he was awarded the ‘National Excellent Doctoral Thesis’ Instructor Award by the Ministry of Education of China and the Academic Degrees Committee of the State Council and his students won the 2011 National Outstanding Doctoral Thesis Award.