The primary task of many applications is approximating/estimating  a function  through  samples drawn from a probability distribution on the input space.  The deep approximation  is to  approximate  a function by compositions of many layers of simple functions, that can be viewed as  a series of nested feature extractors. The  key idea of deep learning  network is to convert layers of compositions to  layers of tuneable parameters that  can be adjusted through a  learning process,  so that it achieves a good approximation with respect to the input data.  In this talk, we  shall discuss mathematical theory behind  this new approach and approximation rate of deep network;   we will also show  how  this new approach  differs from  the classic approximation theory, and  how this new theory can be used to understand and design  deep learning network.

沈佐伟，新加坡国立大学陈振传百年纪念教授，主要研究方向是数据科学中的数学理论及其应用。研究领域包括逼近与小波理论、图像科学、压缩感知及机器学习等。作为国际著名数学家，沈佐伟教授先后受邀在2010年国际数学家大会和2015年国际工业与应用数学大会上作报告。沈佐伟教授是新加坡国家科学院院士，发展中国家科学院院士，美国数学会会士（AMS Fellow），美国工业与应用数学会会士（SIAM Fellow）。