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）。