Abstract:  We shall discuss various Barron type spaces arising from neural network. The connections among them will be clarified, and we shall also establish the sharp imbedding theorems between Barron type spaces and the classical function spaces such as Besov space, Sobolev space and Bessel potential space. As an application, certain new approximation results for the shallow neural network and deep neural network with the Barron class as the target function space will be proved. 

个人简介：明平兵是中国科学院数学与系统科学研究院研究员，并担任科学与工程计算国家重点实验室副主任，主要从事固体多尺度建模、多尺度算法以及机器学习的研究。他于2014年获得国家杰出青年基金。