明平兵,中国科学院数学与系统科学研究院

We shall discuss various Barron type spaces arising from neural networks. The relations among these spaces will be clarified, and we shall also establish the relationship between Barron type spaces and the classical function spaces such as Besov spaces, Sobolev spaces and Bessel potential spaces. As an application, certain new approximation rates for the shallow and deep neural networks with the Barron class as the target function space will be proved. This is a joint work with Yulei Liao (AMSS, CAS) and Yan Meng (RUC).