Barron Spaces and the Application to Neural Network Approximation

主讲人：明平兵 中国科学院研究员

时间：2023年10月27日10：00

地点：三号楼115室

举办单位：数理学院

主讲人介绍：明平兵，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。他预测了石墨烯的理想强度并在Cauchy-Born法则的数学理论、拟连续体方法的稳定性方面有较为系统的工作。他在JAMS, CPAM, ARMA, JMPS,PRB等国际著名学术期刊上发表学术论文六十余篇。他曾应邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等会议上作大会报告。

内容介绍：We shall discuss various Barron type spaces arising from neural network. The relations among them will be clarified, and we also establish the relationship among the spetral Barron space and the classical function spaces such as Besov space, Sobolev space and Bessel potential space, which partly answer the question proposed by Girosi and Anzellotti in 1993. 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. This is a joint work with Yulei Liao (AMSS, CAS) and Yan Meng (RUC).