Barron Spaces and the Application to Neural Network Approximation
科研大讨论系列报告
报告题目(Title)：Barron Spaces and the Application to Neural Network Approximation
报告人(Speaker)：明平兵（中国科学院数学与系统科学研究院，计算数学与科学工程计算研究所）
地点(Place)：后主楼1124
时间(Time)：2023年11月8日（周三）16:00-17:00
邀请人(Inviter)：纪光华，陈华杰
报告摘要
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).Schroedinger-Poisson model is new in the literature.
主讲人简介
中国科学院数学与系统科学研究院研究员，主要从事固体多尺度建模、模拟及多尺度算法的研究，在Cauchy-Born法则的数学理论以及石墨烯理想强度的理论预测领域具有突出贡献；于2014年获得国家杰出青年基金、2019年入选第四批国家“万人计划”中青年科技创新领军人才计划，2023年获第十五届“冯康科学计算奖”；曾应邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等会议上作大会报告。
