报告题目 (Title)：几乎最优的VC维度和伪维度界限用于深度神经网络导数

报告人 (Speaker)：杨雅鸿 博士 （宾夕法尼亚州立大学）

报告时间 (Time)：2023年10月19日（周四） 9:00

报告地点 (Place)：腾讯会议（696406234）

邀请人(Inviter)：秦晓雪

主办部门：理学院数学系

报告摘要：This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural networks (DNNs). Two important applications of these estimations include: 1) Establishing a nearly tight approximation result of DNNs in the Sobolev space; 2) Characterizing the generalization error of machine learning methods with loss functions involving function derivatives. This theoretical investigation fills the gap of learning error estimations for a wide range of physics-informed machine learning models and applications including generative models, solving partial differential equations, operator learning, network compression, distillation, regularization, etc.