»ã±¨±êÌâ (Title)£ºÏÕЩ×îÓŵÄVCά¶ÈºÍαά¶È½çÏÞÓÃÓÚÉî¶ÈÉñ¾­ÍøÂçµ¼Êý

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»ã±¨¹¦·ò (Time)£º2023Äê10ÔÂ19ÈÕ£¨ÖÜËÄ£© 9:00

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»ã±¨ÌáÒª£ºThis 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.