报告题目：Rates for least squares using over-parameterized neural networks

报告时间：2024-04-18   10:00-11:00

报 告 人：杨云斐  博士后(香港城市大学)

报告地点：理学院东北楼一楼报告厅（110）

Abstract：Recent studies showed that deep neural networks can achieve minimax optimal rates for learning smooth function classes. However, most of these results require that the neural networks in use are under-parameterized, which cannot explain the successes of over-parameterized neural networks used in practice. In this talk, we will discuss how to derive convergence rates for neural networks in the over-parameterized regime. We will begin with a discussion on the approximation capacity of ReLU neural networks with certain norm constraints on the weights. By using this result, we show that one can prove nearly optimal learning rates for least squares estimations based on over-parameterized (deep or shallow) neural networks if the weights are properly constrained. Finally, we will also show how to obtain minimax optimal rates for shallow neural networks by using localization technique and generalize the results to regularized least squares.