Guozhi Zhang

This work studies the Lp error of approximating higher-order Korobov functions f∈K^m+1_p(Ω) by deep ReLU convolutional neural networks (CNNs), proving that for depth L≤Csd⁴m³N(log_2 N) there exists a network with inf‖f−f_L‖_Lp(Ω)≤C_m,d‖D^m+1f‖_Lp(Ω)N^−m−1(log_2 N)^(m+2)(d−1), i.e. it improves the classical second-order mixed-derivative rate O(L^−2+1/p) to order (m+1) up to a logarithmic factor, and concludes that the higher-order expressivity of CNNs does not severely suffer from the curse of dimensionality.

This work studies the Lp error of approximating higher-order Korobov functions f∈K^m+1_p(Ω) by deep ReLU convolutional neural networks (CNNs), proving that for depth L≤Csd⁴m³N(log_2 N) there exists a network with inf‖f−f_L‖_Lp(Ω)≤C_m,d‖D^m+1f‖_Lp(Ω)N^−m−1(log_2 N)^(m+2)(d−1), i.e. it improves the classical second-order mixed-derivative rate O(L^−2+1/p) to order (m+1) up to a logarithmic factor, and concludes that the higher-order expressivity of CNNs does not severely suffer from the curse of dimensionality.