Publications [#359801] of Jianfeng Lu

Papers Published

1. Lu, J; Shen, Z; Yang, H; Zhang, S, DEEP NETWORK APPROXIMATION FOR SMOOTH FUNCTIONS, SIAM Journal on Mathematical Analysis, vol. 53 no. 5 (January, 2021), pp. 5465-5506, Society for Industrial & Applied Mathematics (SIAM) [doi]
   (last updated on 2024/04/22)

   Abstract:
   \bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . This paper establishes the optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth simultaneously. To that end, we first prove that multivariate polynomials can be approximated by deep ReLU networks of width \scrO (N) and depth \scrO (L) with an approximation error \scrO (N - L). Through local Taylor expansions and their deep ReLU network approximations, we show that deep ReLU networks of width \scrO (N ln N) and depth \scrO (Lln L) can approximate f \in Cs([0, 1]d) with a nearly optimal approximation error \scrO (\| f\| Cs([0,1]d)N -2s/dL -2s/d). Our estimate is nonasymptotic in the sense that it is valid for arbitrary width and depth specified by N \in \BbbN + and L \in \BbbN +, respectively.