A0640
Title: Approximation of nonlinear functionals using deep ReLU networks
Authors: Jun Fan - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals. However, their theoretical properties are largely unknown beyond the universality of approximation or the existing analysis does not apply to the rectified linear unit (ReLU) activation function. To fill in this void, we investigate here the approximation power of functional deep neural networks associated with the ReLU activation function by constructing a piecewise linear interpolation under a simple triangulation. In addition, we establish rates of approximation of the proposed functional deep ReLU networks under mild regularity conditions.
