Lp Error Estimate of Approximation by a Feed-Forward Neural Network

A feed-forward neural network with one hidden layer is constructed by a novel method to approximate L^p integrable functions. We prove that the constructed feed-forward neural network can approximate any L^p integrable function arbitrarily as long as the number of hidden nodes is sufficiently large. Furthermore, we reveal the relation among the approximation speed, the number of hidden nodes and the L^p-oscillation of the approximated function by designing a novel method. The obtained results are helpful to study the problem of approximation complexity of feed-forward neural networks in L^p space.