Lp Error Estimate of Approximation by a Feed-Forward Neural Network
Jianwei Zhao, Feilong Cao · 2009
A feed-forward neural network with one hidden layer is constructed by a novel method to approximate Lpintegrable functions. We prove that the constructed feed-forward neural network can approximate any Lpintegrable 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 Lp-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 Lpspace.