Approximation to a Compact Set of Functions by Feedforward Neural Networks
Wei Wu, Nan Dong, Zhengxue Li, Jinling Long · 2007
This paper is concerned with the approximation capability of feedforward neural networks to a compact set of functions. We follow a general approach that covers all the existing results and gives some new results in this respect. To elaborate, we have proved the following: If a family of feedforward neural networks is dense inH, a complete linear metric space of functions, then given a compact setV ⊂ Hand an error boundε, one can fix the quantity of the hidden neurons and the weights between the input and hidden layers, such that in order to approximate any functionf ϵ Vwith accuracyε, one only has to further choose suitable weights between the hidden and output layers.