On the approximation capability of neural networks using bell-shaped and sigmoidal functions

The paper deals with the approximation of continuous functions by feedforward neural networks. It presents an explicit formula for function approximators implementable as a four-layer feedforward neural network using bell shaped and sigmoidal activation functions. These four-layer feedforward neural networks have the same number of neurons in the hidden layers as the four-layer neural networks constructed by Ito (1994) and Cardaliaguet-Euvrard (1992).