Approximate representation of a continuous function by a neural network with scaled or unscaled sigmoid units

Summary form only given. The author investigates the capability of three-layered neural networks with a scaled or unscaled sigmoid activation function of the hidden layer units in uniformly approximate representation of continuous functions. For the approximation on a compact set, any sigmoid function can be the activation function without scaling. Even for the approximation of continuous functions on R^d , any sigmoid function if scalable can be the activation function, but only a certain class of sigmoid functions can be without scaling. A necessary and sufficient condition ensuring that a sigmoid function belongs to this class has been obtained. Sketches of constructive proofs of some results, which can be regarded as algorithms for implementing the uniform approximations, were given