Universal learning networks with multiplication neurons and its representation ability

Universal Learning Networks(ULNs) which are super set of supervised learning networks have been already proposed. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them. Most of the functions used are sigmoidal functions. Disadvantages of exiting ULNs mainly lie in that long training time, a large number of nodes in hidden layers, and so on. In this paper, special ULNs with multiplication neurons(M neuron) are proposed, which have M neurons in the hidden layer and normal neurons with sigmoidal functions in the output layer. The computational power of networks models with multiplication neurons is compared with that of ULNs with existing neurons. In particular it is proved that ULNs with multiplication neurons are, with regard to the number of neurons that are needed, computationally more powerful than ULNs with normal sigmodial functions.