DEFANET - A DETERMINISTIC NEURAL NETWORK CONCEPT FOR FUNCTION APPROXIMATION

A deterministic neural network concept for a "universal approximator" is proposed. The network has two hidden layers; only the synapses of the output layer are required to be plastic and only those depend on the function to be approximated. It is shown that a DEterministic Function Approximation Network (DEFAnet) allows to approximate an arbitrary continuous function from the finite-dimensional unit interval into the finite-dimensional real space with arbitrary accuracy; arbitrary Boolean functions may be implemented exactly in a simple subset of DEFAnets. In a supervised learning scheme, convergence to the desired function is guaranteed; back propagation of errors is not required. The concept is also open for reinforcement learning. In addition, when the topology of the network is determined according to the DEFAnet concept, it is possible to calculate all plastic synaptic weights in closed form, thus reducing the training considerably or replacing it altogether. Efficient algorithms for the calculation of synapse weights are given.