Using Three Layer Neural Network to Compute Multi-valued Functions

This paper concerns how to compute multi-valued functions using three-layer feedforward neural networks with one hidden layer. Firstly, we define strongly and weakly symmetric functions. Then we give a network to compute a specific strongly symmetric function. The number of the hidden neurons is given and the weights are 1 or -1. Algorithm 1 modifies the weights to real numbers to compute arbitrary strongly symmetric functions. Theorem 3 extends the results to compute any multi-valued functions. Finally, we compare the complexity of our network with that of binary one. Our network needs fewer neurons.