Approximating many valued mappings using a recurrent neural network

In this paper, a recurrent neural network (RNN) is applied to approximating one to N many valued mappings. The RNN described in this paper has a feedback loop from an output to an input in addition to the conventional multilayer neural network (MLNN). The feedback loop causes dynamic output properties. The convergence property in these properties can be used for this approximating problem. In order to avoid conflict between the overlapped target data y*s and the same input x*, the input data set (x*,y*) and the target data y* are presented to the network in learning phase. By this learning, the network function f(x,z) which satisfies y*=f(x*,y*) is formed. In recalling phase, the solutions y of y=f(x,y) are detected by the feedback dynamics of RNN. The different solutions for the same input x can be gained by changing the initial output value of y. It have been presented in our previous paper that the RNN can approximate many valued continuous mappings by introducing the differential condition to learning. However, if the mapping has discontinuity or changes of value number, it sometimes shows undesirable behavior. In this paper, the integral condition is proposed in order to prevent spurious convergence and to spread the attractive regions to the approximating points