An Addition to Backpropagation for Computing Functional Roots

Many processes are composed of a n-fold repetition ofsome simpler process. If the whole process can be modeledwith a neural network, we present a method to derivea model of the basic process, too, thus performing notonly a system-identification but also a decompositioninto basic blocks. Mathematically this is equivalent to theproblem of computing iterative or functional roots: Giventhe equation F(x)=f(f(x)) and an arbitrary function F(x)we seek a solution for f(x). A special topology of multilayerperceptrons and a simple addition to the delta ruleof backpropagation will allow most NN tools to computegood approximations. Applications range from data analysiswithin chaos theory to the optimization of industrialprocesses, where production lines like steel mills oftenconsist of several identical machines in a row