An Addition to Backpropagation for Computing Functional Roots

Many processes are composed of a n-fold repetition of some simpler process. If the whole process can be modeled with a neural network, we present a method to derive a model of the basic process, too, thus performing not only a system-identification but also a decomposition into basic blocks. Mathematically this is equivalent to the problem of computing iterative or functional roots: Given the equation F(x)=f(f(x)) and an arbitrary function F(x) we seek a solution for f(x). A special topology of multilayer perceptrons and a simple addition to the delta rule of backpropagation will allow most NN tools to compute good approximations. Applications range from data analysis within chaos theory to the optimization of industrial processes, where production lines like steel mills often consist of several identical machines in a row. 1 Functional Roots or Fractional Iterations The concept of the well known square root of a real number can easily be extended to functions. This is an important pa...

• Type: Conference
• Year: 1998
• Where: NC
• Authors: Lars Kindermann
• Keywords: Functional Roots, Many Processes, N-fold Repetition, NC 1998, Neural Networks