Computing iterative roots with second order training methods

Iterative roots are a valuable tool for modeling and analyzing dynamical systems. They provide a natural way to construct a continuous time model from discrete time data. However, they are in most cases extremely difficult to compute analytically. Previously we have demonstrated how to use neural networks to calculate the iterative roots and fractional iterations of functions. We used a special topology of MLPs together with weight sharing. The paper shows how adding a regularization term to the error function can direct any backpropagation based training method to the same result but in a fraction of epochs when using advanced 2-nd order learning rules.