Random iterated neural networks: Properties, evolutionary design and applications.

摘要

A new neural network architecture, called random iterated neural network, is introduced. This architecture is based on the theory of fractals, specifically on random iterated function systems. In this work, the properties of this kind of neural networks, from the point of view of their asymptotic dynamical behavior, are investigated. It is demonstrated that these neural networks are universal approximators of discrete dynamical systems with global attractor and unique invariant physical measure. Also, an evolutionary technique to design random iterated neural networks is developed. The applications of random iterated neural networks in fractal image compression and approximation of dynamical systems are explored, and some experimental results are reported.