Complex Systems

Neural Networks with Complex Activations and Connection Weights Download PDF

Miklos N. Szilagyi
Department of Electrical and Computer Engineering,
University of Arizona, Tucson, AZ 85721, USA

Boaz Salik
Department of Electrical Engineering,
California Institute of Technology, Pasadena, CA 91125, USA


The concept of neural networks is generalized to include complex connections between complex units. A mathematical model is presented. An expression for the network's energy as well as a complex learning rule are proposed. This innovation may lead to new neural network paradigms, architectures, and applications, and may help to better understand biological nervous systems. The similarity between the dynamics of some linear complex networks and the quantum mechanical behavior of atomic systems is shown. The convergence properties of two-neuron complex networks are explored as extensions of the neural description of the Mandelbrot set, and are found to possess similar fractal properties.