Spurious minima and basins of attraction in higher-order Hopfield networks

Abstract

A theoretical investigation of the dynamics of continuous Hopfield networks, in a modified formulation proposed by Abe, is undertaken. The fixed points are classified according to whether they lie inside or they are vertices of the unit hypercube. It is proved that interior equilibria are saddle points. Besides, a procedure is sketched that determines the basins of attraction of stable vertices. The calculations are completed for the two-neuron network. These results contribute to a solid foundation for these systems, needed for the study of practical problems such as local minima or convergence speed. © Springer-Verlag Berlin Heidelberg 2003.