Attraction domains in neural networks

We performed a systematic study of the sizes of the basins of attraction in a Hebbian-type neural network in which small numbers of patterns were stored with non-uniform embedding strengths $w_\mu$. This was done by iterating numerically the flux equations for the “ overlaps ” between the stored patterns and the dynamical state of the system for zero noise level $T$. We found that the existence of attractors related to mixtures of three or more pure memories depends on the specific values of the embedding strengths involved. With the same method we also obtained the domain sizes for the standard Hopfield model for $p \le 18$