Domains of attraction and the density of static metastable states, in single-pattern iterated neural networks
Thomas B. Kepler · Journal of Physics A Mathematical and General · 1991
The author calculates, for a single-pattern iterated network, the density of static metastable states. delta eta / delta m, as a function of the field distribution and the symmetry of the synaptic matrix. The features of this function strongly suggest that the boundary upon which this density vanishes gives the critical overlap for the memory state, i.e. gives a measure of the size of its domain of attraction. This heuristic interpretation is shown to agree with the exact result for vanishing symmetry, the only case where a direct calculation can be performed. He explicitly calculates critical overlaps as a function of symmetry and mean field strength when the field distribution is a delta-function and when it is a unit-width Gaussian.