For a given 0 < δ < 2 if [Nδ] neurons deviating from the memorized patterns are allowed, we constructively show that if and only if α(δ) := p(N)/N = (1 − 2δ)2/(1 − δ)2 all stored patterns are fixed points of the Hopfield model. If [NδN ] neurons are allowed with δN → 0 then αN = (1−2δN )2/(8−1(1−δN ))2 → 0 where 8 is the distribution function of the normal distribution. The result obtained by A...

In the Hopfield model the ability of the network to generalization is studied in the case of the network trained by one input image (the standard).

Although the traditional permute matrix coming along with Hopfield is able to describe many common problems, it seems to have limitation in solving more complicated problem with more constrains, like resource leveling which is actually a NP problem. This paper tries to find a better solution for it by using neural network. In order to give the neural network description of resource leveling pro...

Abstract— In this paper the Hopfield neural networks are adopted to solve the quadratic assignment problem, which is a generalization of the traveling salesman’s problem (TSP), the graph-partitioning problem (GPP), and the matching problem. When the Hopfield neural network was applied alone, a sub-optimal solution was obtained. By adding the 2exchange we obtained a solution very close to the op...