The tight upper bound on the number of stationary points in Hopfield networks

This paper derives the tight upper bound on the number of stationary points that an nth order Hopfield network can have, and provides a characterization of synaptic sign patterns that allow a network to achieve this capacity. We show that n^C_[n/2] is the tight upper bound on the number of stationary points of an n-order Hopfield network. A simple graph theoretic characterization of the maximum capacity networks is given