High-symmetry Hopfield-type neural networks

We study the set of fixed points of a Hopfield-type neural network with a connection matrix constructed from a high-symmetry set of memorized patterns using the Hebb rule. The memorized patterns depending on an external parameter are interpreted as distorted copies of a vector standard to be learned by the network. The dependence of the fixed-point set of the network on the distortion parameter is described analytically. The investigation results are interpreted in terms of neural networks and the Ising model.