Stochastic Pseudo-Spin Neural Network with Tridiagonal Synaptic Connections

This paper proposes a simplified architecture of the pseudospin neural network, which is based on the transformation of the synaptic link matrix into a tridiagonal Hessenberg Matrix (hessenberg neural network). In this case, the interaction between all pseudospin neurons does not disappear, but is taken into account in renormalized connections between the nearest neighboring pseudospin neurons. It is shown that with an increase in the number of neurons, the time to establish synaptic connections (per iteration) in the Hessenberg neural network relative to the time to establish synaptic connections (per iteration) in a fully connected synaptic neural network decreases according to a hyperbolic law.