Аннотация:The probabilistic Hopfield model known also as the Boltzman
machine is a basic example in the zoo of artificial neural networks.
Initially it was designed as a model of associative memory, but played a
fundamental role in understanding the statistical nature of the realm of
neural networks. The close relation between the Boltzman machine and
the Ising model was a challenging observation in [1]. In this note we go
further, we establish another type of structural similarity between these
models sharing the methods of the Bethe ansatz family of integrable statistical
mechanics. We examine the asymmetric model on the triangular
lattice with arbitrary weights. We show that the probability of passing
a trajectory in time dynamics obeys the Gibbs distribution with a partition
function of the Ising model on the cubic lattice with additional
weights on diagonals.