Asymmetric Hopfield neural network and twisted tetrahedron equation

Abstract: We generalize the approach of arXiv:1805.04138 for the case of the Hopfield neural network in the recall stage on a triangular lattice with isotropic weights. It appears that some properties of this model, in particular the probability of passing a trajectory in time dynamics, obeys the Gibbs distribution with a partition function having a vertex realization. Moreover the corresponding weight matrix satisfies the TTE - some deformation of the Zamolodchikov tetrahedron equation, the latter playing the role analogous to the Yang-Baxter equation in 3-dimensional statistical models.