  We find an exact mapping from the generalized Ising models with many-spin
interactions to equivalent Boltzmann machines, i.e., the models with only
two-spin interactions between physical and auxiliary binary variables
accompanied by local external fields. More precisely, the appropriate
combination of the algebraic transformations, namely the star-triangle and
decoration-iteration transformations, allows one to express the model in terms
of fewer-spin interactions at the expense of the degrees of freedom.
Furthermore, the benefit of the mapping in Monte Carlo simulations is
discussed. In particular, we demonstrate that the application of the method in
conjunction with the Swendsen-Wang algorithm drastically reduces the critical
slowing down in a model with two- and three-spin interactions on the Kagom\'e
lattice.
