  We define a message-passing algorithm for computing magnetizations in
Restricted Boltzmann machines, which are Ising models on bipartite graphs
introduced as neural network models for probability distributions over spin
configurations. To model nontrivial statistical dependencies between the spins'
couplings, we assume that the rectangular coupling matrix is drawn from an
arbitrary bi-rotation invariant random matrix ensemble. Using the dynamical
functional method of statistical mechanics we exactly analyze the dynamics of
the algorithm in the large system limit. We prove the global convergence of the
algorithm under a stability criterion and compute asymptotic convergence rates
showing excellent agreement with numerical simulations.
