  We develop an exact mapping between the one-step replica symmetry breaking
cavity method and tensor networks. The two schemes come with complementary
mathematical and numerical toolboxes that could be leveraged to improve the
respective states of the art. As an example, we construct a tensor-network
representation of Survey Propagation, one of the best deterministic k-SAT
solvers. The resulting algorithm outperforms any existent tensor-network solver
by several orders of magnitude. We comment on the generality of these ideas,
and we show how to extend them to the context of quantum tensor networks.
