  We consider rank-one non-symmetric tensor estimation and derive simple
formulas for the mutual information. We start by the order 2 problem, namely
matrix factorization. We treat it completely in a simpler fashion than previous
proofs using a new type of interpolation method developed in [1]. We then show
how to harness the structure in "layers" of tensor estimation in order to
obtain a formula for the mutual information for the order 3 problem from the
knowledge of the formula for the order 2 problem, still using the same kind of
interpolation. Our proof technique straightforwardly generalizes and allows to
rigorously obtain the mutual information at any order in a recursive way.
