Luneau, ClementBarbier, JeanMacris, Nicolas2022-01-312022-01-312022-01-312021-12-0110.1093/imaiai/iaaa022https://infoscience.epfl.ch/handle/20.500.14299/184905WOS:000743948700001We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.Mathematics, AppliedMathematicsmutual informationtensor decompositionadaptive interpolation methodconcentrationreplica formulatext::journal::journal article::research article