
The author presents a new, constructive uniqueness theorem for tensor decomposition that applies to order 3 tensors of format n×n×p and can prove uniqueness of decomposition for generic tensors up to rank r = 4n/3 as soon as p ≥4. This leads to the first efficient algorithm for overcomplete decomposition of generic tensors.


coremsg

efficient-tensor-decomposition-algorithm-for-overcomplete-tensors


Efficient Tensor Decomposition Algorithm for Overcomplete Tensors


title_rewrite


The authors construct explicit sequences of zero-one-valued tensors that universally characterize the worst-case tensor exponent and asymptotic rank in the space of tensors Fd ⊗Fd ⊗Fd.


explicit-universal-sequences-of-tensors-for-characterizing-asymptotic-rank


Explicit Universal Sequences of Tensors for Characterizing Asymptotic Rank
