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インサイト - Tensor analysis
Efficient Tensor Decomposition Algorithm for Overcomplete Tensors
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.
Explicit Universal Sequences of Tensors for Characterizing Asymptotic Rank
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.
