Questions tagged [tensor-rank]

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What does doing a tensor network contraction "for bond dimension k" mean?

I’m a tensor-network newbie and am working through Bridgeman and Chubb’s “Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks” (arXiv:1603.03039v4). At the end of Chapter 1, ...
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Has there been any research on faster tensor inner products?

Matrix multiplication is a well studied problem which is recently back in the news due to deepmind. That got me wondering has anyone looked at the more general problem of faster tensor multiplication? ...
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Computing dual of the spectral norm of tensor of order 3

It is shown in that computing the spectral norm (see Definition 6.6) of a $3^{rd}$ order tensor $T \in \mathbb{R}^{d_1 \times d_2 \times d_3}$ is NP-...
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Deciding bound on Tensor Rank for a fixed value

This question is related to a previous unanswered question of mine. Please see that question for background. When Håstad proved that computing tensor rank is NP-complete, the rank in question was ...
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normalized tensor rank

Is there such a thing as a "normalized tensor rank" for non-square tensors (i.e. a tensor with different sizes along each mode)? For example: If a 3rd order tensor (dimensions = 60 x 120 x 30) has ...
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23 votes
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Complexity of Tensor Rank over an Infinite Field

A tensor is a generalization of vectors and matrices to higher dimensions and the rank of a tensor also generalizes the rank of a matrix. Namely, the rank of a tensor $T$ is the minimum number of rank ...
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What are contravariant tensors of type m choose 0

I am not sure if the following question falls within the scope of this site; if it does not, I will request the moderators to take appropriate action I have been going through Jin-Yi Cai's expository ...
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20 votes
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Explain Gurvits's tensor-rank interpretation of Deolalikar's paper

[Note: I believe this question in no way hinges on the correctness or incorrectness of Deolalikar's paper.] On Scott Aaronson's blog Shtetl Optimized, in the discussion about Deolalikar's recent ...