The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Most Tensor Problems Are NP-Hard
Abstract
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or the spectral norm; and determining the rank or best rank-1 approximation of a 3-tensor. Furthermore, we show that restricting these problems to symmetric tensors does not alleviate their NP-hardness. We also explain how deciding nonnegative definiteness of a symmetric 4-tensor is NP-hard and how computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.
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Cites
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Tensor decompositions for learning latent variable models
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Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm
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Quantum machine learning: a classical perspective
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Discovering faster matrix multiplication algorithms with reinforcement learning
Fawzi, A., Balog, M., Huang, A., Hubert, T., Romera-Paredes, B., Barekatain, M., Novikov, A., R. Ruiz, F. J., Schrittwieser, J., Swirszcz, G., et al. (2022) · Nature · doi:10.1038/s41586-022-05172-4 · Cited by 478
Tensor product methods and entanglement optimization for ab initio quantum chemistry
Szalay, S., Pfeffer, M., Murg, V., Barcza, G., Verstraete, F., Schneider, R., & Legeza, Ö. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24898 · Cited by 314
Metadata
- Authors
- Hillar, C. J., & Lim, L.-H.
- Venue
- Journal of the ACM
- Published
- 2013-11
- Volume
- 60
- Issue
- 6
- Pages
- 1-39
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2079705627
- Cited by
- 1,099
- References
- 16
- FWCI
- 16.25
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
