Tensor Networks

Tensors into networks of smaller tensors

Tensor networks are mathematical representations of quantum many-body states based on their entanglement structure. Different tensor network structures describe different physical situations.

Tensor networks are factorizations of very large tensors into networks of smaller tensors, with applications in applied mathematics, chemistry, physics, machine learning, and many other fields.

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TensorLet Team

The achievement of tensor networks we did by now!

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Related Publications

[NIPS Workshop] W. Lu, X.-Y. Liu, Q. Wu, Y. Sun, A. Walid. Transform-based multilinear dynamical system for tensor time series analysis. NIPS Workshop on Modeling and Decision-Making in the Spatiotemporal Domain, 2018.

X.-Y. Liu and X. Wang. Fourth-order tensor space with two-dimensional discrete transforms. arXiv,2017.

[TIT] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang. Low-tubal-rank tensor completion using alternating minimization. (Major Revision) IEEE Transactions on Information Theory.

[AAAI] F. Jiang, X.-Y. Liu, H. Lu, R. Shen. Efficient multi-dimensional tensor sparse coding using t-linear combinations. AAAI, 2018.

[ICME] T. Deng, F. Qian, X.-Y. Liu, M. Zhang, A. Walid. Tensor sensing for RF tomographic imaging. IEEE ICME, 2018.

[ICASSP] C. Li, Y. Sun, X.-Y. Liu, Y. Li. Tensor subspace detection with tubal-sampling and elementwise-sampling. IEEE ICASSP, 2018.

[ICASSP] F. Jiang, X.-Y. Liu, H. Lu, R. Shen. Anisotropic total variation regularized low-rank tensor completion based on tensor nuclear norm for color image inpainting. IEEE ICASSP, 2018.

C. Zhu, L. Xu, X.-Y. Liu, F. Qian. Tensor-generative adversarial network with two-dimensional sparse coding: application to real-time indoor localization. IEEE International Conference on Communications (ICC), 2018.

[ICME] F. Jiang, X.-Y. Liu, H. Lu, R. Shen. Graph regularized tensor sparse coding for image representation. IEEE ICME, 2017.

[TMC] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang, M.-Y. Wu. Adaptive sampling of RF fingerprints for fine-grained indoor localization. IEEE Transactions on Mobile Computing, 2016.

[ICASSP] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang, M.-Y. Wu. Tensor completion via adaptive sampling of tensor fibers: application to efficient indoor RF fingerprinting. IEEE ICASSP, 2016.

[JMLR] M. Ashraphijuo, X. Wang. Fundamental conditions for low-CP-rank tensor completion. The Journal of Machine Learning Research, 18(1), pp.2116-2145, 2017.

[JMLR] M. Ashraphijuo, X. Wang, V. Aggarwal. Rank determination for low-rank data completion. The Journal of Machine Learning Research, 18(1), pp.3422-3450, 2017.

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