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Applications of Tensor Networks to Machine Learning

The use of tensor networks for machine learning is an emerging topic. One branch of research involves using a tensor network directly as machine learning model architecture. Another uses tensor networks to compress layers in neural network architectures or for other auxilary tasks.

Because tensor networks can be exactly mapped to quantum circuits, an exciting direction for tensor network machine learning is deploying and even training such models on quantum hardware.

Selected Works on Tensor Networks for Machine Learning

Influential or ground breaking works on theory, algorithms, or applications of tensor networks for machine learning. Please help to expand this list by submitting a pull request to the tensornetwork.org Github repository.

Supervised Learning

Unsupervised Learning

Compression of Machine Learning Architectures

Mathematical or Theoretical Works

Language Modeling


  1. Supervised Learning with Tensor Networks, Edwin Stoudenmire, David J Schwab, Advances in Neural Information Processing Systems 29 (2016)
  2. Unsupervised Generative Modeling Using Matrix Product States, Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, Pan Zhang, Phys. Rev. X 8, 031012 (2018)
  3. Tree tensor networks for generative modeling, Song Cheng, Lei Wang, Tao Xiang, Pan Zhang, Phys. Rev. B 99, 155131 (2019)
  4. Tensorizing Neural Networks, Alexander Novikov, Dmitry Podoprikhin, Anton Osokin, Dmitry Vetrov, Advances in Neural Information Processing Systems 28 (2015)
  5. Advances in Neural Information Processing Systems, Ivan Glasser, Ryan Sweke, Nicola Pancotti, Jens Eisert, Ignacio Cirac (2019)
  6. Lower and Upper Bounds on the VC-Dimension of Tensor Network Models, Behnoush Khavari, Guillaume Rabusseau (2021), 2106.11827

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