# Tensor networks for unsupervised machine learning

@article{Liu2021TensorNF, title={Tensor networks for unsupervised machine learning}, author={Jing Liu and Sujie Li and Jiang Zhang and Pan Zhang}, journal={ArXiv}, year={2021}, volume={abs/2106.12974} }

Jing Liu,1 Sujie Li,2, 3 Jiang Zhang,1 and Pan Zhang2, 4, 5, β 1School of Systems Science, Beijing Normal University 2CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 4School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China 5International Centre forβ¦Β

## 7 Citations

### Permutation Search of Tensor Network Structures via Local Sampling

- Computer ScienceICML
- 2022

Theoretically, the counting and metric properties of search spaces of TN-PS are proved and a novel meta-heuristic algorithm is proposed, in which the searching is done by randomly sampling in a neighborhood established in the authors' theory, and then recurrently updating the neighborhood until convergence.

### Generalization and Overfitting in Matrix Product State Machine Learning Architectures

- Computer ScienceArXiv
- 2022

It is speculated that generalization properties of MPS depend on the properties of data: with one-dimensional data (for which the MPS ansatz is the most suitable) MPS is prone to overο¬tting, while with more complex data which cannot be parameterized by MPS exactly, over-tting may be much less signiο¬cant.

### A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom

- Computer ScienceFrontiers in Applied Mathematics and Statistics
- 2022

An introduction to the contraction of tensor networks, to optimal tensor decompositions, and to the manipulation of gauge degrees of freedom in Tensor networks is presented.

### Graphical calculus for Tensor Network Contractions

- Computer Science, Physics
- 2022

This dissertation investigates how effective the existing procedures are at enhancing tensor network contractions and proposes new strategies based on their observations, which are evaluated using a variety of circuits, including the Sycamore circuits used by Google to demonstrate quantum supremacy in 2019.

### Generative modeling with projected entangled-pair states

- Computer ScienceArXiv
- 2022

Techniques from many-body physics have always played a major role in the development of generative machine learning, and can be traced back to the parallels between the respective problems one has to deal with in both fields.

### Grokking phase transitions in learning local rules with gradient descent

- Computer ScienceArXiv
- 2022

A tensor-network map is introduced that connects the proposed grokking setup with the standard (perceptron) statistical learning theory and it is shown thatGrokking is a consequence of the locality of the teacher model and the critical exponent and thegrokking time distributions are numerically determined.

### Deep tensor networks with matrix product operators

- Computer Science
- 2022

Deep tensor networks are introduced, which are exponentially wide neural networks based on the tensor network representation of the weight matrices and random crop training improves the robustness of uniform Tensor network models to image size and aspect ratio changes.

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