Tensor networks for unsupervised machine learning.

Area of Science:

• Machine Learning
• Quantum Many-Body Physics
• Computational Physics

Background:

• Modeling high-dimensional data distributions is crucial in unsupervised machine learning.
• Tensor networks offer a principled understanding of expressive power and bridge classical and quantum computation.
• Existing tensor network models lag behind standard methods like restricted Boltzmann machines and neural networks.

Purpose of the Study:

• To develop a high-performance tensor network model for unsupervised machine learning.
• To combine matrix product states with autoregressive modeling for enhanced capabilities.
• To evaluate the model's performance in generative modeling and reinforcement learning.

Main Methods:

• Developed autoregressive matrix product states (AMPS), integrating quantum many-body physics and machine learning.
• Leveraged matrix product states for tensor network construction.
• Employed autoregressive modeling for probabilistic sequence generation.

Main Results:

• AMPS achieves exact calculation of normalized probability and unbiased sampling.
• The model significantly outperforms existing tensor network models and restricted Boltzmann machines.
• AMPS demonstrates competitive performance against state-of-the-art neural network models in generative tasks and reinforcement learning.

Conclusions:

• Autoregressive matrix product states represent a significant advancement in tensor network-based machine learning.
• The proposed model offers a promising alternative to current state-of-the-art methods.
• AMPS opens new avenues for applying tensor networks in complex data modeling and learning tasks.