Tensor networks for unsupervised machine learning

Abstract

Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the advantages of a principle understanding of the expressive power using entanglement properties, and as a bridge connecting classical computation and quantum computation. Despite the great potential, however, existing tensor network models for unsupervised machine learning only work as a proof of principle, as their performance is much worse than the standard models such as restricted Boltzmann machines and neural networks. In this Letter, we present autoregressive matrix product states (AMPS), a tensor network model combining matrix product states from quantum many-body physics and autoregressive modeling from machine learning. Our model enjoys the exact calculation of normalized probability and unbiased sampling. We demonstrate the performance of our model using two applications, generative modeling on synthetic and real-world data, and reinforcement learning in statistical physics. Using extensive numerical experiments, we show that the proposed model significantly outperforms the existing tensor network models and the restricted Boltzmann machines, and is competitive with state-of-the-art neural network models.

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References in corpus (4)

• MADE: Masked Autoencoder for Distribution Estimation
• Tree Tensor Networks for Generative Modeling
• Simulating the Sycamore quantum supremacy circuits
• Boltzmann machines as two-dimensional tensor networks

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• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Dequantizing quantum machine learning models using tensor networks
• Tensor networks for quantum computing
• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• A Matrix Product State Model for Simultaneous Classification and Generation
• Efficient Optimization of Variational Autoregressive Networks with Natural Gradient
• Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
• Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers
• Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss
• The Cytnx Library for Tensor Networks
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Time series generation for option pricing on quantum computers using tensor network
• Using matrix-product states for time-series machine learning