Generative Tensor Network Classification Model for Supervised Machine Learning

Abstract

Tensor network (TN) has recently triggered extensive interests in developing machine-learning models in quantum many-body Hilbert space. Here we purpose a generative TN classification (GTNC) approach for supervised learning. The strategy is to train the generative TN for each class of the samples to construct the classifiers. The classification is implemented by comparing the distance in the many-body Hilbert space. The numerical experiments by GTNC show impressive performance on the MNIST and Fashion-MNIST dataset. The testing accuracy is competitive to the state-of-the-art convolutional neural network while higher than the naive Bayes classifier (a generative classifier) and support vector machine. Moreover, GTNC is more efficient than the existing TN models that are in general discriminative. By investigating the distances in the many-body Hilbert space, we find that (a) the samples are naturally clustering in such a space; and (b) bounding the bond dimensions of the TN's to finite values corresponds to removing redundant information in the image recognition. These two characters make GTNC an adaptive and universal model of excellent performance.

7 pages, 5 figures

References in corpus (34)

• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Supervised learning with quantum enhanced feature spaces
• The theory of variational hybrid quantum-classical algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum support vector machine for big data classification
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Quantum Convolutional Neural Networks
• An introduction to quantum machine learning
• Quantum Data Fitting
• The iTEBD algorithm beyond unitary evolution
• Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Why does deep and cheap learning work so well?
• Renormalization and tensor product states in spin chains and lattices
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Scaling of entanglement support for Matrix Product States
• Towards Quantum Machine Learning with Tensor Networks
• Differentiable Learning of Quantum Circuit Born Machine
• Tensor network states and geometry
• Unsupervised Generative Modeling Using Matrix Product States
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Lecture Notes of Tensor Network Contractions
• Tree Tensor Networks for Generative Modeling
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
• Learning and Inference on Generative Adversarial Quantum Circuits
• Matrix Product Operators for Sequence to Sequence Learning
• From probabilistic graphical models to generalized tensor networks for supervised learning

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• Multi-class quantum classifiers with tensor network circuits for quantum phase recognition
• Tensor networks for quantum machine learning
• Entanglement-guided architectures of machine learning by quantum tensor network
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Experimental realization of a quantum image classifier via tensor-network-based machine learning
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• Quantum-assisted Monte Carlo algorithms for fermions
• Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations
• Differentiable Programming of Isometric Tensor Networks
• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• Positive unlabeled learning with tensor networks
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• QuFeX: Quantum feature extraction module for hybrid quantum-classical deep neural networks
• Deep tensor networks with matrix product operators
• Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data
• 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
• A Tensor Network Approach to Finite Markov Decision Processes
• Explaining Anomalies with Tensor Networks