Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines

Abstract

We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states respectively.Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the restricted Boltzmann machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches. We verify our reasonings by comparing the performance of RBMs of various architectures on the standard MNIST datasets.

arXiv comment7 pages, 4 figures

References in corpus (43)

• Estimating Mutual Information
• Area laws for the entanglement entropy - a review
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A class of quantum many-body states that can be efficiently simulated
• Many-body quantum state tomography with neural networks
• Area laws in quantum systems: mutual information and correlations
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Quantum Entanglement in Neural Network States
• Why does deep and cheap learning work so well?
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Inverse statistical problems: from the inverse Ising problem to data science
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Unsupervised Generative Modeling Using Matrix Product States
• Learning Thermodynamics with Boltzmann Machines
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Equivalence of restricted Boltzmann machines and tensor network states
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Mutual Information, Neural Networks and the Renormalization Group
• A Neural Decoder for Topological Codes
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• Entanglement entropy of critical spin liquids
• Multitasking associative networks
• Emergence of Compositional Representations in Restricted Boltzmann Machines
• Chiral Topological Phases from Artificial Neural Networks
• A topological insight into restricted Boltzmann machines
• Efficient Estimation of Mutual Information for Strongly Dependent Variables
• Shannon and Rényi mutual information in quantum critical spin chains
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Neural network representation of tensor network and chiral states
• Universal behavior of the Shannon mutual information of critical quantum chains
• Extensive load in multitasking associative networks
• Detecting Classical Phase Transitions with Renyi Mutual Information
• Mutual information in classical spin models
• From Dyson to Hopfield: Processing on hierarchical networks
• Information theoretic aspects of the two-dimensional Ising model
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Can Boltzmann Machines Discover Cluster Updates ?
• Expressive Power and Approximation Errors of Restricted Boltzmann Machines
• Critical entanglement spectrum of one-dimensional symmetry protected topological phases
• Identifying Product Order with Restricted Boltzmann Machines

Cited by in corpus (53)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Parameterized quantum circuits as machine learning models
• Hybrid quantum-classical algorithms and quantum error mitigation
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Towards Quantum Machine Learning with Tensor Networks
• Differentiable Learning of Quantum Circuit Born Machine
• Is quantum advantage the right goal for quantum machine learning?
• Supervised quantum machine learning models are kernel methods
• Quantum Machine Learning for Chemistry and Physics
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Tree Tensor Networks for Generative Modeling
• Quantum Machine Learning: from physics to software engineering
• Learning and Inference on Generative Adversarial Quantum Circuits
• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Adversarial quantum circuit learning for pure state approximation
• Supervised Learning with Projected Entangled Pair States
• Generative model benchmarks for superconducting qubits
• The learnability scaling of quantum states: restricted Boltzmann machines
• Variational inference with a quantum computer
• Generative Tensor Network Classification Model for Supervised Machine Learning
• Quantum Machine Learning for Finance
• Generative Quantum Learning of Joint Probability Distribution Functions
• Trainability barriers and opportunities in quantum generative modeling
• Tensor networks for unsupervised machine learning
• Compressing deep neural networks by matrix product operators
• A performance characterization of quantum generative models
• Estimating expectation values using approximate quantum states
• An evolving objective function for improved variational quantum optimisation
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Mutual Information Scaling for Tensor Network Machine Learning
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• Tangent-Space Gradient Optimization of Tensor Network for Machine Learning
• Parameterized quantum circuits as universal generative models for continuous multivariate distributions
• A Continuous Variable Born Machine
• F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits
• Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification
• Bayesian Learning of Parameterised Quantum Circuits
• Protocols for Trainable and Differentiable Quantum Generative Modelling
• Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK
• Sampling asymmetric open quantum systems for artificial neural networks
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Generative Invertible Quantum Neural Networks
• Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Tensor networks and efficient descriptions of classical data
• Deep tensor networks with matrix product operators
• Classifying topological neural network quantum states via diffusion maps
• Random access codes via quantum contextual redundancy
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• Quantum Compressive Sensing: Mathematical Machinery, Quantum Algorithms, and Quantum Circuitry
• Efficient bit encoding of neural networks for Fock states
• TabularQGAN: A quantum generative model for tabular data synthesis