Scale-invariant feature extraction of neural network and renormalization group flow

Iso, Satoshi; Shiba, Shotaro; Yokoo, Sumito

doi:10.1103/physreve.97.053304

Cited by 73 publications

(109 citation statements)

References 41 publications

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“…When a probability distribution p is given, we can obtain a concrete example of the spin configurations by replacing the expectation value v i p at each site with ±1 with the probability (1 ± v i p )/2. Then the flow of probability distribution can be regarded as the flow of the spin configurations and it can be thought as an "RBM flow" of spin configurations as in [34]. The RBM learning and the process of reconstruction under the learned distributions to produce the RBM flow are schematically presented in Fig.…”

Section: B Rbm Flow Of Configurationsmentioning

confidence: 99%

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Thermodynamics and feature extraction by machine learning

Funai

Giataganas

2020

Phys. Rev. Research

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Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a restricted Boltzmann machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near-criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the renormalization group (RG) flow of the lattice model. Our results suggest an explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated with the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.

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Section: B Rbm Flow Of Configurationsmentioning

confidence: 99%

“…Furthermore, in [34] it has been shown that the critical fixed point of the RG flow and the fixed point of data reconstruction by the ML techniques are coincident. The restricted Boltzmann machine (RBM) [35] plays a fundamental role in this task.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and feature extraction by machine learning

Funai

Giataganas

2020

Phys. Rev. Research

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“…The RBM is trained for the 1-and 2-dimensional Ising models with volumes L = 6, L 2 = 8 × 8 and L 2 = 16 × 16, at various values of temperature. The Ising model and its properties are a paradigm in statistical physics literature, making it a suitable system on which to examine the training procedure and limitations of the RBMs [9,14,16,20]. Moreover, it is possible to generate a large number of Ising configurations using simple Monte Carlo simulations, avoiding the problem of small training sets.…”

Section: Introductionmentioning

confidence: 99%

Machine learning determination of dynamical parameters: The Ising model case

et al. 2019

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We train a set of Restricted Boltzmann Machines (RBMs) on one-and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements of the log-likelihood, with the corresponding partition functions estimated using annealed importance sampling. The effects of various choices of hyper-parameters on training the RBM are discussed in detail, with a generic prescription provided. Finally, we present a closed form expression for extracting the values of couplings, for every n-point interaction between the visible nodes of an RBM, in a binary system such as the Ising model. We aim at using this study as the foundation for further investigations of less well-known systems.

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“…(variational, exact and tractable likelihood, principled structure design via information theory) and high computational efficiency. The NeuralRG approach is closer in spirit to the original proposal based on Bayesian net [20] than more recent discussions on Boltzmann Machines [21,23] and Principal Component Analysis [22]. Figure 1(a) shows the proposed architecture.…”

mentioning

confidence: 97%

Neural Network Renormalization Group

2018

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We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural network directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.

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Scale-invariant feature extraction of neural network and renormalization group flow

Cited by 73 publications

References 41 publications

Thermodynamics and feature extraction by machine learning

Thermodynamics and feature extraction by machine learning

Machine learning determination of dynamical parameters: The Ising model case

Neural Network Renormalization Group

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