This review deals with restricted Boltzmann machine(RBM) under the light of statistical physics.The RBM is a classical family of machine learning(ML) models which played a central role in the development of deep learn...This review deals with restricted Boltzmann machine(RBM) under the light of statistical physics.The RBM is a classical family of machine learning(ML) models which played a central role in the development of deep learning.Viewing it as a spin glass model and exhibiting various links with other models of statistical physics,we gather recent results dealing with mean-field theory in this context.First the functioning of the RBM can be analyzed via the phase diagrams obtained for various statistical ensembles of RBM,leading in particular to identify a compositional phase where a small number of features or modes are combined to form complex patterns.Then we discuss recent works either able to devise mean-field based learning algorithms;either able to reproduce generic aspects of the learning process from some ensemble dynamics equations or/and from linear stability arguments.展开更多
In recent years,a laser-induced breakdown spectrometer(LIBS)combined with machine learning has been widely developed for steel classification.However,the much redundant information of LIBS spectra increases the comput...In recent years,a laser-induced breakdown spectrometer(LIBS)combined with machine learning has been widely developed for steel classification.However,the much redundant information of LIBS spectra increases the computation complexity for classification.In this work,restricted Boltzmann machines(RBM)and principal component analysis(PCA)were used for dimension reduction of datasets,respectively.Then,a support vector machine(SVM)was adopted to process feature information.Two models(RBM-SVM and PCA-SVM)are compared in terms of performance.After optimization,the accuracy of the RBM-SVM model can achieve 100%,and the maximum dimension reduction time is 33.18 s,which is nearly half of that of the PCA model(53.19 s).These results preliminarily indicate that LIBS combined with RBM-SVM has great potential in the real-time classification of steel.展开更多
A biased sampling algorithm for the restricted Boltzmann machine(RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary a...A biased sampling algorithm for the restricted Boltzmann machine(RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte–Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren–Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.展开更多
Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the ...Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.展开更多
基金supported by the Comunidad de Madrid and the Complutense University of Madrid (Spain) through the Atracción de Talento program (Ref. 2019-T1/TIC-13298)
文摘This review deals with restricted Boltzmann machine(RBM) under the light of statistical physics.The RBM is a classical family of machine learning(ML) models which played a central role in the development of deep learning.Viewing it as a spin glass model and exhibiting various links with other models of statistical physics,we gather recent results dealing with mean-field theory in this context.First the functioning of the RBM can be analyzed via the phase diagrams obtained for various statistical ensembles of RBM,leading in particular to identify a compositional phase where a small number of features or modes are combined to form complex patterns.Then we discuss recent works either able to devise mean-field based learning algorithms;either able to reproduce generic aspects of the learning process from some ensemble dynamics equations or/and from linear stability arguments.
基金supported by National Natural Science Foundation of China(No.61705064)the Natural Science Foundation of Hubei Province(No.2021CFB607)+1 种基金the Natural Science Foundation of Xiaogan City(No.XGKJ2021010003)the Project of the Hubei Provincial Department of Education(No.T201617)。
文摘In recent years,a laser-induced breakdown spectrometer(LIBS)combined with machine learning has been widely developed for steel classification.However,the much redundant information of LIBS spectra increases the computation complexity for classification.In this work,restricted Boltzmann machines(RBM)and principal component analysis(PCA)were used for dimension reduction of datasets,respectively.Then,a support vector machine(SVM)was adopted to process feature information.Two models(RBM-SVM and PCA-SVM)are compared in terms of performance.After optimization,the accuracy of the RBM-SVM model can achieve 100%,and the maximum dimension reduction time is 33.18 s,which is nearly half of that of the PCA model(53.19 s).These results preliminarily indicate that LIBS combined with RBM-SVM has great potential in the real-time classification of steel.
基金supported by the financing program AAAA-A16-116021010082-8。
文摘A biased sampling algorithm for the restricted Boltzmann machine(RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte–Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren–Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11934020 and 11874421)the Natural Science Foundation of Beijing(Grant No.Z180013)。
文摘Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.
