Restricted Boltzmann machine: Recent advances and mean-field theory*

Decelle, Aurélien; Furtlehner, Cyril

doi:10.1088/1674-1056/abd160

Cited by 44 publications

(31 citation statements)

References 84 publications

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“…RBMs are energy-based models, which means that for every possible configuration of v, h they assign a scalar value [39] (named usually as energy), defined as:…”

Section: Dataset Comparisons Based On Rbm Energymentioning

confidence: 99%

Hybrid Restricted Boltzmann Machine– Convolutional Neural Network Model for Image Recognition

Sobczak

Kapela

2022

IEEE Access

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Convolutional Neural Networks (CNNs) have become a standard approach to many image processing dilemmas. Consequently, most of the proposed CNN architectures tend to increase the model deepness or layer complexity. Thus, they are composed of many parameters and need considerable computing resources and training examples. However, some recent works show that either shallow neural networks or architectures without convolutions can achieve similar results with these models often being used in systems with limited resources. Consideration of these aspects led us to a relatively simple preprocessing layer that increases the accuracy of CNN or may reduce its complexity. The layer is composed of two parts: the first is used to transform RGB data to binary representation, the second is a neural network that transforms the binary data into a multi-channel, real-value matrix and is trained in a fully unsupervised manner. Our proposal also includes a metric that may be used for measuring the similarity of training data, with the latter proving useful when performing transfer learning. Our experiments show that the resulting architecture not only helps to improve accuracy but is also more robust to image noise, including adversarial attacks, when compared to state-of-the-art models.

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“…RBMs are energy-based models, which means that for every possible configuration of v, h they assign a scalar value [39] (named usually as energy), defined as:…”

Section: Dataset Comparisons Based On Rbm Energymentioning

confidence: 99%

Hybrid Restricted Boltzmann Machine– Convolutional Neural Network Model for Image Recognition

Sobczak

Kapela

2022

IEEE Access

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“…Some variants of Boltzmann machine, such as restricted Boltzmann machine (RBM) [3,4] and deep Boltzmann machine (DBM) [5], exist. Boltzmann machines and its variants have developed mainly in the machine-learning field; however, recently, they are also actively investigated in physics [6,7,8,9,10]. The evaluation of expectations on the Ising model is quite fundamental in almost all applications of this model.…”

Section: Introductionmentioning

confidence: 99%

Composite Spatial Monte Carlo Integration Based on Generalized Least Squares

Sekimoto¹,

Yasuda²

2022

Preprint

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Although evaluation of the expectations on the Ising model is essential in various applications, this is frequently infeasible because of intractable multiple summations (or integrations). Spaitial Monte Carlo integration (SMCI) is a sampling-based approximation, and can provide high-accuracy estimations for such intractable expectations. To evaluate the expectation of a function of variables in a specific region (called target region), SMCI considers a larger region containing the target region (called sum region). In SMCI, the multiple summation for the variables in the sum region is precisely executed, and that in the outer region is evaluated by the sampling approximation such as the standard Monte Carlo integration. It is guaranteed that the accuracy of the SMCI estimator is monotonically improved as the size of the sum region increases. However, a haphazard expansion of the sum region could cause a combinatorial explosion. Therefore, we hope to improve the accuracy without such region expansion. In this study, based on the theory of generalized least squares, a new effective method is proposed by combining multiple SMCI estimators. The validity of the proposed method is demonstrated theoretically and numerically. The results indicate that the proposed method can be effective in the inverse Ising problem (or Boltzmann machine learning).

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“…Because of the clear correspondence between BMs and statistical mechanics of random systems, there have been analyses of the typical properties of RBMs using methods of the statistical mechanics of random systems [19,20]. In order to evaluate the typical properties, it is necessary to introduce an ensemble into RBMs, and previous studies can be mainly categorized into two types of ensembles.…”

Section: Introductionmentioning

confidence: 99%

Statistical-mechanical study of deep Boltzmann machine given weight parameters after training by singular value decomposition

Ichikawa,

Hukushima

2022

Preprint

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Restricted Boltzmann machine: Recent advances and mean-field theory*

Cited by 44 publications

References 84 publications

Hybrid Restricted Boltzmann Machine– Convolutional Neural Network Model for Image Recognition

Hybrid Restricted Boltzmann Machine– Convolutional Neural Network Model for Image Recognition

Composite Spatial Monte Carlo Integration Based on Generalized Least Squares

Statistical-mechanical study of deep Boltzmann machine given weight parameters after training by singular value decomposition

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