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Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training,…

Machine Learning · Computer Science 2018-10-17 Eric W. Tramel , Marylou Gabrié , Andre Manoel , Francesco Caltagirone , Florent Krzakala

Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…

Machine Learning · Computer Science 2018-03-12 Son N. Tran , Srikanth Cherla , Artur Garcez , Tillman Weyde

In this paper, we investigate the feature encoding process in a prototypical energy-based generative model, the Restricted Boltzmann Machine (RBM). We start with an analytical investigation using simplified architectures and data…

Machine Learning · Computer Science 2025-02-11 Dimitrios Bachtis , Giulio Biroli , Aurélien Decelle , Beatriz Seoane

Restricted Boltzmann machines (RBMs) constitute one of the main models for machine statistical inference and they are widely employed in Artificial Intelligence as powerful tools for (deep) learning. However, in contrast with countless…

Disordered Systems and Neural Networks · Physics 2019-03-12 Elena Agliari , Adriano Barra , Brunello Tirozzi

Restricted Boltzmann machine (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function.…

Computational Physics · Physics 2020-04-28 David Yevick , Roger Melko

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

Machine Learning · Computer Science 2022-09-27 Lennart Dabelow , Masahito Ueda

We introduce a regularized fluctuating lattice Boltzmann model (Reg-FLBM) for the D3Q27 lattice, which incorporates thermal fluctuations through Hermite-based projections to ensure compliance with the fluctuation-dissipation theorem. By…

Computational Physics · Physics 2025-11-14 Marco Lauricella , Andrea Montessori , Adriano Tiribocchi , Sauro Succi

A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently…

Machine Learning · Computer Science 2019-02-19 Jérôme Tubiana , Simona Cocco , Rémi Monasson

The restricted Boltzmann machine (RBM) is a two-layer energy-based model that uses its hidden-visible connections to learn the underlying distribution of visible units, whose interactions are often complicated by high-order correlations.…

Statistical Mechanics · Physics 2022-12-07 Jing Gu , Kai Zhang

Restricted Boltzmann machines (RBMs) are endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties (compared with more…

Machine Learning · Computer Science 2015-10-22 Sai Zhang

Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating…

Disordered Systems and Neural Networks · Physics 2021-10-27 Clément Roussel , Simona Cocco , Rémi Monasson

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…

Computational Physics · Physics 2019-08-14 Guido Cossu , Luigi Del Debbio , Tommaso Giani , Ava Khamseh , Michael Wilson

We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($\xi=k_B T/U_0 \ll 1$), there exists a range of…

Statistical Mechanics · Physics 2020-10-21 Lucianno Defaveri , Celia Anteneodo , David A. Kessler , Eli Barkai

We show that Restricted Boltzmann Machines (RBMs) provide a flexible generative framework for modeling spin configurations in disordered yet strongly correlated phases of frustrated magnets. As a benchmark, we first demonstrate that an RBM…

Strongly Correlated Electrons · Physics 2026-02-19 Ho Jang , Jackson C. Glass , Gia-Wei Chern

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of…

Neural and Evolutionary Computing · Computer Science 2017-02-06 Nan Wang , Jan Melchior , Laurenz Wiskott

We study the features extracted by the Restricted Boltzmann Machine (RBM) when it is trained with spin configurations of Ising model at various temperatures. Using the trained RBM, we obtain the flow of iterative reconstructions (RBM flow)…

Machine Learning · Computer Science 2021-11-23 Shotaro Shiba Funai

In this paper, we present a new idea for Transfer Learning (TL) based on Gibbs Sampling. Gibbs sampling is an algorithm in which instances are likely to transfer to a new state with a higher possibility with respect to a probability…

Machine Learning · Computer Science 2020-06-26 Hossein Shahabadi Farahani , Alireza Fatehi , Mahdi Aliyari Shoorehdeli

Restricted Boltzmann Machines (RBMs) are powerful tools for modeling complex systems and extracting insights from data, but their training is hindered by the slow mixing of Markov Chain Monte Carlo (MCMC) processes, especially with highly…

Machine Learning · Computer Science 2025-12-09 Nicolas Béreux , Aurélien Decelle , Cyril Furtlehner , Lorenzo Rosset , Beatriz Seoane

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…

Disordered Systems and Neural Networks · Physics 2023-07-17 Aurélien Decelle , Cyril Furtlehner

Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally…

Machine Learning · Computer Science 2014-10-02 Guillaume Desjardins , Heng Luo , Aaron Courville , Yoshua Bengio