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Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…

Quantum Physics · Physics 2022-08-25 Liming Zhao , Lin-chun Wan , Ming-Xing Luo

Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…

Computer Vision and Pattern Recognition · Computer Science 2016-01-06 Guanglei Qi , Yanfeng Sun , Junbin Gao , Yongli Hu , Jinghua Li

The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well…

Machine Learning · Computer Science 2025-11-13 Yizhou Xu , Florent Krzakala , Lenka Zdeborová

Restricted Boltzmann Machine (RBM) is a generative stochastic energy-based model of artificial neural network for unsupervised learning. Recently, RBM is well known to be a pre-training method of Deep Learning. In addition to visible and…

Neural and Evolutionary Computing · Computer Science 2018-07-12 Shin Kamada , Takumi Ichimura

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

Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive…

Machine Learning · Statistics 2014-10-27 Vincent Dumoulin , Ian J. Goodfellow , Aaron Courville , Yoshua Bengio

Restricted Boltzmann Machines are generative models that consist of a layer of hidden variables connected to another layer of visible units, and they are used to model the distribution over visible variables. In order to gain a higher…

Computer Vision and Pattern Recognition · Computer Science 2023-06-20 Arkaitz Bidaurrazaga , Aritz Pérez , Roberto Santana

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to…

Machine Learning · Computer Science 2020-11-03 Haik Manukian , Yan Ru Pei , Sean R. B. Bearden , Massimiliano Di Ventra

Many computer vision applications involve modeling complex spatio-temporal patterns in high-dimensional motion data. Recently, restricted Boltzmann machines (RBMs) have been widely used to capture and represent spatial patterns in a single…

Computer Vision and Pattern Recognition · Computer Science 2017-10-24 Siqi Nie , Ziheng Wang , Qiang Ji

Restricted Boltzmann machines (RBM) are generative models capable to learn data with a rich underlying structure. We study the teacher-student setting where a student RBM learns structured data generated by a teacher RBM. The amount of…

Machine Learning · Computer Science 2025-05-21 Robin Thériault , Francesco Tosello , Daniele Tantari

Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic models that have recently been applied to a wide range of problems, including collaborative filtering, classification, and modeling motion capture data. While much…

Machine Learning · Computer Science 2012-02-20 Volodymyr Mnih , Hugo Larochelle , Geoffrey E. Hinton

Restricted Boltzmann machines (RBM) and its variants have become hot research topics recently, and widely applied to many classification problems, such as character recognition and document categorization. Often, classification RBM ignores…

Machine Learning · Computer Science 2015-04-21 Gang Chen , Sargur H. Srihari

Understanding the results of deep neural networks is an essential step towards wider acceptance of deep learning algorithms. Many approaches address the issue of interpreting artificial neural networks, but often provide divergent…

Machine Learning · Computer Science 2021-11-16 Vadim Borisov , Johannes Meier , Johan van den Heuvel , Hamed Jalali , Gjergji Kasneci

Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn…

Quantum Physics · Physics 2021-09-07 Liming Zhao , Siyi Yang , Patrick Rebentrost

We propose a novel quantum model for the restricted Boltzmann machine (RBM), in which the visible units remain classical whereas the hidden units are quantized as noninteracting fermions. The free motion of the fermions is parametrically…

Disordered Systems and Neural Networks · Physics 2021-02-15 Ya. S. Lyakhova , E. A. Polyakov , A. N. Rubtsov

The infinite restricted Boltzmann machine (iRBM) is an extension of the classic RBM. It enjoys a good property of automatically deciding the size of the hidden layer according to specific training data. With sufficient training, the iRBM…

Machine Learning · Computer Science 2018-07-30 Xuan Peng , Xunzhang Gao , Xiang Li

Large-scale electrophysiological recordings now allow simultaneous monitoring of thousands of neurons across multiple brain regions, revealing structured variability in neural population activity. Understanding how these collective patterns…

Neurons and Cognition · Quantitative Biology 2026-03-12 Nicolas Béreux , Giovanni Catania , Aurélien Decelle , Francesca Mignacco , Alfonso de Jesús Navas Gómez , Beatriz Seoane

Statistical analysis of evolutionary-related protein sequences provides insights about their structure, function, and history. We show that Restricted Boltzmann Machines (RBM), designed to learn complex high-dimensional data and their…

Quantitative Methods · Quantitative Biology 2019-02-28 Jérôme Tubiana , Simona Cocco , Rémi Monasson

Boltzmann Machines constitute a class of neural networks with applications to image reconstruction, pattern classification and unsupervised learning in general. Their most common variants, called Restricted Boltzmann Machines (RBMs) exhibit…

Quantum Physics · Physics 2020-03-30 Lorenzo Rocutto , Claudio Destri , Enrico Prati

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…

Quantum Physics · Physics 2022-10-06 Xiao-Qi Sun , Tamra Nebabu , Xizhi Han , Michael O. Flynn , Xiao-Liang Qi