Restricted Boltzmann Machines

Also known as RBM

Restricted Boltzmann Machines study how a simple network of visible and hidden units can represent and learn probability distributions. Researchers train them with sampling-based methods such as Gibbs updates and deep tempering, while theoretical work examines mixing times, model capacity, and how choices like activation functions affect learning. Applications include generating data, rejecting out-of-distribution inputs, modeling audio, and representing quantum states or molecular configurations. A central challenge is that sampling can be slow or unstable, and proposed alternatives—including quantum samplers—must be compared fairly with well-tuned classical methods.

Latest papers

18 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Going deep, reaching further: What can Boltzmann machines efficiently represent?
Oct 29, 2026Tobias Reinhart, Gemma De les CovesRestricted Boltzmann Machines
Institute for Theoretical Physics, University of Innsbruck,, Technikerstr. 21a, A-6020 Innsbruck, Austria · ICREA, Institució Catalana d’Estudis i Recerca Avançats, Passeig Lluís Companys 23, 08010 Barcelona · Departament d’Enginyeria, Universitat Pompeu Fabra, Carrer Tànger 122, 08018 Barcelona
Recurrent Temporal Restricted Boltzmann Machines as Unsupervised Encoders for Biomechanical Movement Sequences
Oct 17, 2026Wafi Sharif, Nicholas LaHayeMotion Representation Learning Time Series Representation Learning
Queens High School for the Sciences · Jet Propulsion Laboratory, California Institute of Technology
Feature-Context Consistency: Unsupervised Adversarial Detection with Drift Stability on Attributed Graphs
Oct 12, 2026Firas Bayram, Maxime CordyGraph-Based Anomaly Detection Anomaly Detection
SnT, University of Luxembourg Luxembourg
Hyperbolic Restricted Boltzmann Machine Neural Quantum State
Sep 22, 2026H. L. DaoNeural Quantum States Quantum Many-Body Physics
Nonlocal Transition Kernel for Efficient Learning of Restricted Boltzmann Machines
Aug 18, 2026Kaiji Sekimoto, Muneki YasudaRestricted Boltzmann Machines Markov Chain Monte Carlo
Graduate School of Science and Engineering, Yamagata University, Japan
Variational Quantum Conditional Boltzmann Machines for Time-Series Forecasting: Architectures, Symmetric Hyperparameter Evaluation, and a Nonlinear Benchmark
Jul 27, 2026Gerhard Hellstern, Danyal Maheshwari, Martin Zaefferer +2Time Series Forecasting Forecasting Benchmarks
Centre of Finance DHBW Stuttgart Stuttgart, Germany · Zentrum für Digitale Innovationen DHBW Ravensburg Ravensburg, Germany · DATEV eG Nürnberg, Germany
Exploration of the generative capabilities of Boltzmann machines applied to social systems under the majority rule
Jul 25, 2026Mauricio A. Valle, Gonzalo A. RuzGenerative Modeling Restricted Boltzmann Machines
Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Millennium Nucleus for Social Data Science (SODAS) Santiago, Chile · Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Millennium Nucleus for Social Data Science (SODAS) Millennium Nucleus in Data Science for Plant Resilience (PhytoLearning) Santiago, Chile
Machine-Learned Compact Subspace Generation for Quantum Selected Configuration Interaction within Density Matrix Embedding Framework
Jul 22, 2026Ashish Kumar Patra, Anurag K. S. V., Ruchika Bhat +3Quantum Chemistry Restricted Boltzmann Machines
1Qclairvoyance Quantum Labs, Secunderabad, TG 500094, India. · 2The University of Arizona, Tucson, AZ 85721, USA. · 3Indian Institute of Technology Bombay, Mumbai, MH 400076, India.
PolarBM: Complex-valued Boltzmann Machine for Modeling Audio Signals in Polar and Log-polar Coordinates
Jul 14, 2026Toru Nakashika, Kohei YatabeUnsupervised Representation Learning Complex-Valued Neural Networks
Graduate School of Informatics and Engineering, the University of Electro-Communications, Tokyo 182-8585, Japan · Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan
Learning from Noise: Effective-Rank Collapse and Out-of-Distribution Rejection in Restricted Boltzmann Machines
Jul 11, 2026Oshada Rathnayake, Nikhil ShuklaEnergy-Based Models Classification
University of Virginia, Charlottesville, VA, 22903, USA
Explaining Machine Learning and Memorization with Statistical Mechanics
Jun 30, 2026Robin TheriaultStatistical Physics of Learning Neural Network Memorization
Faculty of Science
Bridging the NISQ and Fault-Tolerant Regimes: Generative-ML-Assisted Quantum Selected CI for Molecular Simulations
Jun 29, 2026Anurag K. S. V., Ashish Kumar Patra, Manas Mukherjee +4Quantum Chemistry Restricted Boltzmann Machines
Qclairvoyance Quantum Labs, Secunderabad, TG 500094, India · Centre for Quantum Technologies, National University of Singapore, SG 117543, Singapore · The University of Arizona, Tucson, AZ 85721, USA +1
Activation Functions, Statistics and Learning of Higher-Order Interactions in Restricted Boltzmann Machines
May 18, 2026Giovanni di Sarra, Yasser RoudiUnsupervised Representation Learning Neural Network Activation Functions
Kavli Institute for Systems Neuroscience, Norwegian University of Science and Technology, 7491 Trondheim, Norway · Department of Mathematics, King’s College London, London, Strand, WC2R 2LS, UK
Three-in-One World Model: Energy-Based Consistency, Prediction, and Counterfactual Inference for Marketing Intervention
May 8, 2026Junichiro NiimiCausal Effect Estimation World Model Learning
1Meijo University
Lecture Notes on Statistical Physics and Neural Networks
May 7, 2026Olaf HohmPhase Transitions Restricted Boltzmann Machines
Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 2, D-12489 Berlin, Germany
Rapid mixing in positively weighted restricted Boltzmann machines
Apr 1, 2026Weiming Feng, Heng Guo, Minji YangRestricted Boltzmann Machines Markov Chain Monte Carlo
School of Computing and Data Science, The University of Hong Kong, HK · School of Informatics, University of Edinburgh, Informatics Forum, UK
Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study
Mar 3, 2026Görkem Can SüleymanoğluRestricted Boltzmann Machines Energy-Based Models
Owner and Software Developer, Kuanka Publishing LLC, Turkey. · Ph.D. Student in Economics, Selçuk University, Institute of Social Sciences, Turkey.
Comparison of D-Wave Quantum Annealing and Gibbs Monte Carlo for Sampling from a Probability Distribution of a Restricted Boltzmann Machine
Aug 13, 2025Abdelmoula El-Yazizi, Yaroslav KoshkaMarkov Chain Monte Carlo Quantum Annealing
Department of Electrical and Computer Engineering, Mississippi State University, Starkville, MS 39762, USA

Oct 29, 2026J/K move · Enter open · S save

Going deep, reaching further: What can Boltzmann machines efficiently represent?

Tobias Reinhart, Gemma De les Coves

Institute for Theoretical Physics, University of Innsbruck,, Technikerstr. 21a, A-6020 Innsbruck, Austria · ICREA, Institució Catalana d’Estudis i Recerca Avançats, Passeig Lluís Companys 23, 08010 Barcelona · Departament d’Enginyeria, Universitat Pompeu Fabra, Carrer Tànger 122, 08018 Barcelona

Restricted Boltzmann Machines

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While universal approximation theorems theoretically underpin the representation capabilities of machine learning models, they have two shortcomings: They do not focus on efficient representations and they tend to be insensitive to depth and other heuristically important properties. In this work we show that these two shortcomings are intertwined. We prove that machine learning models which are deeper or have higher-order interactions can efficiently represent a larger set of functions, i.e. have larger efficient reach. It follows that deep Boltzmann machines (DBMs) have maximal efficient reach, restricted Boltzmann machines (RBMs) sub-maximal, and k-body generalizations of RBMs form a hierarchy between the two, even though all are universal. More generally, (i) we provide a full characterization of machine learning models with maximal efficient reach; (ii) we derive separations between deep and shallow models for three representation tasks; and (iii) we prove that the efficient reach of shallow models constitutes an infinite hierarchy indexed by the interaction order. The proofs draw on different methodologies, namely on (i) a recent characterization of universal spin models; (ii) computational complexity bounds for spin models; and (iii) communication complexity bounds applied to shallow models. This work shows that universal machine learning models can strongly differ in their efficient representation capabilities, and provides a theoretical foundation for heuristic observations.