mlsanityData to 7 Oct 2026

Restricted Boltzmann Machine, recent advances and mean-field theory

arXiv 2011.11307 ↗First posted 23 Nov 2020cond-mat.dis-nn cond-mat.stat-mech cs.LGcited by 31

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Abstract (arXiv)

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 it 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 it ensemble dynamics equations or/and from linear stability arguments.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Nov 2020.

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Citing papers per year: 2021: 1; 2022: 6; 2023: 6; 2024: 8; 2025: 8; 2026: 2.

31 papers.

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  1. 2024Cascade of phase transitions in the training of Energy-based modelscited by 12
  2. 2021Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machinescited by 11
  3. 2022Learning a Restricted Boltzmann Machine using biased Monte Carlo samplingcited by 11
  4. 2023Explaining the effects of non-convergent sampling in the training of Energy-Based Modelscited by 11
  5. 2023Inferring effective couplings with Restricted Boltzmann Machinescited by 8
  6. 2024Fast training and sampling of Restricted Boltzmann Machinescited by 8
  7. 2023Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physicscited by 7
  8. 2024Stochastic weight matrix dynamics during learning and Dyson Brownian motioncited by 7
  9. 2022Free Energy Evaluation Using Marginalized Annealed Importance Samplingcited by 5
  10. 2023Unsupervised hierarchical clustering using the learning dynamics of RBMscited by 4
  11. 2023Parallel Learning by Multitasking Neural Networkscited by 3
  12. 2024Fundamental operating regimes, hyper-parameter fine-tuning and glassiness: towards an interpretable replica-theory for trained restricted Boltzmann machinescited by 3
19 more
  1. 2024The effect of priors on Learning with Restricted Boltzmann Machinescited by 3
  2. 2022p-Adic Statistical Field Theory and Deep Belief Networkscited by 2
  3. 2024Modeling Structured Data Learning with Restricted Boltzmann Machines in the Teacher-Student Settingcited by 2
  4. 2025Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplingscited by 2
  5. 2022A simple probabilistic neural network for machine understandingcited by 1
  6. 2023Statistical Mechanics of Learning via Reverberation in Bidirectional Associative Memoriescited by 1
  7. 2025On the role of non-linear latent features in bipartite generative neural networkscited by 1
  8. 2025Saddle Hierarchy in Dense Associative Memorycited by 1
  9. 2025Phase diagram and eigenvalue dynamics of stochastic gradient descent in multilayer neural networkscited by 1
  10. 2022Composite Spatial Monte Carlo Integration Based on Generalized Least Squarescited by 0
  11. 2022Optimizing Connectivity through Network Gradients for Restricted Boltzmann Machinescited by 0
  12. 2024Dataset-Free Weight-Initialization on Restricted Boltzmann Machinecited by 0
  13. 2024Random Matrix Theory for Stochastic Gradient Descentcited by 0
  14. 2025Exploring the Energy Landscape of RBMs: Reciprocal Space Insights into Bosons, Hierarchical Learning and Symmetry Breakingcited by 0
  15. 2025Effective Method for Inverse Ising Problem under Missing Observations in Restricted Boltzmann Machinescited by 0
  16. 2025Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensionscited by 0
  17. 2025Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machinescited by 0
  18. 2026Activation Functions, Statistics and Learning of Higher-Order Interactions in Restricted Boltzmann Machinescited by 0
  19. 2026Equilibrium Training of Energy-Based Models with Parallel Trajectory Temperingcited by 0