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Phase transitions in Restricted Boltzmann Machines with generic priors

arXiv 1612.03132 ↗First posted 9 Dec 2016cond-mat.dis-nn cs.LG physics.data-ancited by 20

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Abstract (arXiv)

We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalisation in a teacher-student scenario of unsupervised learning.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Dec 2016.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 6; 2025: 6; 2026: 1.

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  1. 2024A phase transition between positional and semantic learning in a solvable model of dot-product attentioncited by 30
  2. 2021Quantum field-theoretic machine learningcited by 16
  3. 2022Supervised Hebbian Learningcited by 16
  4. 2021Restricted Boltzmann Machines as Models of Interacting Variablescited by 9
  5. 2023Hopfield model with planted patterns: a teacher-student self-supervised learning modelcited by 7
  6. 2025Unified CNNs and transformers underlying learning mechanism reveals multi-head attention modus vivendicited by 6
  7. 2024Dense Hopfield Networks in the Teacher-Student Settingcited by 4
  8. 2025Low-latency vision transformers via large-scale multi-head attentioncited by 4
  9. 2024Fundamental operating regimes, hyper-parameter fine-tuning and glassiness: towards an interpretable replica-theory for trained restricted Boltzmann machinescited by 3
  10. 2024The effect of priors on Learning with Restricted Boltzmann Machinescited by 3
  11. 2022Recurrent neural networks that generalize from examples and optimize by dreamingcited by 2
  12. 2024Modeling Structured Data Learning with Restricted Boltzmann Machines in the Teacher-Student Settingcited by 2
8 more
  1. 2023Statistical Mechanics of Learning via Reverberation in Bidirectional Associative Memoriescited by 1
  2. 2024Role of Delay in Brain Dynamicscited by 1
  3. 2025On the role of non-linear latent features in bipartite generative neural networkscited by 1
  4. 2025Saddle Hierarchy in Dense Associative Memorycited by 1
  5. 2025Phase diagram and eigenvalue dynamics of stochastic gradient descent in multilayer neural networkscited by 1
  6. 2023Unsupervised and Supervised learning by Dense Associative Memory under replica symmetry breakingcited by 0
  7. 2025Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modelingcited by 0
  8. 2026Activation Functions, Statistics and Learning of Higher-Order Interactions in Restricted Boltzmann Machinescited by 0