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 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 ensemble dynamics equations or/and from linear stability arguments.
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Ural Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, RussiaUral Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Medvedeva, Darya
Iskakov, Sergei
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Ural Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USAUral Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Iskakov, Sergei
Krien, Friedrich
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Univ Hamburg, Inst Theoret Phys, Jungiusstr 9, D-20355 Hamburg, GermanyUral Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Krien, Friedrich
Mazurenko, Vladimir V.
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Ural Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, RussiaUral Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Mazurenko, Vladimir V.
Lichtenstein, Alexander I.
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Ural Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia
Univ Hamburg, Inst Theoret Phys, Jungiusstr 9, D-20355 Hamburg, GermanyUral Fed Univ, Theoret Phys & Appl Math Dept, Mira Str 19, Ekaterinburg 620002, Russia