Restricted Boltzmann machine:Recent advances and mean-field theory

• 作者: Aurelien Decelle Cyril Furtlehner
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: TOPICAL REVIEW—Machine learning in statistical physics
• 页码范围: 1-25
• 页数: 25页
• 语种: 英文
• DOI: 10.1088/1674-1056/abd160

摘要

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.