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This chapter explores the foundations, evolution, and significance of Boltzmann MachinesBoltzmannBoltzmann machine (BMs) and their variants within the context of neural networksNeural network and deepLearningdeep learning learningDeepdeep learning. Rooted in the Boltzmann distributionBoltzmannBoltzmann distribution from statisticalStatistical physics, these energy-based models draw inspiration from the Ising modelIsing model and the Hopfield networkHopfield network, offering a probabilistic framework for learning data representationsRepresentation. The chapter tracesTrace the development of BMs andRestricted Boltzmann machine Restricted Boltzmann MachinesBoltzmannrestricted Boltzmann machine (RBMs), emphasizing their architecturesArchitecture, learning algorithms, and their role in unsupervisedUnsupervised feature learning through maximum likelihoodLikelihood estimation andSamplingGibbs sampling Gibbs samplingGibbsGibbs sampling. The chapter also introducesBeliefbelief network Deep Belief NetworksDeepdeep belief network (DBNs), which are formed by stacking multiple RBMs into deep generative modelsGenerativegenerative model. This greedyLayer layer-wise training approach addressed the vanishing gradient problem and marked a significant milestone in the resurgence of deepLearningdeep learning learningDeepdeep learning. However, the emergence of Rectified Linear Units (ReLU)ReLU and dropoutDropout regularizationRegularization subsequently enhanced the effectiveness of backpropagation, reducing the need for unsupervisedUnsupervised pretraining. The chapter begins with essential background concepts, including graphical modelsSamplingGibbs sampling, Gibbs samplingGibbsGibbs sampling, and the Ising and Hopfield models. It then presents the RBM, its conditional variant, and concludes with the structure and training of DBNs. Collectively, these models represent a pivotal historical phase in the evolution of deep Learningdeep learning learningDeepdeep learning. Today, their main importance is historical and conceptual, as modern neural networksNeural network typically rely on backpropagation-based training without RBM pretraining.

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Boltzmann Machines A chemical structure showing a molecule with a central six-membered ring containing one nitrogen atom and five carbon atoms. Attached to the ring are various groups: a hydroxyl group (OH) connected to a carbon, a methyl group (CH3), and a side chain with a nitrogen atom bonded to two methyl groups. The structure highlights the arrangement of atoms and bonds important for understanding the molecule’s chemical properties and potential biological activity.

  • 章节

  • 发表日期：

    2026年

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  • Benyamin Ghojogh,
  • Ali Ghodsi

摘要

This chapter explores the foundations, evolution, and significance of Boltzmann MachinesBoltzmannBoltzmann machine (BMs) and their variants within the context of neural networksNeural network and deepLearningdeep learning learningDeepdeep learning. Rooted in the Boltzmann distributionBoltzmannBoltzmann distribution from statisticalStatistical physics, these energy-based models draw inspiration from the Ising modelIsing model and the Hopfield networkHopfield network, offering a probabilistic framework for learning data representationsRepresentation. The chapter tracesTrace the development of BMs andRestricted Boltzmann machine Restricted Boltzmann MachinesBoltzmannrestricted Boltzmann machine (RBMs), emphasizing their architecturesArchitecture, learning algorithms, and their role in unsupervisedUnsupervised feature learning through maximum likelihoodLikelihood estimation andSamplingGibbs sampling Gibbs samplingGibbsGibbs sampling. The chapter also introducesBeliefbelief network Deep Belief NetworksDeepdeep belief network (DBNs), which are formed by stacking multiple RBMs into deep generative modelsGenerativegenerative model. This greedyLayer layer-wise training approach addressed the vanishing gradient problem and marked a significant milestone in the resurgence of deepLearningdeep learning learningDeepdeep learning. However, the emergence of Rectified Linear Units (ReLU)ReLU and dropoutDropout regularizationRegularization subsequently enhanced the effectiveness of backpropagation, reducing the need for unsupervisedUnsupervised pretraining. The chapter begins with essential background concepts, including graphical modelsSamplingGibbs sampling, Gibbs samplingGibbsGibbs sampling, and the Ising and Hopfield models. It then presents the RBM, its conditional variant, and concludes with the structure and training of DBNs. Collectively, these models represent a pivotal historical phase in the evolution of deep Learningdeep learning learningDeepdeep learning. Today, their main importance is historical and conceptual, as modern neural networksNeural network typically rely on backpropagation-based training without RBM pretraining.