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Boltzmann Machines
Boltzmann Machines Geoffrey E. Hinton March 25, 2007. A Boltzmann Machine is a network of symmetrically connected, neuron- like units that make stochastic decisions about whether to be on or off. Boltz- mann Machines have a simple learning algorithm that allows them to discover interesting features in datasets composed of binary vectors. The learning al- gorithm is very slow in networks with many layers of feature detectors, but it can be made much faster by learning one layer of feature detectors at a time. Boltzmann Machines are used to solve two quite different computational problems. For a search problem, the weights on the connections are fixed and are used to represent the cost function of an optimization problem. The stochastic dynamics of a Boltzmann machine then allow it to sample binary state vectors that represent good solutions to the optimization problem.
More speci cally, the aim is to nd weights and biases that de ne a Boltz-mann distribution in which the training vectors have high probability. By di erentiating Eq. 3 and using the fact that @E(v)=@wij = sv i s v j it can be shown that X v2data @logP(v) @wij = hsisjidata hsisjimodel (5) where hsisjidata is the expected value of sisj in the ...
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