Stochastic Networks

  • Ovidiu CalinEmail author
Part of the Springer Series in the Data Sciences book series (SSDS)


This chapter deals with stochastic networks, such as Hopfield networks and Boltzmann machines. A Hopfield network is an ensemble of perceptrons which interact with each other, until a certain cost function which is defined in terms of the interaction between the neurons (called energy function) is minimized. They are useful in solving combinatorial optimization problems. A Boltzmann machine is like a Hopfield network for which the perceptrons have been replaced by binary stochastic neurons. This way, a Boltzmann machine can be seen as the noisy version of a Hopfield network. They are used to avoid Hopfield networks to get stuck in local minima of the energy function. We also present the equilibrium distribution of a Boltzmann machine, its entropy, and its associated Fisher information metric.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsEastern Michigan UniversityYpsilantiUSA

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