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Boltzmann machine

A graphical representation of an example Boltzmann machine.
A graphical representation of an example Boltzmann machine. Each undirected edge represents dependency. In this example there are 3 hidden units and 4 visible units. This is not a restricted Boltzmann machine.

A Boltzmann machine (also called Sherrington–Kirkpatrick model with external field or stochastic Ising model), named after Ludwig Boltzmann is a spin-glass model with an external field, i.e., a Sherrington–Kirkpatrick model,[1] that is a stochastic Ising model. It is a statistical physics technique applied in the context of cognitive science.[2] It is also classified as a Markov random field.[3]

Boltzmann machines are theoretically intriguing because of the locality and Hebbian nature of their training algorithm (being trained by Hebb's rule), and because of their parallelism and the resemblance of their dynamics to simple physical processes. Boltzmann machines with unconstrained connectivity have not been proven useful for practical problems in machine learning or inference, but if the connectivity is properly constrained, the learning can be made efficient enough to be useful for practical problems.[4]

They are named after the Boltzmann distribution in statistical mechanics, which is used in their sampling function. They were heavily popularized and promoted by Geoffrey Hinton, Terry Sejnowski and Yann LeCun in cognitive sciences communities, particularly in machine learning,[2] as part of "energy-based models" (EBM), because Hamiltonians of spin glasses as energy are used as a starting point to define the learning task.[5]

  1. ^ Sherrington, David; Kirkpatrick, Scott (1975), "Solvable Model of a Spin-Glass", Physical Review Letters, 35 (35): 1792–1796, Bibcode:1975PhRvL..35.1792S, doi:10.1103/PhysRevLett.35.1792
  2. ^ a b Ackley, David H.; Hinton, Geoffrey E.; Sejnowski, Terrence J. (1985). "A Learning Algorithm for Boltzmann Machines" (PDF). Cognitive Science. 9 (1): 147–169. doi:10.1207/s15516709cog0901_7. Archived from the original (PDF) on 18 July 2011.
  3. ^ Hinton, Geoffrey E. (2007-05-24). "Boltzmann machine". Scholarpedia. 2 (5): 1668. Bibcode:2007SchpJ...2.1668H. doi:10.4249/scholarpedia.1668. ISSN 1941-6016.
  4. ^ Osborn, Thomas R. (1 January 1990). "Fast Teaching of Boltzmann Machines with Local Inhibition". International Neural Network Conference. Springer Netherlands. pp. 785. doi:10.1007/978-94-009-0643-3_76. ISBN 978-0-7923-0831-7.
  5. ^ Nijkamp, E.; Hill, M. E; Han, T. (2020), "On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models", Proceedings of the AAAI Conference on Artificial Intelligence, 4 (34): 5272–5280, arXiv:1903.12370, doi:10.1609/aaai.v34i04.5973
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