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Cited by 3,402Neural Networks and ApplicationsBayesian Modeling and Causal InferenceMachine Learning and Algorithms

A learning algorithm for Boltzmann machines

Ackley, David H., Hinton, Geoffrey E., Sejnowski, Terrence J.·1985·Cognitive Science
DOI 10.1207/s15516709cog0901_7
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Abstract

The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure.

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29 of 29 references verified0 citation errors · 0 not checkable

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  • It took another 24 years before the connectionist research community invented a learning algorithm for multilayer networks of stochastic binary neurons.

    “It would take another 24 years before the connectionist research community invented a learning algorithm for multilayer networks of stochastic binary neurons (Ackley et al., 1985) and rediscovered the backpropagation algorithm for deterministic, real-valued neurons and applied them to neural networks (Rumelhart et al., 1986).”

    From Large Language Models and the Reverse Turing Test (2023) · cites this paper as Ackley et al., 1985

  • The quantum Boltzmann machine extends the classical Boltzmann machine.

    “The quantum Boltzmann machine (Amin et al. , 2018) (QBM) extends the classical Boltzmann machine (Ackley et al. , 1985), a neural architecture capable of several tasks including generative modeling of data.”

    From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Ackley et al. , 1985

  • Neural networks dating back to the Boltzmann machine take a sampling approach to probabilistic inference.

    “Moreover, neural networks dating back to the Boltzmann machine [87] take a sampling approach to probabilistic inference.”

    From Bayesian Brains without Probabilities (2016) · cites this paper as [87]

  • Spiking network models with standard membrane potential can emulate any Boltzmann machine.

    “As shown below, these spiking network models can emulate any Boltzmann machine (BM) [36].”

    From Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons (2011) · cites this paper as [36]

  • Other classical methods based on machine learning and Markov Chain Monte Carlo, such as the Boltzmann machine, could achieve higher accuracy by requiring more computational resources than the inverse Bethe approximation used here.

    “Other classical methods based on machine learning and Markov Chain Monte Carlo, such as the Boltzmann machine, 55 could achieve higher accuracy by requiring more computational resources than the inverse Bethe approximation used here.”

    From A generative modeling approach for benchmarking and training shallow quantum circuits (2019) · cites this paper as [55]

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Authors
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J.
Affiliations
Carnegie Mellon University (US)
Corresponding author
Ackley, David H.
ORCID
Ackley, David H.
Venue
Cognitive Science
Publisher
Wiley
Published
1985-01
Volume
9
Issue
1
Pages
147-169
ISSN
  • 0364-0213 (ISSN-L)
  • 1551-6709
DOI
10.1207/s15516709cog0901_7
OpenAlex
W2042492924
Cited by
3,402
References
29
Citations by year
2026: 21 · 2025: 72 · 2024: 99 · 2023: 141 · 2022: 158 · 2021: 204 · 2020: 169 · 2019: 178 · 2018: 162 · 2017: 140 · 2016: 118 · 2015: 102 · 2014: 86 · 2013: 102 · 2012: 90
FWCI
122.23
Type
journal article
Language
en
Open access
closed
Licence
onlinelibrary.wiley.com/termsAndConditions#vor (vor, 9172 d)
Locations
Cognitive Science (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
Keywords
Boltzmann machine, learning algorithms, constraint satisfaction, parallel search, statistical mechanics, internal representations, constraint encoding

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