The DOI matches its Crossref record; 29 of the 30 references it cites were found in a registry or an index.
A learning algorithm for Boltzmann machines
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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In the citing paper
“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
In the citing paper
“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
In the citing paper
“For many classes of generative models, there is a much simpler way to reduce diversity: reducing the temperature [1].”
From Diffusion Models Beat GANs on Image Synthesis (2021) · cites this paper as [1]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“This illustrates the power of Born machines 24 to approximate Boltzmann machines 55 when the data require thermal-like features.”
From A generative modeling approach for benchmarking and training shallow quantum circuits (2019) · cites this paper as [55]
In the citing paper
“Originally named Harmonium by Smolensky, RBM is a variant of Boltzmann machines [2] with the restriction that there are no connections within any of the network layers, whether it is visible or hidden.”
From A comprehensive survey on machine learning for networking: Evolution, applications and research opportunities (2018) · cites this paper as [2]
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Metadata
- 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
- OpenAlex
- W2042492924
- Cited by
- 3,402
- References
- 30
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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