The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
An Efficient Learning Procedure for Deep Boltzmann Machines
Open accessAbstract
We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer pretraining phase that initializes the weights sensibly. The pretraining also allows the variational inference to be initialized sensibly with a single bottom-up pass. We present results on the MNIST and NORB data sets showing that deep Boltzmann machines learn very good generative models of handwritten digits and 3D objects. We also show that the features discovered by deep Boltzmann machines are a very effective way to initialize the hidden layers of feedforward neural nets, which are then discriminatively fine-tuned.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A fast learning algorithm for deep belief nets
Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006) · Neural Computation · doi:10.1162/neco.2006.18.7.1527 · Cited by 16,336
Self-citationA Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
Training Products of Experts by Minimizing Contrastive Divergence
Hinton, G. E. (2002) · Neural Computation · doi:10.1162/089976602760128018 · Cited by 4,879 · cited 12×
“Instead of viewing this learning procedure as a gross approximation to maximum likelihood learning, it can be viewed as a much better approximation to minimizing the difference of two divergences (Hinton, 2002), and so it is called contrastive divergence (CD) learning.”
BackgroundMethodInfluentialSelf-citationGreedy layer-wise training of deep networks
Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0024 · Cited by 4,841
An Introduction to Variational Methods for Graphical Models
Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999) · Machine Learning · doi:10.1023/a:1007665907178 · Cited by 3,791
A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants
Neal, R. M., & Hinton, G. E. (1998) · Learning in Graphical Models · doi:10.1007/978-94-011-5014-9_12 · Cited by 2,187
Self-citationRestricted Boltzmann machines for collaborative filtering
Salakhutdinov, R., Mnih, A., & Hinton, G. (2007) · Proceedings of the 24th international conference on Machine learning · doi:10.1145/1273496.1273596 · Cited by 1,885
Self-citationLearning methods for generic object recognition with invariance to pose and lighting
LeCun, Y., Huang, F. J., & Bottou, L. (2004) · Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004. · doi:10.1109/cvpr.2004.1315150 · Cited by 1,324
Cited by
Representation Learning: A Review and New Perspectives
Bengio, Y., Courville, A., & Vincent, P. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.50 · Cited by 13,001
Deep learning for computer vision: A brief review
Voulodimos, A., Doulamis, N., Doulamis, A., & Protopapadakis, E. (2018) · Computational Intelligence and Neuroscience · doi:10.1155/2018/7068349 · Cited by 3,403
Remote Sensing Image Scene Classification: Benchmark and State of the Art
Cheng, G., Han, J., & Lu, X. (2017) · Proceedings of the IEEE · doi:10.1109/jproc.2017.2675998 · Cited by 2,926
Deep learning for visual understanding: A review
Guo, Y., Liu, Y., Oerlemans, A., Lao, S., Wu, S., & Lew, M. S. (2016) · Neurocomputing · doi:10.1016/j.neucom.2015.09.116 · Cited by 2,504
Deep learning for computational biology
Angermueller, C., Pärnamaa, T., Parts, L., & Stegle, O. (2016) · Molecular Systems Biology · doi:10.15252/msb.20156651 · Cited by 1,473
Metadata
- Authors
- Salakhutdinov, R., & Hinton, G.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 2012-08
- Volume
- 24
- Issue
- 8
- Pages
- 1967-2006
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2071709160
- Cited by
- 484
- References
- 8
- FWCI
- 27.86
- Type
- journal article
- Language
- en
- Open access
- green
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 ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: An Efficient Learning Procedure for Deep Boltzmann Machines. https://app.cochat.ai/papers/10.1162/neco_a_00311
- The paper
- Salakhutdinov, R., & Hinton, G. (2012). An Efficient Learning Procedure for Deep Boltzmann Machines. Neural Computation. https://doi.org/10.1162/neco_a_00311
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.