The DOI matches its Crossref record; 27 of the 29 references it cites were found in a registry or an index.
A Connection Between Score Matching and Denoising Autoencoders
Abstract
Denoising autoencoders have been previously shown to be competitive alternatives to restricted Boltzmann machines for unsupervised pretraining of each layer of a deep architecture. We show that a simple denoising autoencoder training criterion is equivalent to matching the score (with respect to the data) of a specific energy-based model to that of a nonparametric Parzen density estimator of the data. This yields several useful insights. It defines a proper probabilistic model for the denoising autoencoder technique, which makes it in principle possible to sample from them or rank examples by their energy. It suggests a different way to apply score matching that is related to learning to denoise and does not require computing second derivatives. It justifies the use of tied weights between the encoder and decoder and suggests ways to extend the success of denoising autoencoders to a larger family of energy-based models.
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“Adaptive Denoising Purification (ADP) [273] demonstrates that an EBM trained with denoising score matching [240] can effectively purify attacked images within just a few steps.”
From Diffusion Models: A Comprehensive Survey of Methods and Applications (2024) · cites this paper as [240]
Citations
Cites
Advances in neural information processing systems 7
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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
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
Self-citationExtracting and composing robust features with denoising autoencoders
Vincent, P., Larochelle, H., Bengio, Y., & Manzagol, P.-A. (2008) · Proceedings of the 25th international conference on Machine learning - ICML '08 · doi:10.1145/1390156.1390294 · Cited by 7,436
Self-citationTraining Products of Experts by Minimizing Contrastive Divergence
Hinton, G. E. (2002) · Neural Computation · doi:10.1162/089976602760128018 · Cited by 4,879 · cited 3×
“1Specifically SM (Hyvärinen, 2005), minimum velocity learning (Movellan, 2008), and certain forms of contrastive divergence (Hinton, 2002; Welling & Hinton, 2002) are all recast as minimizing the Kullback-Leibler divergence between the data distribution and the distribution obtained after running, for infinitesimal ti…”
BackgroundMethodGreedy 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
Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91197-x · Cited by 4,081
(2010) · Journal of Machine Learning Research · doi:10.5555/1756006.1953039 · Cited by 4,051
Self-citationWhy Does Unsupervised Pre-training Help Deep Learning?
Erhan, D., Bengio, Y., Courville, A. C., Manzagol, P.-A., Vincent, P., & Samy Bengio, A. (2010) · Cited by 2,180
Self-citationAdvances in Neural Information Processing Systems 18
Murray, I., Mackay, D., Zoubin Ghahramani, A., & Skilling, J. (2006) · Cited by 1,927
Research works printed but not linked: 4
- Erhan D., 2010, Journal of Machine Learning Research, 11, 625
- Gallinari P., 1987, Proceedings of COGNITIVA 87
- Hyvärinen A., 2005, Journal of Machine Learning Research, 6, 695
- Vincent P., 2010, Journal of Machine Learning Research, 11, 3371
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George, A. J., Veiga, R., & Macris, N. (2026) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ae9379
DCDP: Decoupled Data Consistency via Diffusion Purification for Inverse Problems
Li, X., Kwon, S. M., Liang, S., Alkhouri, I., Ravishankar, S., & Qu, Q. (2026) · IEEE International Conference on Computational Photography (ICCP) · doi:10.1109/iccp69532.2026.11668875
Siren-SPI: zero-shot single-pixel imaging via implicit neural representation and score-based prior
Li, Z., Qin, L., Meng, X., Yin, Y., & Yang, X. (2026) · Chinese Optics Letters · doi:10.3788/col202624.091104
Metadata
- Authors
- Vincent, P.
- Affiliations
- Université de Montréal (CA)
- Corresponding author
- Vincent, Pascal
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 2011-07
- Volume
- 23
- Issue
- 7
- Pages
- 1661-1674
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2013035813
- Cited by
- 1,011
- References
- 29
- Citations by year
- 2026: 131 · 2025: 254 · 2024: 198 · 2023: 126 · 2022: 46 · 2021: 59 · 2020: 52 · 2019: 29 · 2018: 20 · 2017: 22 · 2016: 20 · 2015: 14 · 2014: 9 · 2013: 14 · 2012: 9
- FWCI
- 11.49
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Keywords
- score matching, denoising autoencoder, energy-based models, unsupervised pre-training, restricted Boltzmann machine, probabilistic models, deep learning architectures
- MeSH terms
- Computer Simulation, Models, Statistical
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