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The dropout learning algorithm
Open accessAbstract
Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations.
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“As a result, it is strong in the mid-range of weights, plays a less significant role when weights are small and gradually weakens with saturation.”
From ModDrop: Adaptive Multi-Modal Gesture Recognition (2016) · cites this paper as [52]
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“It has been shown though [52], that in dropout-like [53] systems activation units of complete models produce a weighted normalized geometric mean of per-model outputs.”
From ModDrop: Adaptive Multi-Modal Gesture Recognition (2016) · cites this paper as [52]
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“Finally, as has been shown by [52] for dropout, the multiplier proportional to the derivative of the sigmoid activation makes the regularization effect adaptive to the magnitude of the weights.”
From ModDrop: Adaptive Multi-Modal Gesture Recognition (2016) · cites this paper as [52]
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Baldi, P., Sadowski, P., & Lu, Z. (2017) · Neural Networks · doi:10.1016/j.neunet.2017.08.008 · Cited by 28
Self-citationBellin, N., Calzolari, M., Callegari, E., Bonilauri, P., Grisendi, A., Dottori, M., & Rossi, V. (2021) · Infection Genetics and Evolution · doi:10.1016/j.meegid.2021.105034 · Cited by 29
Metadata
- Authors
- Baldi, P., & Sadowski, P.
- Affiliations
- University of California, Irvine (US)
- Corresponding author
- Baldi, Pierre
- Venue
- Artificial Intelligence
- Publisher
- Elsevier BV
- Published
- 2014-05
- Volume
- 210
- Pages
- 78-122
- ISSN
- 0004-3702 (ISSN-L)
- PMC
- PMC3996711
- OpenAlex
- W2164370980
- Cited by
- 340
- References
- 50
- Citations by year
- 2026: 12 · 2025: 23 · 2024: 39 · 2023: 38 · 2022: 19 · 2021: 40 · 2020: 45 · 2019: 31 · 2018: 26 · 2017: 21 · 2016: 24 · 2015: 10 · 2014: 11
- FWCI
- 21.93
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Artificial Intelligence (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- eScholarship (California Digital Library) (submittedVersion, cc-by-nc-nd)
- Funders
- NSF (IIS-0513376, NSF-IIS-1321053)
- NIH (LM010235)
- NIH NLM (T15 LM07443)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Keywords
- dropout, neural network training, ensemble averaging, logistic function, rectified linear units, stochastic neurons, stochastic gradient descent, regularization, weight decay, sparse representation, variance minimization, co-adaptation
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