Dilution and dropout (also called DropConnect) are
regularization
Regularization may refer to:
* Regularization (linguistics)
* Regularization (mathematics)
* Regularization (physics)
* Regularization (solid modeling)
* Regularization Law, an Israeli law intended to retroactively legalize settlements
See also ...
techniques for reducing
overfitting
mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitt ...
in
artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
s by preventing complex co-adaptations on
training data
In machine learning, a common task is the study and construction of algorithms that can learn from and make predictions on data. Such algorithms function by making data-driven predictions or decisions, through building a mathematical model from ...
. They are an efficient way of performing model averaging with neural networks.
''Dilution'' refers to thinning weights,
while ''dropout'' refers to randomly "dropping out", or omitting, units (both hidden and visible) during the training process of a neural network.
Both trigger the same type of regularization.
Types and uses
Dilution is usually split in ''weak dilution'' and ''strong dilution''. Weak dilution describes the process in which the finite fraction of removed connections is small, and strong dilution refers to when this fraction is large. There is no clear distinction on where the limit between strong and weak dilution is, and often the distinction is dependent on the precedent of a specific use-case and has implications for how to solve for exact solutions.
Sometimes dilution is used for adding damping noise to the inputs. In that case, weak dilution refers to adding a small amount of damping noise, while strong dilution refers to adding a greater amount of damping noise. Both can be rewritten as variants of weight dilution.
These techniques are also sometimes referred to as random pruning of weights, but this is usually a non-recurring one-way operation. The network is pruned, and then kept if it is an improvement over the previous model. Dilution and dropout both refer to an iterative process. The pruning of weights typically does not imply that the network continues learning, while in dilution/dropout, the network continues to learn after the technique is applied.
Generalized linear network
Output from a layer of linear nodes, in an artificial neural net can be described as
:*
– output from node
:*
– real weight before dilution, also called the Hebb connection strength
:*
– input from node
This can be written in vector notation as
:*
– output vector
:*
– weight matrix
:*
– input vector
Equations (1) and (2) are used in the subsequent sections.
Weak dilution
During weak dilution, the finite fraction of removed connections (the weights) is small, giving rise to a tiny uncertainty. This edge-case can be solved exactly with
mean field theory
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
. In weak dilution the impact on the weights can be described as
:*
– diluted weight
:*
– real weight before dilution
:*
– the probability of
, the probability of keeping a weight
The interpretation of probability
can also be changed from keeping a weight into pruning a weight.
In vector notation this can be written as
where the function
imposes the previous dilution.
In weak dilution only a small and fixed fraction of the weights are diluted. When the number of terms in the sum goes to infinite (the weights for each node) it is still infinite (the fraction is fixed), thus
mean field theory
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
can be applied. In the notation from Hertz et al.
this would be written as
:*
the mean field temperature
:*
– a scaling factor for the temperature from the probability of keeping the weight
:*
– real weight before dilution, also called the Hebb connection strength
:*
– the mean stable equilibrium states
There are some assumptions for this to hold, which are not listed here.
Strong dilution
When the dilution is strong, the finite fraction of removed connections (the weights) is large, giving rise to a huge uncertainty.
Dropout
Dropout is a special case of the previous weight equation (), where the aforementioned equation is adjusted to remove a whole row in the vector matrix, and not only random weights
:*
– the probability
to keep a row in the weight matrix
:*
– real row in the weight matrix before dropout
:*
– diluted row in the weight matrix
Because dropout removes a whole row from the vector matrix, the previous (unlisted) assumptions for weak dilution and the use of mean field theory are not applicable.
The process by which the node is driven to zero, whether by setting the weights to zero, by “removing the node”, or by some other means, does not impact the end result and does not create a new and unique case. If the neural net is processed by a high-performance digital array-multiplicator, then it is likely more effective to drive the value to zero late in the process graph. If the net is processed by a constrained processor, perhaps even an analog neuromorph processor, then it is likely a more power-efficient solution is to drive the value to zero early in the process graph.
Google's patent
Although there have been examples of randomly removing connections between
neurons
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
in a neural network to improve models,
this technique was first introduced with the name ''dropout'' by
Geoffrey Hinton
Geoffrey Everest Hinton One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 6 December 1947) is a British-Canadian cognitive psychologist and computer scientist, most noted for his work on ar ...
, et al. in 2012.
Google
Google LLC () is an American multinational technology company focusing on search engine technology, online advertising, cloud computing, computer software, quantum computing, e-commerce, artificial intelligence, and consumer electronics. ...
currently holds the patent for the dropout technique.
[The patent is most likely not valid due to previous art. “Dropout” has been described as “dilution” in previous publications. It is described by Hertz, Krogh, and Palmer in ''Introduction to the Theory of Neural Computation'' (1991) , pp. 45, ''Weak Dilution''. The text references Sompolinsky ''The Theory of Neural Networks: The Hebb Rules and Beyond'' in ''Heidelberg Colloquium on Glossy Dynamics'' (1987) and Canning and Gardner ''Partially Connected Models of Neural Networks'' in ''Journal of Physics'' (1988). It goes on to describe strong dilution. This predates Hinton's paper.]
See also
*
AlexNet
AlexNet is the name of a convolutional neural network (CNN) architecture, designed by Alex Krizhevsky in collaboration with Ilya Sutskever and Geoffrey Hinton, who was Krizhevsky's Ph.D. advisor.
AlexNet competed in the ImageNet Large Scale Visu ...
*
Notes
References
{{Reflist
Artificial neural networks
Deep learning