# Quickprop

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{{short description|Algorithm}}
'''Quickprop''' is an iterative method for determining the minimum of the [loss function](/source/loss_function) of an [artificial neural network](/source/artificial_neural_network),<ref>{{cite web|url=https://www.researchgate.net/publication/303969910 |title=Evaluation of QuickProp for Learning Deep Neural Networks -- A Critical Review}}</ref> following an algorithm inspired by the [Newton's method](/source/Newton's_method). Sometimes, the algorithm is classified to the group  of the second order learning methods. It follows a quadratic approximation of the previous [gradient](/source/gradient) step and the current gradient, which is expected to be close to the minimum of the loss function, under the assumption that the loss function is locally approximately square, trying to describe it by means of an upwardly open [parabola](/source/parabola). The minimum is sought in the vertex of the parabola. The procedure requires only local information of the [artificial neuron](/source/artificial_neuron) to which it is applied.
The <math> k </math>-th approximation step is given by:

<math> \Delta^{(k)} \, w_{ij} = \Delta^{(k-1)} \, w_{ij} \left ( \frac{\nabla_{ij} \, E^{(k)}}{\nabla_{ij} \, E^{(k-1)} - \nabla_{ij} \, E^{(k)}} \right) </math>

Where <math> w_{ij} </math> is the weight of input <math>i</math> of neuron <math> j </math>, and <math> E </math> is the loss function.

The Quickprop algorithm is an implementation of the error [backpropagation](/source/backpropagation) algorithm, but the network  can behave chaotically during the learning phase due to large step sizes.

==References==
{{Reflist}}

== Bibliography ==

*Scott E. Fahlman: ''[https://www.cs.cmu.edu/afs/cs.cmu.edu/user/sef/www/publications/qp-tr.ps An Empirical Study of Learning Speed in Back-Propagation Networks]'', September 1988

Category:Machine learning algorithms
Category:Artificial neural networks
Category:Computational neuroscience

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