# Learning representations by back-propagating errors

TL;DR: Back-propagation repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector, which helps to represent important features of the task domain.

Abstract: We describe a new learning procedure, back-propagation, for networks of neurone-like units. The procedure repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector. As a result of the weight adjustments, internal ‘hidden’ units which are not part of the input or output come to represent important features of the task domain, and the regularities in the task are captured by the interactions of these units. The ability to create useful new features distinguishes back-propagation from earlier, simpler methods such as the perceptron-convergence procedure1.

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^{1}, Facebook

^{2}, Université de Montréal

^{3}, Google

^{4}, University of Toronto

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### Cites background from "Learning representations by back-pr..."

...~ yi = @ (yi; F (xi)) @F (xi) F (x)=Fm 1(x) = 2yi (1 + exp(2yiFm 1(xi)): (19)...

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...Here the second derivatives at the mth iteration are j~ yij (2 j~ yij) with ~ yi given by (19)....

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...Such expansions (2) are at the heart of many function approximation methods such as neural networks (Rumelhart, Hinton, and Williams 1986), radial basis functions (Powell CSIRO CMIS, Locked Bag 17, North Ryde NSW 1670; jhf@stat.stanford.edu 1987), MARS (Friedman 1991), wavelets (Donoho 1993), and…...

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