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It is closely related to the Gauss–Newton algorithm, and is part of continuing research in neural backpropagation.

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When an input vector is presented to the network, it is propagated forward through the network, layer by layer, until it reaches the output layer.

The output of the network is then compared to the desired output, using a loss function.

The sign of the gradient of a weight indicates whether the error varies directly with, or inversely to, the weight.

Therefore, the weight must be updated in the opposite direction, "descending" the gradient.

The gradient descent method involves calculating the derivative of the squared error function with respect to the weights of the network. Assuming one output neuron, is included to cancel the exponent when differentiating.

Later, the expression will be multiplied with an arbitrary learning rate, so that it doesn't matter if a constant coefficient is introduced now.

This technique is also sometimes called backward propagation of errors, because the error is calculated at the output and distributed back through the network layers.

The backpropagation algorithm has been repeatedly rediscovered and is equivalent to automatic differentiation in reverse accumulation mode.

For each neuron is important, since a high value can cause too strong a change, causing the minimum to be missed, while a too low learning rate slows the training unnecessarily.

Optimizations such as Quickprop are primarily aimed at speeding up error minimization; other improvements mainly try to increase reliability.

Therefore, the error also depends on the incoming weights to the neuron, which is ultimately what needs to be changed in the network to enable learning.

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