Backpropagation or the backward propagation of errors is a common method of training artificial neural networks and used in conjunction with an optimization method such as gradient descent. The algorithm repeats a two-phase cycle, propagation, and weight update. 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, and an error value is calculated for each of the neurons in the output layer. The error values are then propagated backward, starting from the output, until each neuron has an associated error value which roughly represents its contribution to the original output. Backpropagation uses these error values to calculate the gradient of the loss function with respect to the weights in the network. In the second phase, this gradient is fed to the optimization method, which in turn uses it to update the weights, in an attempt to minimize the loss function. The importance of this process is that, as the network is trained, the neurons in the intermediate layers organize themselves in such a way that the different neurons learn to recognize different characteristics of the total input space.

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