text: In a multi-layered network, backpropagation uses the following steps: Propagate training data through the model from input to predicted output by computing the successive hidden layers' outputs and finally the final layer's output (the feedforward step). Adjust the model weights to reduce the error relative to the weights. The error is typically the squared difference between prediction and target. For each weight, the slope or derivative of the error is found, and the weight adjusted by a negative multiple of this derivative, so as to go downslope toward the minimum-error configuration. This derivative is easy to calculate for final layer weights, and possible to calculate for one layer given the next layer's derivatives. Starting at the end, then, the derivatives are calculated layer by layer toward the beginning -- thus "backpropagation". Repeatedly update the weights until they converge or the model has undergone enough iterations.It is an efficient application of the Leibniz chain rule (1673) to such networks. It is also known as the reverse mode of automatic differentiation or reverse accumulation, due to Seppo Linnainmaa (1970). The term "back-propagating error correction" was introduced in 1962 by Frank Rosenblatt, but he did not know how to implement this, even though Henry J. Kelley had a continuous precursor of backpropagation already in 1960 in the context of control theory.Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single input output example, and does so efficiently, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this can be derived through dynamic programming. Gradient descent, or variants such as stochastic gradient descent, are commonly used. Strictly the term backpropagation refers only to the algorithm for computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm including how the gradient is used, such as by stochastic gradient descent. In 1986 David E. Rumelhart et al. published an experimental analysis of the technique. This contributed to the popularization of backpropagation and helped to initiate an active period of research in multilayer perceptrons.