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Backpropagation computes the gradient of the loss with respect to neural network weights using an efficient reverse application of the chain rule.
Backpropagation is a gradient-computation method used to train neural networks. Its purpose is to efficiently calculate how the loss (error) changes with respect to each network weight for a given input–output example. It does this by applying the chain rule in an efficient “reverse” way: derivatives are propagated backward from the output layer to the input layer, avoiding redundant calculations. In practice, backpropagation is often used together with an optimization step such as gradient descent. After computing the gradient of the loss with respect to the weights, the learning algorithm updates the parameters in the direction that reduces the loss (e.g., moving weights in the negative gradient direction). Although “backpropagation” strictly refers to the gradient-calculation algorithm, the term is commonly used loosely to include the full training procedure (gradient computation plus parameter updates).
Backpropagation computes the gradient of the loss with respect to neural network weights using an efficient reverse application of the chain rule.
It propagates derivative information backward layer-by-layer (from output to input), caching needed activations/derivatives to avoid redundant work.
The computed gradients are typically used by an optimizer (e.g., stochastic gradient descent or Adam) to update weights to reduce loss.
An algorithm that efficiently computes gradients of a neural network’s loss with respect to its weights by propagating derivatives backward through layers.
A function that measures the discrepancy between the network’s predicted output and the target output, producing a scalar error to differentiate.
A calculus rule for computing derivatives of composed functions, which backpropagation applies in reverse across network layers.
A vector of partial derivatives showing how the loss changes as each weight changes, used to guide parameter updates.
A general differentiation strategy in which backpropagation is a special case, computing gradients efficiently for functions represented as computational graphs.
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