In Depth
Backpropagation (backward propagation of errors) is the fundamental algorithm that makes neural network training possible. It works by passing input data forward through the network to produce a prediction, comparing that prediction to the correct answer to calculate error, and then propagating that error backward through each layer to determine how much each weight contributed to the mistake.
The algorithm uses the chain rule of calculus to efficiently compute gradients (rates of change) for every parameter in the network. These gradients indicate both the direction and magnitude of adjustments needed to reduce errors. When combined with an optimizer like gradient descent, backpropagation enables networks to systematically improve their predictions over millions of training iterations.
Backpropagation was popularized in the 1980s by David Rumelhart, Geoffrey Hinton, and Ronald Williams, though the mathematical foundations existed earlier. It remains the backbone of virtually all deep learning training today, from small classifiers to models with hundreds of billions of parameters. Understanding backpropagation is essential for anyone working in AI development or model optimization.