Introduction
A network with hundreds of thousands of weights makes a prediction, and it's wrong. Which weights should change, and by how much? Trying each weight one at a time would take forever.
Backpropagation answers this question for all weights at once, efficiently. It's the algorithm that made multilayer networks trainable and remains the engine of all deep learning today.
The idea is like a company investigating a bad result. The final mistake is traced back: how much did the last department contribute? And how much of that came from the department before it? Responsibility flows backwards through the chain, and each person learns how much their own choices contributed — so everyone can adjust a little.