What is backpropagation? Sending the error backward through a neural network to work out how to fix each weight

Sending the error backward through a neural network to work out how to fix each weight.

Backpropagation is the core method for training neural networks with many layers. The network gives an answer and you measure the error. Then the error is passed backward, from the last layer toward the first, working out how much each weight contributed to the mistake and adjusting it by that much.

With one layer it's easy to see which numbers to blame; with many layers, the ones in the middle are hard to judge. Backpropagation solves this with the chain rule from calculus. Earlier work described it in the 1970s, and a 1986 paper by Rumelhart, Hinton and Williams made it widely known. Today's large language models are still trained this way.

Think of it like this

When a group project gets a low mark, you trace back from the final presentation through each step to see where things went wrong and by how much. Big contributors to the mistake get fixed a lot; small ones get fixed a little.

For example

If an AI calls a cat photo a "dog", backpropagation nudges millions of numbers that fed into that mistake, all at once.

Common mix-ups

Mix-upBackpropagation means redoing the network's whole calculation from scratch.
ActuallyNudging each number one at a time and recalculating every time would mean billions of fresh runs. Backpropagation finds the direction to fix every number at once in a single backward sweep, cutting the work to just a few times the cost of one forward calculation.
Mix-upBackpropagation was first thought of in 1986.
ActuallyIn 1974 Paul Werbos had already described training multi-layer networks by backpropagating errors in his Harvard PhD thesis. It's the usual reference point when people argue over who came first.

Try it in class

For teachers at the start of a lesson — or for students working on their own.

Question: When the result is off, how do you share out the blame between the steps?
Activity: Run a four-step paper-plane factory (fold → shape the wings → fold the tail → throw). Measure how far short of the target it lands, then work backwards from the thrower and agree as a group how much of the shortfall each step is responsible for. Change the high-blame steps the most, fly again, and record how the distance changes.