Backpropagation
Backpropagation is the computational procedure by which learning computer programs figure out which of their internal adjustment knobs are responsible for an error. It works backwards from the result through the program and forms the basis of virtually all modern AI training.
Modern AI programs consist of millions or billions of numbers that can be called adjustment knobs. These numbers determine which answer the program gives to an input. At the start they are chosen randomly, and the answers are correspondingly wrong. Backpropagation is the procedure that calculates, for each individual one of these numbers, how much it is to blame for the error. Afterwards, all the numbers can be shifted a tiny bit in the right direction. Repeating this millions of times turns random numbers into a program that writes texts or recognizes images.
Why deep learning could not exist without error backpropagation
The fundamental problem with learning is: you only see that the result was wrong. You do not see which of the billions of numbers is to blame for it. Without a procedure for assigning blame, you would have to test each number individually. For a large language model, that would mean billions of test runs for a single learning step. Even on the fastest computers, that would take longer than the universe has existed.
Backpropagation solves this in a single backward pass. Regardless of whether a model has a thousand or a trillion adjustment knobs, one backward pass costs roughly as much computing time as one forward pass. This efficiency is the actual breakthrough. It is the reason deep neural networks became trainable at all.
The idea has been known since the 1970s and was popularized in a famous 1986 paper. However, it only became practically usable around 2012, when graphics cards became cheap and fast enough. Almost everything that today falls under the buzzword AI is based on this one algorithm. A Nobel Prize in Physics went in 2024, among others, to Geoffrey Hinton, one of the authors of that paper.
The chain of blame assignment
A neural network is built up in layers. The input travels forward from layer to layer until a result emerges at the end. This path is called the forward pass. At the end, the result is compared with the correct answer and an error value is calculated. The larger this number, the worse the prediction was.
Now it goes backwards. For the last layer, it is easy to determine how a change in its adjustment knobs affects the error. From this result follows what share of the error the second-to-last layer had. In this way, the information passes backward layer by layer until the first one is reached. Mathematically, this relies on the chain rule from calculus, that is, the derivative of nested functions.
A comparison helps: imagine a long supply chain at the end of which stands a defective product. You don’t ask all suppliers at once, but instead work your way back station by station. Each station tells the previous one what share of the defect came from there. After one pass, everyone involved knows how much they need to change. Backpropagation distributes the error to the adjustment knobs in exactly this way.
A common misconception: backpropagation itself doesn’t change anything. It only calculates the directional information, the so-called gradients. The actual adjusting is handled by a second procedure, usually called gradient descent. How large the steps are is determined by the learning rate — a value that developers set by hand.
Backprop in training reports and data centers
In everyday life, one rarely encounters the term directly, but its consequences constantly. Every language model, every facial recognition system in a phone, and every translation service was trained this way. In program libraries like PyTorch or TensorFlow, the procedure is hidden behind a single command. Developers don’t write it themselves; they call it up.
In business news, backpropagation appears indirectly when training costs are discussed. The backward pass requires roughly twice as much computing effort as the forward pass and must store all intermediate results. This is why training is so much more expensive than later running a model. The enormous demand for graphics cards is directly tied to this.
Typical problems of the procedure are also discussed in technical articles. As networks become very deep, the values propagating backward can become smaller and smaller and practically vanish. This is referred to as the vanishing gradient. Architectures such as Transformers contain components specifically developed to counteract exactly this.