Backpropagation: Definition and Examples

Backpropagation, or backward propagation of errors, is the central algorithm for training artificial neural networks. Its principle relies on computing the partial derivatives of the loss function with respect to each weight in the network, by backpropagating the error from the output layer to the input layers. It is thanks to this algorithm that language models like GPT or Claude can learn from billions of examples.

Concretely, the process unfolds in two phases. First, a forward pass where data flows through the network layer by layer to produce a prediction. Then, the backward pass where the error between the prediction and the expected result is computed, then propagated in reverse through the network using the chain rule. Each weight thus receives a signal indicating in which direction and by how much it should be adjusted.

The algorithm works in tandem with an optimizer (such as SGD or Adam) that uses the gradients computed by backpropagation to update the weights. The learning rate controls the magnitude of these updates: too high, the model diverges; too low, learning is excessively slow. This delicate balance makes training neural networks both an art and a science.

Although the concept was formalized in the 1980s by Rumelhart, Hinton, and Williams, backpropagation remains the cornerstone of training all deep learning models today, from convolutional networks for vision to transformers powering generative AI. For prompt engineering practitioners, understanding this mechanism helps grasp why a model responds in a certain way and what its inherent limitations are.