How does backpropagation work in neural networks?

Backpropagation in neural networks is a method used to adjust the weights of neurons based on the error rate obtained in the output.

Backpropagation, short for "backward propagation of errors," is a key algorithm in training many types of neural networks, including multilayer perceptron (MLP) networks. It's a supervised learning technique, meaning it learns from data that includes both the input and the desired output.

The process begins with a forward pass, where the input data is passed through the network to generate an output. This output is then compared to the desired output, and the difference between the two is calculated as an error. The goal of backpropagation is to minimise this error.

The error is then propagated backwards through the network, starting from the final layer. This is where the name 'backpropagation' comes from. The weights of the neurons are adjusted in a way that the error is reduced. This adjustment is done using a method called gradient descent.

Gradient descent is an optimisation algorithm that's used to minimise the error function. It works by calculating the gradient of the error function with respect to the network's weights, and then adjusting the weights in the direction that decreases the error. The size of the adjustment is determined by the learning rate, a hyperparameter that controls how quickly the network learns.

The backpropagation process is repeated for a number of epochs, or complete passes through the training dataset, until the network's performance on the data is satisfactory. The result is a trained network that can accurately map inputs to outputs.

In summary, backpropagation is a crucial part of training neural networks. It involves a forward pass to generate an output, calculating the error by comparing this output to the desired output, and then adjusting the weights of the neurons to minimise this error. This process is repeated until the network is sufficiently trained.