Backpropagation

Backpropagation, short for 'backward propagation of errors,' is the cornerstone algorithm for training artificial neural networks. It provides an efficient way to compute the gradients of the loss function with respect to all the weights in the network. This gradient information is then used by an optimization algorithm, like gradient descent, to update the weights in a way that minimizes the loss. The process consists of two main passes: a forward pass and a backward pass. In the forward pass, an input is fed into the network, and its value propagates through the layers, neuron by neuron, until it reaches the output layer. At the output, the network's prediction is compared to the true label using a loss function to calculate the overall error. The backward pass is where the learning happens. The algorithm starts at the output layer and calculates the gradient of the loss with respect to the weights of that final layer. It then moves backward through the network, layer by layer. At each layer, it uses the chain rule from calculus to compute the gradient of the loss with respect to that layer's weights, reusing the gradients from the subsequent layer. This chain-like calculation is what gives the algorithm its efficiency. It effectively determines how much each individual weight in the network contributed to the final error. Once these gradients are calculated for all weights, the optimization algorithm takes over and updates each weight by a small amount in the direction that will decrease the error. This forward-backward cycle is repeated many times over the entire training dataset until the model's loss converges to a minimum.