Backpropagation

Backpropagation is a method used to train artificial neural networks, which are machine learning models that are inspired by the structure and function of the human brain. The method is used to adjust the weights of the connections between the neurons in the network in order to minimize the error between the network's predictions and the true values of the input data.

The backpropagation algorithm is typically used in conjunction with a supervised learning task, in which the network is given a set of input-output pairs and the goal is to learn a mapping from inputs to outputs. The algorithm consists of two main steps: forward propagation and backward propagation.

Forward Propagation

In the forward propagation step, the input is passed through the network, and the output is computed by applying the activation function to the weighted sum of the inputs at each neuron. The activation function is a mathematical function that determines the output of a neuron given its input. Commonly used activation functions include sigmoid, ReLU, and tanh.

Backward Propagation

The backward propagation step is where the weights of the network are adjusted. The goal is to adjust the weights so that the error between the network's predictions and the true values is minimized. The error is typically measured using a loss function, such as mean squared error or cross-entropy.

To compute the gradient of the loss function with respect to the weights, the backpropagation algorithm uses the chain rule of calculus. The chain rule states that the derivative of a composite function can be computed by multiplying the derivative of the outer function by the derivative of the inner function. In the case of backpropagation, the outer function is the loss function and the inner function is the activation function of the neurons.

The weights are then adjusted using an optimization algorithm such as gradient descent, in which the weights are updated in the opposite direction of the gradient of the loss function. This process is repeated for multiple iterations, until the error between the network's predictions and the true values is sufficiently small.

Explain Like I'm 5 (ELI5)

Backpropagation is a way for a computer to learn how to do something, like recognizing pictures or understanding speech. It helps the computer figure out if it got the answer right or wrong and makes changes so it can do better next time. It's like when your teacher marks your test, they tell you what you got wrong and how you can improve next time. Backpropagation is a way for the computer to do that on its own.