An artificial neural network's learning rule or learning process is a method, mathematical logic or algorithm which improves the network's performance and/or training time. Usually, this rule is applied repeatedly over the network. It is done by updating the weight and bias^{[broken anchor]} levels of a network when it is simulated in a specific data environment. A learning rule may accept existing conditions (weights and biases) of the network, and will compare the expected result and actual result of the network to give new and improved values for the weights and biases. Depending on the complexity of the model being simulated, the learning rule of the network can be as simple as an XOR gate or mean squared error, or as complex as the result of a system of differential equations.

The learning rule is one of the factors which decides how fast or how accurately the neural network can be developed. Depending on the process to develop the network, there are three main paradigms of machine learning:

A lot of the learning methods in machine learning work similar to each other, and are based on each other, which makes it difficult to classify them in clear categories. But they can be broadly understood in 4 categories of learning methods, though these categories don't have clear boundaries and they tend to belong to multiple categories of learning methods -

Though these learning rules might appear to be based on similar ideas, they do have subtle differences, as they are a generalisation or application over the previous rule, and hence it makes sense to study them separately based on their origins and intents.

Developed by Donald Hebb in 1949 to describe biological neuron firing. In the mid-1950s it was also applied to computer simulations of neural networks.

${\displaystyle \Delta w_{i}=\eta x_{i}y}$

Where ${\displaystyle \eta }$ represents the learning rate, ${\displaystyle x_{i}}$ represents the input of neuron i, and y is the output of the neuron. It has been shown that Hebb's rule in its basic form is unstable. Oja's Rule, BCM Theory are other learning rules built on top of or alongside Hebb's Rule in the study of biological neurons.

The perceptron learning rule originates from the Hebbian assumption, and was used by Frank Rosenblatt in his perceptron in 1958. The net is passed to the activation (transfer) function and the function's output is used for adjusting the weights. The learning signal is the difference between the desired response and the actual response of a neuron. The step function is often used as an activation function, and the outputs are generally restricted to -1, 0, or 1.