What is a linear activation function?

A linear activation function is an activation function that returns an output proportional to its input.

The simplest form is:

f(x) = x

This is also called the identity activation function.

How does it behave?

If the input is:

x = 3

then:

f(x) = 3

If the input is:

x = -2

then:

f(x) = -2

So the activation does not introduce any nonlinearity.

Where is linear activation used?

Linear activation is commonly used in the output layer of regression models when the prediction can take any real value.

For example:

Hidden layers → Linear output → Predicted house price

Why is it usually not used in hidden layers?

If every hidden layer uses only linear transformations, stacking many layers is mathematically equivalent to using a single linear transformation.

This means the network cannot learn complex nonlinear relationships.

That is why hidden layers usually use nonlinear activation functions such as ReLU, GELU, or tanh.

Can a linear activation have a slope other than 1?

Yes. A more general linear function can be written as:

f(x) = ax

However, in neural networks, the term linear activation usually refers to the identity function f(x) = x.

For the reason hidden layers need nonlinearity, see “Why do neural networks need nonlinear activation functions?”.

In short, a linear activation function leaves the input essentially unchanged and is mainly useful in output layers for tasks such as regression.