A rectified linear unit (ReLU) is an activation function that outputs the input directly if the input is positive, and otherwise outputs zero. ReLU introduces non-linearity to a neural network while still mimicking linear behavior. The advantage of ReLU is that it has sparse activation and efficient computation; however, it is also non-differentiable at zero, which can introduce problems.

ReLU is based on a rectifier function, $f\left(x\right)=max(0,x)$, also known as a ramp function. Both the function and its derivative are monotonic and the range of the function is $[0,\infty )$. Other versions of the function exist, such as leaky ReLU, which is typically defined as $f\left(x\right)=x$ when $x$ is positive, else $f\left(x\right)=0.01x$.

ReLU is the most commonly used activation function due to its simplicity and efficiency.