The rectified linear unit function

The rectified linear unit, better known as ReLU, is the most widely used activation function:

The ReLU function has the advantage of being non linear. Thus, backpropagation is easy and can therefore stack multiple hidden layers activated by the ReLU function, where for x<=0, the function f(x) = 0 and for x>0, f(x)=x.

The main advantage of the ReLU function over other activation functions is that it does not activate all the neurons at the same time. This can be observed from the preceding graph of the ReLU function, where we see that if the input is negative it outputs zero and the neuron does not activate. This results in a sparse network, and fast and easy computation.

Looking at the preceding gradients graph of ReLU preceding, we can see the negative side of the graph shows a constant zero. Therefore, activations falling in that region will have zero gradients and therefore, weights will not get updated. This leads to inactivity of the nodes/neurons as they will not learn. To overcome this problem, we have Leaky ReLUs, which modify the function as:

This prevents the gradient from becoming zero in the negative side and the weight training continues, but slowly, owing to the low value of .