The Exponential Linear Unit (ELU) function is a relatively recent modification to the ReLU function. It looks very similar to the ReLU function, but it has very different mathematical properties. The following screenshot shows the ELU function:
The preceding screenshot shows that, at 0, we don't have a corner. In the case of the ReLU function, we have a corner. In this function, instead of a single value going to 0, we have the ELU function slowly going to the negative alpha parameter.