Softmax

The Softmax can refer to two mathematical functions:

In machine learning a softmax is the function which normalizes a vector of values to a probability vector: $\text{softmax}(\mathbf{x}) = \dfrac{e^{\mathbf{x}}}{\sum_i e^{x_i}}$ where $\mathbf{x} = (x_i) \in \mathbb{R}^n$ . This function could also be called soft-argmax because it is a smooth approximation of the discrete argmax function.
It may also refer to a smoothed maximum function like $\epsilon \log \sum_i \exp (x_i / \epsilon)$ which approximates the $\text{max}$ function in the limit $\epsilon \rightarrow 0$