Softmax

A smoothed variation of the maximization function that is derivable which is important for Backpropagation.

$\sigma :\mathbb{R}\times {\mathbb{R}}^k\to {\mathbb{R}}^k$ ${\sigma }_{\beta }(z{)}_i:=\frac{e^{\beta z_i}}{{\sum }_{j=1}^k{e}^{\beta z_j}}$ where $z=⟨z_1,\dots ,z_k⟩,i\in \{1,\dots ,k\}$

and $e^{\beta }$ is called the base. For $\beta =1$ the function is also called the standard softmax function.