ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11394 on D5752: Softmax function
F11394
Formulation 0
Let $\exp$ be the D1932: Standard natural real exponential function.
The softmax function with respect to $N \in 2, 3, 4, \ldots$ is the D4363: Euclidean real function \begin{equation} \mathbb{R}^N \to (0, 1)^N, \quad x \mapsto \frac{1}{\sum_{n = 1}^N \exp(x_n)} \left( \exp (x_1), \ldots, \exp(x_N) \right) \end{equation}