ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5752
Softmax function

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 $$\mathbb{R}^N \to (0, 1)^N, \quad x \mapsto \frac{1}{\sum_{n = 1}^N \exp(x_n)} \left( \exp (x_1), \ldots, \exp(x_N) \right)$$

Let $t \mapsto e^t$ 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 $$\mathbb{R}^N \to (0, 1)^N, \quad x \mapsto \frac{1}{\sum_{n = 1}^N e^{x_n}} \left( e^{x_1}, \ldots, e^{x_N} \right)$$