Show that the softmax function [ text { softmax }: boldsymbol{z} mapsto frac{exp (boldsymbol{z})}{sum_{k} exp left(z_{k} ight)}
Question:
Show that the softmax function
\[ \text { softmax }: \boldsymbol{z} \mapsto \frac{\exp (\boldsymbol{z})}{\sum_{k} \exp \left(z_{k}\right)} \]
satisfies the invariance property:
\[ \operatorname{softmax}(\boldsymbol{z})=\operatorname{softmax}(\boldsymbol{z}+c \times \mathbf{1}), \text { for any constant } c \]
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Related Book For
Data Science And Machine Learning Mathematical And Statistical Methods
ISBN: 9781118710852
1st Edition
Authors: Dirk P. Kroese, Thomas Taimre, Radislav Vaisman, Zdravko Botev
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