# Softmax

The softmax turns $$n$$ numbers in $$\mathbb R^N$$ into a probability distribution proportional to the size of the numbers.

Given an $$n$$-dimensional vector $$\mathbf v$$ with all component terms in $$\mathbb R^N$$, the softmax of $$\mathbb v$$ is: $\mathrm{softmax}(\mathbb v)_i = \frac{\exp{(v_i)}} {\sum_{j=1}^{n} \exp{(v_i)}}$