Consider the function $f: \mathbb{R}^d \mapsto \mathbb{R}^d$ whose components are given by
$$
f_i(x)=\frac{x_i^2}{\sum_{k=1}^d x_k^2}
$$
for $i=1, \ldots, d$ and $x \in \mathbb{R}^d$.
We can see that $0 \leq f_i \leq 1$ for each $i=1, \ldots, d$ and $\sum_{i=1}^d f_i=1$. Thus, $f$ normalizes the input vector $x$ to a probability distribution, just like Softmax does! That said, what is one way in which our function $f$ differs from the Softmax function?
