Suppose you have data as follows.
| | Age | Points |
| ----- | --- | ------ |
| Alice | $1$ | $2$ |
| Bob | $3$ | $4$ |
BatchNorm (resp. LayerNorm) maps each $X\in\{\{1,3\},\{2,4\}\}$ (resp.
$X\in\{\{1,2\},\{3,4\}\}$) to
$$
\gamma
\left(
\frac{x-\mu}{\sigma}
\;\middle|\;
x\in X
\right)
+
\beta
$$
where $\gamma\in\mathbb{R}$ is a learned scale parameter of $X$, and
$\beta\in\mathbb{R}$ is a learned shift parameter of $X$, and
$\mu\in\mathbb{R}$ is the mean of $X$, and $\sigma\in\mathbb{R}$ is the
standard deviation of $X$.