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In the Vectorization section,

We have
$\mathbf{X} \in \mathbb{R}^{n \times d}$, $\mathbf{W} \in \mathbb{R}^{d \times q}$.

Now, since:
$$\mathbf{O} = \mathbf{X} \mathbf{W} + \mathbf{b}$$
and
$$\hat{\mathbf{Y}} = \mathrm{softmax}(\mathbf{O}),$$

we require $\mathbf{b} \in \mathbb{R}^{n \times q}$. This ensures that the softmax operation can be computed row-wise on $\mathbf{O}$.

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