Question 41: α22: _

You are given the encoder hidden states $h_1, h_2, h_3 \in \mathbb{R}^2$ and the decoder hidden state $s_2 \in \mathbb{R}^2$ at time step $t = 2$.

Use **dot-product attention**, where the attention score is computed as:

$e_{tj} = s_t^\top h_j \quad \text{and} \quad \alpha_{tj} = \frac{\exp(e_{tj})}{\sum_{k=1}^{3} \exp(e_{tk})}$

The context vector is then computed as:

$c_t = \sum_{j=1}^{3} \alpha_{tj} h_j$

Use the following values:

$s_2 = \begin{bmatrix} 1 \\ 0 \end{bmatrix}, \quad h_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}, \quad h_2 = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, \quad h_3 = \begin{bmatrix} 2 \\ 3 \end{bmatrix}$

Note: Use approximate values of exponential $\exp(1) \approx 2.72$, $\exp(2) \approx 7.39$, etc.

Answer the given subquestions:

α22: _________________