Question 11: Consider a vocabulary \mathcal{V}, \mathcal{V} =([start]…

Consider a vocabulary $\mathcal{V}$,

$\mathcal{V} =$([start], breaking, ground, a, is, seismology, study, experience, earth quake,[end]).

Assume that we have a pre-trained GPT model for text generation and the first input token to the model is always the special token [start]. The prediction probabilities outputted by the model are given below.

$\hat{Y} = \begin{bmatrix} 0.04 & 0.01 & 0.14 & 0.07 & 0.09 & 0.41 & 0.08 & 0.05 & 0.08 & 0.01 \\ 0.10 & 0.03 & 0.06 & 0.16 & 0.43 & 0.01 & 0.06 & 0.09 & 0.01 & 0.04 \\ 0.06 & 0.08 & 0.28 & 0.29 & 0.03 & 0.08 & 0.04 & 0.08 & 0.04 & 0.04 \\ 0.11 & 0.03 & 0.48 & 0.02 & 0.01 & 0.07 & 0.06 & 0.14 & 0.07 & 0.01 \\ 0.09 & 0.29 & 0.04 & 0.01 & 0.04 & 0.03 & 0.25 & 0.05 & 0.15 & 0.06 \\ 0.14 & 0.22 & 0.13 & 0.08 & 0.01 & 0.03 & 0.06 & 0.23 & 0.08 & 0.03 \end{bmatrix}$

The columns of the matrix are in the same order as the words listed in the vocabulary set above

The zeroth row of the matrix is the output probability distribution by the model given the special [Start] token as input. Following the Greedy Search decoding strategy, the subsequent rows give the conditional probability distribution conditioned over the previous tokens. If you think the given information is insufficient for any sub-questions, then enter -1 as your answer

Based on the above data, answer the given subquestions.