Question 21: Consider the CBOW model for learning word embeddings wit…

Consider the CBOW model for learning word embeddings with embedding dimension two. The window size is one, that is, we only use the previous word as the context to predict the current word. The vocabulary is made up of the words {“one”, “two”, “three”, “four”}. At some point during training, the word and context matrices are given below. The first column in each matrix corresponds to the embedding for “one”, the second column is for “two” and so on:

$W_{\text{word}} = \begin{bmatrix} 1 & 1 & 1 & 1 \\ -1 & 1 & 2 & -2 \end{bmatrix}, \quad W_{\text{context}} = \begin{bmatrix} 0 & 1 & 0 & 1 \\ -1 & 0 & 1 & 1 \end{bmatrix}$

The sample that has come up now during training is “two three”. Note that “three” is to be considered as the true label here. Enter your answer correct to two places after the decimal for both sub-questions.

Based on the above data, answer the given subquestions.

Find the probability of predicting “three” given “two” as context.