In TF$-$IDF,

$[3$ pts$]$ when a $100-$word document contains the term "cat" $12$ times, compute TF value of 'cat'.

$[3$ pts$]$ The size of the corpus is $10$ million documents. If we assume there are $0\mathrm{.}3$ million documents

that contain the term "cat". Compute IDF $($use the log form$)$

$[2$ pt$]$ Compute TF$-$IDF of 'cat'

In CBOW,

$[3$ pts$]$ Can we use a vocabulary index method $($instead of a one$-$hot vector$)$ as an input to CBOW

$[2$ pts$]$ The activation function of the output layer should be softmax. Explain the reason.

$[3$ pts$]$ After training is done in CBOW, how do we extract the word embedding vector for a certain

word.

$[3$ pts$]$ In Skip$-$Gram, show that $F=$exp$(x)$ satisfies the following:

$F((w_i-w_j)tilde(w{)}_k)=\frac{F(w_i\text{t}\text{i}\text{l}\text{d}\text{e}(w{)}_k)}{F(w_j\text{t}\text{i}\text{l}\text{d}\text{e}(w{)}_k)}$