Neural Information Retrieval $(17)$

$1.$ Consider Vocabulary $=\{$the$,$ quick, brown, fox, jumped$\},$ so V $=5.$ What is the VxV matrix of $1-$hot embeddings of each term in the vocabulary? $(2)$

$2.$ Given a training set $$the quick brown fox jumped$,$ what are all possible windows of size $3($k$=3)?(2)$

$3.$ Given the following matrices Win and Wout in the Skip Gram architecture with a hidden layer of size $3,$ and the window $$quick brown fox$.$

Win $=[2,2,4.$

$3\mathrm{.}1\mathrm{.}3.$

$2\mathrm{.}1\mathrm{.}3.$

$1\mathrm{.}3\mathrm{.}3$

$\mathrm{.}6\mathrm{.}1\mathrm{.}2]$

Wout $=[\mathrm{.}4\mathrm{.}1\mathrm{.}4.$

$6\mathrm{.}8\mathrm{.}3.$

$6\mathrm{.}1\mathrm{.}5.$

$3\mathrm{.}4\mathrm{.}1.$

$3\mathrm{.}5\mathrm{.}2]$

Compute:

a$.$ p$($quick$|$brown$)$

b$.$ p$($fox$|$brown$)$

c$.$ Total loss