Which of the following properties can be seen as an advantage of word embeddings over one-hot vectors?

You are building a co-occurrence matrix for a language with a vocabulary of 100000 words. How many entries does the complete matrix have? Assume that all words in the vocabulary can be used both as target words (words that you want to get word embeddings for) and context words.

Which of the following words would you not expect to see as a close neighbour of the word life?

Here are two word vectors:

$\mathbf{a} = \begin{bmatrix} -2 & 2 \end{bmatrix}$

$\mathbf{b} = \begin{bmatrix} 1 & 0 \end{bmatrix}$

What is the cosine similarity of these two vectors, rounded to two decimals?

The Embedding Projector allows you to explore the vector spaces of pre-trained word embeddings. Load the default vector space (Word2Vec 10K) and search for the word ‘artificial’. What is the cosine distance of the nearest neighbour of this word in the original space?

(Cosine distance is defined as $1-c$ where $c$ is the cosine similarity.)

In the prediction-based approach to learning word embeddings, we obtain these embeddings as the by-product of learning to solve a training task. Which training task should you choose to let similar word vectors have similar meaning?