#cbow

Question 1: Single choice

CBOW predicts the center word $w_c$ from the average $\bar{\mathbf{v}}_o$ of its context-word vectors. How is it trained with negative sampling?

Maximize $\log\sigma(\mathbf{u}_c^\top\bar{\mathbf{v}}_o) + \sum_{k=1}^{K}\log\sigma(-\mathbf{u}_{h_k}^\top\bar{\mathbf{v}}_o)$ for noise words $h_k$ 1
Maximize $\log\sigma(\mathbf{u}_c^\top\bar{\mathbf{v}}_o)$ alone, because noise words are only needed in skip-gram2
Sample $K$ noise context words and score each one separately against the center word, as skip-gram does3
Normalize $\exp(\mathbf{u}_c^\top\bar{\mathbf{v}}_o)$ by the sum of $\exp(\mathbf{u}_i^\top\bar{\mathbf{v}}_o)$ over every word $i$ in the whole vocabulary4