showed that relations between words are reflected to a large extent in the offsets between their vector embeddings (queen -king = woman -man), and thus the vector of the hidden word b * will be similar to the vector b − a + a * , suggesting that the analogy question can be solved by optimizing: where V is the vocabulary and sim is a similarity measure.
they used the cosine similarity measure, defined as: resulting in: Equation 4 has been referred to as CosAdd model.