$2\mathrm{.}1$ What is the main advantage of the Negative Sampling Model for word representations compared to the Word$2$Vec Model? Choose the most significant option:

a$)$ the error function at output layer is changed from negative log probability to binary log error

b$)$ instead of using word$-$pairs of a given window size as training samples, samples are created for context words using one positive target and a fixed number of negative targets

c$)$ the softmax calculation for probability of each of the $10K($say$)$ words in the vocab is replaced by a sigmoid calculation for the words in the sample, and only the error from these samples is used to modulate the corresponding weights leaving the other weights unaffected for that training sample

d$)$ an empirical formula is used for selection of negative samples.