Skip-Gram approximates each m i,j by the inner product of the corresponding input and output vectors, that is: 2.1.1 SkipGram with negative sampling The primitive training sample for SkipGram is a pair of a target word and its corresponding context word.
we can represent the training data of SkipGram as a list of input and output index pairs, that is, the estimation problem of 'SkipGram with negative sampling (SGNS)' is defined as the minimization problem of objective function Ψ: where the optimization parameters are e i and o j for all i and j.