An inner product with the zero vector is always 0, so we can infer from the SGNS identity in (2) that PMI( / 0, •) − log k = 0 for every word in the vocabulary.
the vectors x, y, z, / 0 are all coplanar, and we know from the csPMI theorem that if a linear analogy holds over the csPMI of the sum and one word is equal to the log probability of the other word shifted by a model-specific constant.