The word2vec software of Tomas Mikolov and colleagues 1 has gained a lot of traction lately, and provides state-of-the-art word embeddings. The learning models behind the software are described in two research papers [1, 2]. We found the description of the models in these papers to be somewhat cryptic and hard to follow. While the motivations and presentation may be obvious to the neural-networks language-modeling crowd, we had to struggle quite a bit to figure out the rationale behind the equations. This note is an attempt to explain equation (4) (negative sampling) in " Distributed Representations of Words and Phrases and their Compositionality " by 1 The skip-gram model The departure point of the paper is the skip-gram model. In this model we are given a corpus of words w and their contexts c. We consider the conditional probabilities p(c|w), and given a corpus T ext, the goal is to set the parameters θ of p(c|w; θ) so as to maximize the corpus probability: arg max θ w∈T ext   c∈C(w) p(c|w; θ)   (1) in this equation, C(w) is the set of contexts of word w. Alternatively: arg max θ (w,c)∈D p(c|w; θ) (2) here D is the set of all word and context pairs we extract from the text.