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The word2vec software of Tomas Mikolov and colleagues(https://code.google.com/p/word2vec/ ) has gained a lot of traction lately, andprovides state-of-the-art word embeddings. The learning models behind thesoftware are described in two research papers. We found the description of themodels in these papers to be somewhat cryptic and hard to follow. While themotivations and presentation may be obvious to the neural-networkslanguage-modeling crowd, we had to struggle quite a bit to figure out therationale 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 Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Corrado and Jeffrey Dean.

word2vec Explained: deriving Mikolov et al.'s negative-sampling word-embedding method