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

TL;DR

This paper clarifies the negative sampling method used in Mikolov et al.'s word2vec model, making the underlying equations and rationale more accessible to researchers and practitioners.

Contribution

It provides a detailed explanation and derivation of the negative sampling technique in Mikolov et al.'s word2vec, which was previously cryptic.

Findings

Clarified the mathematical derivation of negative sampling

Improved understanding of word2vec training process

Enhanced accessibility of the model's core equations

Abstract

The word2vec software of Tomas Mikolov and colleagues (https://code.google.com/p/word2vec/ ) 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. 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 Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Corrado and Jeffrey Dean.