The Spectral Underpinning of word2vec

word2vec due to Mikolov \textit{et al.} (2013) is a word embedding method that is widely used in natural language processing. Despite its great success and frequent use, theoretical justification is still lacking. The main contribution of our paper is to propose a rigorous analysis of the highly nonlinear functional of word2vec. Our results suggest that word2vec may be primarily driven by an underlying spectral method. This insight may open the door to obtaining provable guarantees for word2vec. We support these findings by numerical simulations. One fascinating open question is whether the nonlinear properties of word2vec that are not captured by the spectral method are beneficial and, if so, by what mechanism.