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In this paper we perform a rigorous mathematical analysis of the word2vecmodel, especially when it is equipped with the Skip-gram learning scheme. Ourgoal is to explain how embeddings, that are now widely used in NLP (NaturalLanguage Processing), are influenced by the distribution of terms in thedocuments of the considered corpus. We use a mathematical formulation to shedlight on how the decision to use such a model makes implicit assumptions on thestructure of the language. We show how Markovian assumptions, that we discuss,lead to a very clear theoretical understanding of the formation of embeddings,and in particular the way it captures what we call frequentist synonyms. Theseassumptions allow to produce generative models and to conduct an explicitanalysis of the loss function commonly used by these NLP techniques. Moreover,we produce synthetic corpora with different levels of structure and showempirically how the word2vec algorithm succeed, or not, to learn them. It leadsus to empirically assess the capability of such models to capture structures ona corpus of around 42 millions of financial News covering 12 years. That for,we rely on the Loughran-McDonald Sentiment Word Lists largely used on financialtexts and we show that embeddings are exposed to mixing terms with oppositepolarity, because of the way they can treat antonyms as frequentist synonyms.Beside we study the non-stationarity of such a financial corpus, that hassurprisingly not be documented in the literature. We do it via time series ofcosine similarity between groups of polarized words or company names, and showthat embedding are indeed capturing a mix of English semantics and joineddistribution of words that is difficult to disentangle.

Do Word Embeddings Really Understand Loughran-McDonald's Polarities?