Word2Vec model does not use any neural network. It uses logistic regression only.
Consider the following paragraph from p:18 of Vector Semantics and Embeddings
We’ll see how to do neural networks in the next chapter, but word2vec is a much simpler model than the neural network language model, in two ways. First,word2vec simplifies the task (making it binary classification instead of word prediction). Second, word2vec simplifies the architecture (training a logistic regression classifier instead of a multi-layer neural network with hidden layers that demand more sophisticated training algorithms). The intuition of skip-gram is:
Treat the target word and a neighboring context word as positive examples.
Randomly sample other words in the lexicon to get negative samples.
Use logistic regression to train a classifier to distinguish those two cases.
Use the learned weights as the embeddings.
But, why it is called a neural model then? Is there any version of Word2Vec tat do use neural networks in it?