What exactly does word2vec learn?

What exactly does word2vec learn, and how? Answering this question amounts to understanding representation learning in a minimal yet interesting language modeling task. Despite the fact that word2vec is a well-known precursor to modern language models, for many years, researchers lacked a quantitative and predictive theory describing its learning process. In our new paper , we finally provide such a theory. We prove that there are realistic, practical regimes in which the learning problem reduces to unweighted least-squares matrix factorization . We solve the gradient flow dynamics in closed form; the final learned representations are simply given by PCA. Learning dynamics of word2vec . When trained from small initialization, word2vec learns in discrete, sequential steps. Left: rank-incrementing learning steps in the weight matrix, each decreasing the loss. Right: three time slices of the latent embedding space showing how embedding vectors expand into subspaces of increasing dimension at each learning step, continuing until model capacity is saturated. Before elaborating on this result, let’s motivate the problem. word2vec is a well-known algorithm for learning dense vector repres