This implies that the co-occurrence matrix M d that is reconstructed using the debiased word matrix W d is also unbiased with respect to S. The subspace projection method is therefore far more powerful than initially stated in<cite> Bolukbasi et al. (2016)</cite> : not only can it be applied to any embedding model that implicitly does matrix factorization (e.g., GloVe, SGNS), but debiasing word vectors in this way is equivalent to training on a perfectly unbiased corpus when there is no reconstruction error.