Let X and Y be the English and Chinese embedding spaces.
in order to achieve multilingual alignment, we learn a mapping W ∈ R d×d from X to Y via a seed dictionary with a size of m, by optimizing: where  Next, we retrieve translation candidates for each token w i in s. we first project w i into the aligned embedding space (i.e., by applying W on x i ), and then we explore its neighborhood to find the nearest Chinese words as its translation candidates.