Sho Yokoi, Ryo Takahashi ,Reina Akama, Jun Suzuki, Kentaro Inui Abstract A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically inferior to the simple cosine similarity between general-purpose sentence vectors. To address this issue, we focus on and demonstrate the fact that the norm of word vectors is a good proxy for word importance, and their angle is a good proxy for word similarity. Alignment-based approaches do not distinguish them, whereas sentence-vector approaches automatically use the norm as the word importance. Accordingly, we propose a method that first decouples word vectors into their norm and direction, and then computes alignment-based similarity using earth mover’s distance (i.e., optimal transport cost), which we refer to as word rotator’s distance. Besides, we find how to “grow” ...