One key principle for assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are both intuitive and interpretable; however, they are empirically inferior to the simple cosine similarity between general-purpose sentence vectors. To remedy this , we focus on  the fact that the norm of word vectors is a good proxy for word importance, and the angle of them is a good proxy for word similarity. Alignment-based approaches do not distinguish the norm and direction , whereas sentence-vector approaches automatically use the norm as the word importance. Accordingly, we propose to decouple word vectors into their norm and direction then computing the alignment-based similarity using earth mover's distance (  optimal transport cost), which we refer to as word rotator's distance. Furthermore, we demonstrate how to grow the norm and direction of word vectors (vector converter) ; this is a new systematic approach derived from the sentence-vector estimation methods , which can significantly improve the performance of the proposed method . On several STS benchmarks, our simple proposed methods outperformed not only alignment-based approaches but also strong baselines. 
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 the norm and direction of word vectors (vector converter) , which is a new systematic approach derived from sentence-vector estimation methods . On several textual similarity datasets, the combination of these simple proposed methods outperformed not only alignment-based approaches but also strong baselines. The source code is available at URL
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