Closed Form Word Embedding Alignment We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the average cosine similarity between two embeddings of the same vocabulary into the same dimensional space. Our methods extend approaches known as Absolute Orientation, which are popular for aligning objects in threedimensions, and generalize an approach by Smith et al. (ICLR 2017). We prove new results for optimal scaling and for maximizing cosine similarity. Then we demonstrate how to evaluate the similarity of embeddings from different sources or mechanisms, and that certain properties like synonyms and analogies are preserved across the embeddings and can be enhanced by simply aligning and averaging ensembles of embeddings.

Guiding Crosslingual Entity Alignment via Adversarial Knowledge Embedding Crosslingual Entity Alignment (CEA) aims at identifying entities with their counterparts in different language knowledge graphs. Knowledge embedding alignment plays an important role in CEA due to its advantages of easy implementation and runtime robustness. However, existing embedding alignment methods havenxe2x80x99t considered the problem of embedding distribution alignment which refers to the alignment of spatial shapes of embedding spaces. To this end, we present a new Adversarial Knowledge Embedding framework (AKE for short) that jointly learns the representation, mapping and adversarial modules in an endtoend manner. By reducing the discrepancy of embedding distributions, AKE can approximately preserve an isomorphism between source and target embeddings. In addition, we introduce two new orthogonality constraints into mapping to obtain the selfconsistency and numerical stability of transformation. Experiments on realworld datasets demonstrate that our method significantly outperforms stateoftheart baselines.