Rotate King to get Queen: Word Relationships as Orthogonal Transformations in Embedding Space

Kawin Ethayarajh


Abstract
A notable property of word embeddings is that word relationships can exist as linear substructures in the embedding space. For example, ‘gender’ corresponds to v_woman - v_man and v_queen - v_king. This, in turn, allows word analogies to be solved arithmetically: v_king - v_man + v_woman = v_queen. This property is notable because it suggests that models trained on word embeddings can easily learn such relationships as geometric translations. However, there is no evidence that models exclusively represent relationships in this manner. We document an alternative way in which downstream models might learn these relationships: orthogonal and linear transformations. For example, given a translation vector for ‘gender’, we can find an orthogonal matrix R, representing a rotation and reflection, such that R(v_king) = v_queen and R(v_man) = v_woman. Analogical reasoning using orthogonal transformations is almost as accurate as using vector arithmetic; using linear transformations is more accurate than both. Our findings suggest that these transformations can be as good a representation of word relationships as translation vectors.
Anthology ID:
D19-1354
Volume:
Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)
Month:
November
Year:
2019
Address:
Hong Kong, China
Editors:
Kentaro Inui, Jing Jiang, Vincent Ng, Xiaojun Wan
Venues:
EMNLP | IJCNLP
SIG:
SIGDAT
Publisher:
Association for Computational Linguistics
Note:
Pages:
3503–3508
Language:
URL:
https://aclanthology.org/D19-1354
DOI:
10.18653/v1/D19-1354
Bibkey:
Cite (ACL):
Kawin Ethayarajh. 2019. Rotate King to get Queen: Word Relationships as Orthogonal Transformations in Embedding Space. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 3503–3508, Hong Kong, China. Association for Computational Linguistics.
Cite (Informal):
Rotate King to get Queen: Word Relationships as Orthogonal Transformations in Embedding Space (Ethayarajh, EMNLP-IJCNLP 2019)
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PDF:
https://aclanthology.org/D19-1354.pdf