A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs

Katsuhiko Hayashi, Masashi Shimbo

Abstract
Bilinear diagonal models for knowledge graph embedding (KGE), such as DistMult and ComplEx, balance expressiveness and computational efficiency by representing relations as diagonal matrices. Although they perform well in predicting atomic relations, composite relations (relation paths) cannot be modeled naturally by the product of relation matrices, as the product of diagonal matrices is commutative and hence invariant with the order of relations. In this paper, we propose a new bilinear KGE model, called BlockHolE, based on block circulant matrices. In BlockHolE, relation matrices can be non-commutative, allowing composite relations to be modeled by matrix product. The model is parameterized in a way that covers a spectrum ranging from diagonal to full relation matrices. A fast computation technique can be developed on the basis of the duality of the Fourier transform of circulant matrices.
Anthology ID:
D19-1246
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:
2422–2430
Language:
URL:
https://aclanthology.org/D19-1246
DOI:
10.18653/v1/D19-1246
Bibkey:
Cite (ACL):
Katsuhiko Hayashi and Masashi Shimbo. 2019. A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs. 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 2422–2430, Hong Kong, China. Association for Computational Linguistics.
Cite (Informal):
A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs (Hayashi & Shimbo, EMNLP-IJCNLP 2019)
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