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        <title>A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs</title>
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    <name type="personal">
        <namePart type="given">Katsuhiko</namePart>
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            <publisher>Association for Computational Linguistics</publisher>
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    <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.</abstract>
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    <identifier type="doi">10.18653/v1/D19-1246</identifier>
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        <date>2019-nov</date>
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%0 Conference Proceedings
%T A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs
%A Hayashi, Katsuhiko
%A Shimbo, Masashi
%S Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)
%D 2019
%8 nov
%I Association for Computational Linguistics
%C Hong Kong, China
%F hayashi-shimbo-2019-non
%X 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.
%R 10.18653/v1/D19-1246
%U https://aclanthology.org/D19-1246
%U https://doi.org/10.18653/v1/D19-1246
%P 2422-2430

Markdown (Informal)

[A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs](https://aclanthology.org/D19-1246) (Hayashi & Shimbo, EMNLP 2019)

• A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs (Hayashi & Shimbo, EMNLP 2019)

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.