On the Equivalence of Holographic and Complex Embeddings for Link Prediction

Katsuhiko Hayashi, Masashi Shimbo


Abstract
We show the equivalence of two state-of-the-art models for link prediction/knowledge graph completion: Nickel et al’s holographic embeddings and Trouillon et al.’s complex embeddings. We first consider a spectral version of the holographic embeddings, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting model reveals that it can be viewed as an instance of the complex embeddings with a certain constraint imposed on the initial vectors upon training. Conversely, any set of complex embeddings can be converted to a set of equivalent holographic embeddings.
Anthology ID:
P17-2088
Volume:
Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)
Month:
July
Year:
2017
Address:
Vancouver, Canada
Venue:
ACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
554–559
Language:
URL:
https://aclanthology.org/P17-2088
DOI:
10.18653/v1/P17-2088
Bibkey:
Cite (ACL):
Katsuhiko Hayashi and Masashi Shimbo. 2017. On the Equivalence of Holographic and Complex Embeddings for Link Prediction. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 554–559, Vancouver, Canada. Association for Computational Linguistics.
Cite (Informal):
On the Equivalence of Holographic and Complex Embeddings for Link Prediction (Hayashi & Shimbo, ACL 2017)
Copy Citation:
PDF:
https://aclanthology.org/P17-2088.pdf
Note:
 P17-2088.Notes.pdf