Unified Interpretation of Softmax Cross-Entropy and Negative Sampling: With Case Study for Knowledge Graph Embedding

Hidetaka Kamigaito, Katsuhiko Hayashi


Abstract
In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss functions. We attempted to solve this problem by using the Bregman divergence to provide a unified interpretation of the softmax cross-entropy and negative sampling loss functions. Under this interpretation, we can derive theoretical findings for fair comparison. Experimental results on the FB15k-237 and WN18RR datasets show that the theoretical findings are valid in practical settings.
Anthology ID:
2021.acl-long.429
Original:
2021.acl-long.429v1
Version 2:
2021.acl-long.429v2
Version 3:
2021.acl-long.429v3
Volume:
Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)
Month:
August
Year:
2021
Address:
Online
Venues:
ACL | IJCNLP
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
5517–5531
Language:
URL:
https://aclanthology.org/2021.acl-long.429
DOI:
10.18653/v1/2021.acl-long.429
Bibkey:
Cite (ACL):
Hidetaka Kamigaito and Katsuhiko Hayashi. 2021. Unified Interpretation of Softmax Cross-Entropy and Negative Sampling: With Case Study for Knowledge Graph Embedding. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 5517–5531, Online. Association for Computational Linguistics.
Cite (Informal):
Unified Interpretation of Softmax Cross-Entropy and Negative Sampling: With Case Study for Knowledge Graph Embedding (Kamigaito & Hayashi, ACL 2021)
Copy Citation:
PDF:
https://aclanthology.org/2021.acl-long.429.pdf
Video:
 https://aclanthology.org/2021.acl-long.429.mp4
Code
 kamigaito/acl2021kge
Data
FB15kFB15k-237WN18WN18RR