Why does PairDiff work? - A Mathematical Analysis of Bilinear Relational Compositional Operators for Analogy Detection

Huda Hakami, Kohei Hayashi, Danushka Bollegala

Abstract
Representing the semantic relations that exist between two given words (or entities) is an important first step in a wide-range of NLP applications such as analogical reasoning, knowledge base completion and relational information retrieval. A simple, yet surprisingly accurate method for representing a relation between two words is to compute the vector offset (PairDiff) between their corresponding word embeddings. Despite the empirical success, it remains unclear as to whether PairDiff is the best operator for obtaining a relational representation from word embeddings. We conduct a theoretical analysis of generalised bilinear operators that can be used to measure the l2 relational distance between two word-pairs. We show that, if the word embed- dings are standardised and uncorrelated, such an operator will be independent of bilinear terms, and can be simplified to a linear form, where PairDiff is a special case. For numerous word embedding types, we empirically verify the uncorrelation assumption, demonstrating the general applicability of our theoretical result. Moreover, we experimentally discover PairDiff from the bilinear relational compositional operator on several benchmark analogy datasets.
Anthology ID:
C18-1211
Volume:
Proceedings of the 27th International Conference on Computational Linguistics
Month:
August
Year:
2018
Address:
Santa Fe, New Mexico, USA
Editors:
Emily M. Bender, Leon Derczynski, Pierre Isabelle
Venue:
COLING
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
2493–2504
Language:
URL:
https://aclanthology.org/C18-1211
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Cite (ACL):
Huda Hakami, Kohei Hayashi, and Danushka Bollegala. 2018. Why does PairDiff work? - A Mathematical Analysis of Bilinear Relational Compositional Operators for Analogy Detection. In Proceedings of the 27th International Conference on Computational Linguistics, pages 2493–2504, Santa Fe, New Mexico, USA. Association for Computational Linguistics.
Cite (Informal):
Why does PairDiff work? - A Mathematical Analysis of Bilinear Relational Compositional Operators for Analogy Detection (Hakami et al., COLING 2018)
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