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Title: Knowledgebra: An Algebraic Learning Framework for Knowledge Graph
Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective.  more » « less
Award ID(s):
1920147 1910303 1933525
PAR ID:
10342594
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Machine Learning and Knowledge Extraction
Volume:
4
Issue:
2
ISSN:
2504-4990
Page Range / eLocation ID:
432 to 445
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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