One of the fundamental problems in Artificial Intelligence is to perform complex multihop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary firstorder logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also thatmore »
Query2box: Reasoning Over Knowledge Graphs In Vector Space Using Box Embeddings
Answering complex logical queries on largescale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query. However, prior work models queries as single points in the vector space, which is problematic because a complex query represents a potentially large set of its answer entities, but it is unclear how such a set can be represented as a single point. Furthermore, prior work can only handle queries that use conjunctions (^) and existential quantifiers (9). Handling queries with logical disjunctions (_) remains an open problem. Here we propose QUERY2BOX, an embeddingbased framework for reasoning over arbitrary queries with ^, _, and 9 operators in massive and incomplete KGs. Our main insight is that queries can be embedded as boxes (i.e., hyperrectangles), where a set of points inside the box corresponds to a set of answer entities of the query. We show that conjunctions can be naturally represented as intersections of boxes and also prove a negative result that handling disjunctions would require embedding with dimension proportional more »
 Award ID(s):
 1835598
 Publication Date:
 NSFPAR ID:
 10198852
 Journal Name:
 International Conference on Learning Representations (ICLR)
 Sponsoring Org:
 National Science Foundation
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