Related papers: Embedding Knowledge Graphs in Degenerate Clifford …

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller…

Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…

We introduce a new method DOLORES for learning knowledge graph embeddings that effectively captures contextual cues and dependencies among entities and relations. First, we note that short paths on knowledge graphs comprising of chains of…

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…

Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present…

Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood…

Real-world knowledge can take various forms, including structured, semi-structured, and unstructured data. Among these, knowledge graphs are a form of structured human knowledge that integrate heterogeneous data sources into structured…

Knowledge graph (KG) entity typing aims at inferring possible missing entity type instances in KG, which is a very significant but still under-explored subtask of knowledge graph completion. In this paper, we propose a novel approach for KG…

Knowledge graphs represent information as structured triples and serve as the backbone for a wide range of applications, including question answering, link prediction, and recommendation systems. A prominent line of research for exploring…

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…

Representation learning for knowledge graphs (KGs) has focused on the problem of answering simple link prediction queries. In this work we address the more ambitious challenge of predicting the answers of conjunctive queries with multiple…

Closed form expressions for a multivector exponential and logarithm are presented in real Clifford geometric algebras Cl(p,q)when n=p+q=1 (complex and hyperbolic numbers) and n=2 (Hamilton, split and conectorine quaternions). Starting from…

Representation learning of knowledge graphs aims to embed entities and relations into low-dimensional vectors. Most existing works only consider the direct relations or paths between an entity pair. It is considered that such approaches…

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…

Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known…

Multilingual knowledge graph (KG) embeddings provide latent semantic representations of entities and structured knowledge with cross-lingual inferences, which benefit various knowledge-driven cross-lingual NLP tasks. However, precisely…

Knowledge representation (KR) is vital in designing symbolic notations to represent real-world facts and facilitate automated decision-making tasks. Knowledge graphs (KGs) have emerged so far as a popular form of KR, offering a contextual…

Knowledge Graph Completion is a task of expanding the knowledge graph/base through estimating possible entities, or proper nouns, that can be connected using a set of predefined relations, or verb/predicates describing interconnections of…

Traditional way of storing facts in triplets ({\it head\_entity, relation, tail\_entity}), abbreviated as ({\it h, r, t}), makes the knowledge intuitively displayed and easily acquired by mankind, but hardly computed or even reasoned by AI…

We prove that quadratic regular algebras of global dimension three on degree-one generators are related to graded skew Clifford algebras. In particular, we prove that almost all such algebras may be constructed as a twist of either a…