Related papers: Embedding Knowledge Graphs in Degenerate Clifford …
We introduce a notion of matrix valued Gram decompositions for correlation matrices whose study is motivated by quantum information theory. We show that for extremal correlations, the matrices in such a factorization generate a Clifford…
Inductive knowledge graph completion has been considered as the task of predicting missing triplets between new entities that are not observed during training. While most inductive knowledge graph completion methods assume that all entities…
Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
We introduce Natural Qubit Algebra (NQA), a compact real operator calculus for qubit systems based on a $2\times2$ block alphabet $\{I,X,Z,W\}\subset\mathrm{Mat}(2,\mathbb{R})$ and tensor-word representations. The resulting multiplication…
A Knowledge Graph (KG) is the directed graphical representation of entities and relations in the real world. KG can be applied in diverse Natural Language Processing (NLP) tasks where knowledge is required. The need to scale up and complete…
Classification of finite dimensional representations of the q-deformed Heisenberg algebra $H_q(3)$ is made by the help of Clifford algebra of polynomials and generalized Grassmann algebra. Special attention is paid when $q$ is a primitive…
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG they are brittle…
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform…
Capturing associations for knowledge graphs (KGs) through entity alignment, entity type inference and other related tasks benefits NLP applications with comprehensive knowledge representations. Recent related methods built on Euclidean…
A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE…
Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…
By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line,…
Neural models of Knowledge Base data have typically employed compositional representations of graph objects: entity and relation embeddings are systematically combined to evaluate the truth of a candidate Knowedge Base entry. Using a model…
Knowledge is captured in the form of entities and their relationships and stored in knowledge graphs. Knowledge graphs enhance the capabilities of applications in many different areas including Web search, recommendation, and natural…
In recent years, we have witnessed the proliferation of knowledge graphs (KG) in various domains, aiming to support applications like question answering, recommendations, etc. A frequent task when integrating knowledge from different KGs is…
Distance based knowledge graph embedding methods show promising results on link prediction task, on which two topics have been widely studied: one is the ability to handle complex relations, such as N-to-1, 1-to-N and N-to-N, the other is…
In this paper, theory and construction of spinor representations of real Clifford algebras $\cl_{p,q}$ in minimal left ideals are reviewed. Connection with a general theory of semisimple rings is shown. The actual computations can be found…
Knowledge graphs (KGs) play a crucial role in many applications, such as question answering, but incompleteness is an urgent issue for their broad application. Much research in knowledge graph completion (KGC) has been performed to resolve…
We consider Clifford algebras with nonsymmetric bilinear forms, which are isomorphic to the standard symmetric ones, but not equal. Observing, that the content of physical theories is dependent on the injection $\oplus^n\bigwedge…