Related papers: Embedding Knowledge Graphs in Degenerate Clifford …
Knowledge bases, and their representations in the form of knowledge graphs (KGs), are naturally incomplete. Since scientific and industrial applications have extensively adopted them, there is a high demand for solutions that complete their…
Formulas to calculate multivector exponentials in a base-free representation and in a orthonormal basis are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on the analysis of roots of characteristic…
Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relations) that preserve task-relevant structure encoded within…
For each quadratic form Q in Quad(V) over a given vector space over a field R we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form $x…
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…
Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the…
Deep learning currently dominates the benchmarks for various NLP tasks and, at the basis of such systems, words are frequently represented as embeddings --vectors in a low dimensional space-- learned from large text corpora and various…
This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…
Knowledge graph embedding (KGE) models have been proposed to improve the performance of knowledge graph reasoning. However, there is a general phenomenon in most of KGEs, as the training progresses, the symmetric relations tend to zero…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
Most existing knowledge graphs suffer from incompleteness. Embedding knowledge graphs into continuous vector spaces has recently attracted increasing interest in knowledge base completion. However, in most existing embedding methods, only…
Knowledge Graphs (KGs) have found many applications in industry and academic settings, which in turn, have motivated considerable research efforts towards large-scale information extraction from a variety of sources. Despite such efforts,…
Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…
We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP model chooses a set of…
Knowledge Graph Embedding (KGE) methods have gained enormous attention from a wide range of AI communities including Natural Language Processing (NLP) for text generation, classification and context induction. Embedding a huge number of…
In the first article of this work [... I: The transposition map] we showed that real Clifford algebras CL(V,Q) posses a unique transposition anti-involution \tp. There it was shown that the map reduces to reversion (resp. conjugation) for…
In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial…
Knowledge graphs (KGs) that modelings the world knowledge as structural triples are inevitably incomplete. Such problems still exist for multimodal knowledge graphs (MMKGs). Thus, knowledge graph completion (KGC) is of great importance to…
We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras $\cl(Q)$ to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in $\cl(Q),$…
We present different methods for symbolic computer algebra computations in higher dimensional (\ge9) Clifford algebras using the \Clifford\ and \Bigebra\ packages for \Maple(R). This is achieved using graded tensor decompositions,…