Knowledge Graph Embeddings in Geometric Algebras
This work addresses knowledge graph completion for AI applications, offering a novel framework that subsumes and improves upon prior methods, though it is incremental in advancing geometric algebra-based embeddings.
The authors tackled knowledge graph embedding by proposing GeomE, a framework using geometric algebra with multivector representations and geometric product, which outperformed existing state-of-the-art models in link prediction on multiple benchmarks.
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor Octonion) representations, all of which are subsumed into a geometric algebra. In this work,we introduce a novel geometric algebra-based KG embedding framework, GeomE, which uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.