M\"{o}biusE: Knowledge Graph Embedding on M\"{o}bius Ring

TL;DR

M"{o}biusE introduces a novel knowledge graph embedding method using a M"{o}bius ring, enhancing expressiveness and outperforming previous models like TorusE in key metrics.

Contribution

It proposes a new embedding strategy on M"{o}bius rings that improves expressiveness over TorusE by leveraging nonlinear interactions.

Findings

M"{o}biusE outperforms TorusE in key embedding metrics.

The model demonstrates increased nonlinear representativeness.

Experimental results show superior accuracy in knowledge graph tasks.

Abstract

In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy, called M\"{o}biusE, in which the entities and relations are embedded to the surface of a M\"{o}bius ring. The proposition of such a strategy is inspired by the classic TorusE, in which the addition of two arbitrary elements is subject to a modulus operation. In this sense, TorusE naturally guarantees the critical boundedness of embedding vectors in KGE. However, the nonlinear property of addition operation on Torus ring is uniquely derived by the modulus operation, which in some extent restricts the expressiveness of TorusE. As a further generalization of TorusE, M\"{o}biusE also uses modulus operation to preserve the closeness of addition operation on it, but the coordinates on M\"{o}bius ring interacts with each other in the following way: {\em \color{red} any vector on the surface of a M\"{o}bius ring moves along its parametric trace will goes to the right opposite direction after a cycle}. Hence, M\"{o}biusE assumes much more nonlinear representativeness than that of TorusE, and in turn it generates much more precise embedding results. In our experiments, M\"{o}biusE outperforms TorusE and other classic embedding strategies in several key indicators.