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

In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy, called MöbiusE, in which the entities and relations are embedded to the surface of a Möbius 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, MöbiusE also uses modulus operation to preserve the closeness of addition operation on it, but the coordinates on Möbius ring interacts with each other in the following way: any vector on the surface of a Möbius ring moves along its parametric trace will goes to the right opposite direction after a cycle. Hence, MöbiusE assumes much more nonlinear representativeness than that of TorusE, and in turn it generates much more precise embedding results. In our experiments, MöbiusE outperforms TorusE and other classic embedding strategies in several key indicators.