Compounding Geometric Operations for Knowledge Graph Completion (2023)

Abstract: Geometric transformations including translation, rotation, and scaling are commonly used operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE). Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a composite one, the new model is named CompoundE. By casting CompoundE in the framework of group theory, we show that quite a few distanced-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based scoring functions to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we perform three prevalent KG prediction tasks including link prediction, path query answering, and entity typing, on a range of datasets. CompoundE outperforms extant models consistently, demonstrating its effectiveness and flexibility.

## introduction knowledge graphs (kgs) such as dbpedia @xcite , yago @xcite , nell @xcite , wikidata @xcite , freebase @xcite , and conceptnet @xcite have been created and made available to the public to facilitate research on kg modeling and applications. triples, denoted by (h, r, t), are basic elements of a kg, where h and t are head and tail entities while r is the relation connecting them. kg representation learning, also known as knowledge graph embedding (kge), has been intensively studied in recent years. yet, it remains one of the most fundamental problems in artificial intelligence (ai) research. kge is critical to many downstream applications such as question answering @xcite knowledge integration @xcite ), text analysis @xcite , entity classification @xcite , etc. there are several challenges in the design of good kge models. complex relation patterns (e.g. 1-to-n, n-to-1, and n-to-n, antisymmetric, transitive, hierarchical relations, etc.) remain difficult to model. also, each of extant kge models has its own strengths and weaknesses. it is desired yet unclear how to design a kge model that leverages strengths of some models and complements weaknesses of others. geometric operations such as translation and rotation belong to the family of affine transformations. these operations have been used to build effective kge models such as transe, rotate, and pairre. previous kges often use a single type of operation to model all relation patterns with different properties. this could be problematic since each operator may have modeling limitations. a synergy of different transformations may complement the weaknesses of individual operators. in fact, generic compound operations yielded from a cascade of affine transformations find numerous applications in image processing @xcite , including image warping @xcite , image morphing @xcite , and robot motion planning @xcite . motivated by the synergy, we propose a new kge model to address the above-mentioned challenges. since translation, rotation, and scaling operations are cascaded to form a compound operation, the proposed kge model is named compounde. compound operations inherit many desirable properties from the affine group, allowing compounde to model complex relations in different kgs. there are four main contributions of this work. they are summarized below. the rest of this paper is organized as follows. recent kge models for both distance-based and entity-transformation-based categories are first reviewed in section 2. then, we present compounde, show its relationship with previous kg embedding models, and explain the reason why it can model complex relations well in section 3. experiment details and performance comparisons are given in section 4. finally, concluding remarks are given and possible extensions are suggested in section 5. ## conclusion and future work a new kge model called compounde was proposed in this work. we showed that quite a few distance-based kge models are special cases of compounde. extensive experiments were conducted for three different knowledge graph prediction tasks including link prediction, path query answering, and entity typing. competitive experimental results demonstrate the effectiveness of com-pounde. we also mathematically prove the properties of compounde and its capability of modeling different relation patterns. we also explain the performance difference of different compounde forms, especially for the complex relation patterns. we are interested in exploring two topics as future extensions. first, we may consider more complex operations in compounde. for example, there is a recent trend to extend 2d rotations to 3d rotations for rotation-based embeddings such as ro-tate3d @xcite , su2e @xcite . it is worthwhile to explore compounde3d. second, compounde is expected to be useful in many model ent. emb.