Knowledge Graphs (KGs) and their machine learning counterpart, Knowledge Graph Embedding Models (KGEMs), have seen ever-increasing use in a wide variety of academic and applied settings. In particular, KGEMs are typically applied to KGs to solve the link prediction task; i.e. to predict new facts in the domain of a KG based on existing, observed facts. While this approach has been shown substantial power in many end-use cases, it remains incompletely characterised in terms of how KGEMs react differently to KG structure. This is of particular concern in light of recent studies showing that KG structure can be a significant source of bias as well as partially determinant of overall KGEM performance. This paper seeks to address this gap in the state-of-the-art. This paper provides, to the authors' knowledge, the first comprehensive survey exploring established relationships of Knowledge Graph Embedding Models and Graph structure in the literature. It is the hope of the authors that this work will inspire further studies in this area, and contribute to a more holistic understanding of KGs, KGEMs, and the link prediction task.

Knowledge graph embedding models (KGEMs) developed for link prediction learn vector representations for graph entities, known as embeddings. A common tacit assumption is the KGE entity similarity assumption, which states that these KGEMs retain the graph's structure within their embedding space, i.e., position similar entities close to one another. This desirable property make KGEMs widely used in downstream tasks such as recommender systems or drug repurposing. Yet, the alignment of graph similarity with embedding space similarity has rarely been formally evaluated. Typically, KGEMs are assessed based on their sole link prediction capabilities, using ranked-based metrics such as Hits@K or Mean Rank. This paper challenges the prevailing assumption that entity similarity in the graph is inherently mirrored in the embedding space. Therefore, we conduct extensive experiments to measure the capability of KGEMs to cluster similar entities together, and investigate the nature of the underlying factors. Moreover, we study if different KGEMs expose a different notion of similarity. Datasets, pre-trained embeddings and code are available at: https://github.com/nicolas-hbt/similar-embeddings.

Knowledge graph embedding models (KGEMs) have gained considerable traction in recent years. These models learn a vector representation of knowledge graph entities and relations, a.k.a. knowledge graph embeddings (KGEs). Learning versatile KGEs is desirable as it makes them useful for a broad range of tasks. However, KGEMs are usually trained for a specific task, which makes their embeddings task-dependent. In parallel, the widespread assumption that KGEMs actually create a semantic representation of the underlying entities and relations (e.g., project similar entities closer than dissimilar ones) has been challenged. In this work, we design heuristics for generating protographs -- small, modified versions of a KG that leverage RDF/S information. The learnt protograph-based embeddings are meant to encapsulate the semantics of a KG, and can be leveraged in learning KGEs that, in turn, also better capture semantics. Extensive experiments on various evaluation benchmarks demonstrate the soundness of this approach, which we call Modular and Agnostic SCHema-based Integration of protograph Embeddings (MASCHInE). In particular, MASCHInE helps produce more versatile KGEs that yield substantially better performance for entity clustering and node classification tasks. For link prediction, using MASCHinE substantially increases the number of semantically valid predictions with equivalent rank-based performance.

Knowledge graph embedding models (KGEMs) are used for various tasks related to knowledge graphs (KGs), including link prediction. They are trained with loss functions that are computed considering a batch of scored triples and their corresponding labels. Traditional approaches consider the label of a triple to be either true or false. However, recent works suggest that all negative triples should not be valued equally. In line with this recent assumption, we posit that negative triples that are semantically valid w.r.t. domain and range constraints might be high-quality negative triples. As such, loss functions should treat them differently from semantically invalid negative ones. To this aim, we propose semantic-driven versions for the three main loss functions for link prediction. In an extensive and controlled experimental setting, we show that the proposed loss functions systematically provide satisfying results on three public benchmark KGs underpinned with different schemas, which demonstrates both the generality and superiority of our proposed approach. In fact, the proposed loss functions do (1) lead to better MRR and Hits@10 values, (2) drive KGEMs towards better semantic awareness as measured by the Sem@K metric. This highlights that semantic information globally improves KGEMs, and thus should be incorporated into loss functions. Domains and ranges of relations being largely available in schema-defined KGs, this makes our approach both beneficial and widely usable in practice.

Abstract: We show that extending an embedding of a graph Γ in a surface to an embedding of a Hamiltonian supergraph can be blocked by certain planar subgraphs but, for some subdivisions of Γ, Hamiltonian extensions must exist. Abstract: Knowledge graph embedding models (KGEMs) are used for various tasks related to knowledge graphs (KGs), including link prediction. They are trained with loss functions that are computed considering a batch of scored triples and their corresponding labels. Traditional approaches consider the label of a triple to be either true or false. However, recent works suggest that all negative triples should not be valued equally.

Recently, knowledge graph embeddings (KGEs) received significant attention, and several software libraries have been developed for training and evaluating KGEs. While each of them addresses specific needs, we re-designed and re-implemented PyKEEN, one of the first KGE libraries, in a community effort. PyKEEN 1.0 enables users to compose knowledge graph embedding models (KGEMs) based on a wide range of interaction models, training approaches, loss functions, and permits the explicit modeling of inverse relations. Besides, an automatic memory optimization has been realized in order to exploit the provided hardware optimally, and through the integration of Optuna extensive hyper-parameter optimization (HPO) functionalities are provided.