Title: Beyond Link Prediction: On Pre-Training Knowledge Graph Embeddings. Abstract: Knowledge graph embeddings (KGE) models provide low-dimensional representations of the entities and relations in a knowledge graph (KG). Most prior work focused on training and evaluating KGE models for the task of link prediction; the question of whether or not KGE models provide useful representations more generally remains largely open. In this work, we explore the suitability of KGE models (i) for more general graph-structure prediction tasks and (ii) for downstream tasks such as entity classification. For (i), we found that commonly trained KGE models often perform poorly at structural tasks other than link prediction. Based on this observation, we propose a more general multi-task training approach, which includes additional self-supervised tasks such as neighborhood prediction or domain prediction. In our experiments, these multi-task KGE models showed significantly better overall performance for structural prediction tasks. For (ii), we investigate whether KGE models provide useful features for a variety of downstream tasks. Here we view KGE models as a form of self-supervised pre-training and study the impact of both model training and model selection on downstream task performance. We found that multi-task pre-training can (but does not always) significantly improve performance and that KGE models can (but do not always) compete with or even outperform task-specific GNNs trained in a supervised fashion. Our work suggests that more research is needed on how to pre-train KGE models and on their suitability for downstream applications.