Inthispaper,we first theoretically showthat the transitive relations can be modeled with projections. Wethen propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the aboverelation patterns.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the above relation patterns. Experimental results show that the proposed Rot-Pro model effectively learns the transitivity pattern and achieves the state-of-the-art results on the link prediction task in the datasets containing transitive relations.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities.

Continual Multi-Agent Reinforcement Learning (Co-MARL) requires agents to address catastrophic forgetting issues while learning new coordination policies with the dynamics team. In this paper, we delve into the core of Co-MARL, namely Relation Patterns, which refer to agents' general understanding of interactions. In addition to generality, relation patterns exhibit task-specificity when mapped to different action spaces. To this end, we propose a novel method called General Relation Patterns-Guided Task-Specific Decision-Maker (RPG). In RPG, agents extract relation patterns from dynamic observation spaces using a relation capturer. These task-agnostic relation patterns are then mapped to different action spaces via a task-specific decision-maker generated by a conditional hypernetwork. To combat forgetting, we further introduce regularization items on both the relation capturer and the conditional hypernetwork. Results on SMAC and LBF demonstrate that RPG effectively prevents catastrophic forgetting when learning new tasks and achieves zero-shot generalization to unseen tasks.

Knowledge graphs (KGs), structured as multi-relational data of entities and relations, are vital for tasks like data analysis and recommendation systems. Knowledge graph completion (KGC), or link prediction, addresses incompleteness of KGs by inferring missing triples (h, r, t). It is vital for downstream applications. Region-based embedding models usually embed entities as points and relations as geometric regions to accomplish the task. Despite progress, these models often overlook semantic hierarchies inherent in entities. To solve this problem, we propose SectorE, a novel embedding model in polar coordinates. Relations are modeled as annular sectors, combining modulus and phase to capture inference patterns and relation attributes. Entities are embedded as points within these sectors, intuitively encoding hierarchical structure. Evaluated on FB15k-237, WN18RR, and YAGO3-10, SectorE achieves competitive performance against various kinds of models, demonstrating strengths in semantic modeling capability.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together.

Relation extraction (RE) aims to identify semantic relationships between entities within text. Despite considerable advancements, existing models predominantly require extensive annotated training data, which is both costly and labor-intensive to collect. Moreover, these models often struggle to adapt to new or unseen relations. Few-shot learning, aiming to lessen annotation demands, typically provides incomplete and biased supervision for target relations, leading to degraded and unstable performance. To accurately and explicitly describe relation semantics while minimizing annotation demands, we explore the definition only zero-shot RE setting where only relation definitions expressed in natural language are used to train a RE model. We introduce REPaL, comprising three stages: (1) We leverage large language models (LLMs) to generate initial seed instances from relation definitions and an unlabeled corpus. (2) We fine-tune a bidirectional Small Language Model (SLM) with initial seeds to learn relations for the target domain. (3) We expand pattern coverage and mitigate bias from initial seeds by integrating feedback from the SLM's predictions on the unlabeled corpus and the synthesis history. To accomplish this, we leverage the multi-turn conversation ability of LLMs to generate new instances in follow-up dialogues, informed by both the feedback and synthesis history. Studies reveal that definition-oriented seed synthesis enhances pattern coverage whereas indiscriminately increasing seed quantity leads to performance saturation. Experiments on two datasets show REPaL significantly improved cost-effective zero-shot performance by large margins.

Knowledge Graph Embedding (KGE) techniques play a pivotal role in transforming symbolic Knowledge Graphs (KGs) into numerical representations, thereby enhancing various deep learning models for knowledge-augmented applications. Unlike entities, relations in KGs are the carriers of semantic meaning, and their accurate modeling is crucial for the performance of KGE models. Firstly, we address the complex mapping properties inherent in relations, such as one-to-one, one-to-many, many-to-one, and many-to-many mappings. We provide a comprehensive summary of relation-aware mapping-based models, models that utilize specific representation spaces, tensor decomposition-based models, and neural network-based models. Next, focusing on capturing various relation patterns like symmetry, asymmetry, inversion, and composition, we review models that employ modified tensor decomposition, those based on modified relation-aware mappings, and those that leverage rotation operations. Subsequently, considering the implicit hierarchical relations among entities, we introduce models that incorporate auxiliary information, models based on hyperbolic spaces, and those that utilize the polar coordinate system. Finally, in response to more complex scenarios such as sparse and dynamic KGs, this paper discusses potential future research directions. We explore innovative ideas such as integrating multimodal information into KGE, enhancing relation pattern modeling with rules, and developing models to capture relation characteristics in dynamic KGE settings.

Temporal knowledge graph completion aims to infer the missing facts in temporal knowledge graphs. Current approaches usually embed factual knowledge into continuous vector space and apply geometric operations to learn potential patterns in temporal knowledge graphs. However, these methods only adopt a single operation, which may have limitations in capturing the complex temporal dynamics present in temporal knowledge graphs. Therefore, we propose a simple but effective method, i.e. TCompoundE, which is specially designed with two geometric operations, including time-specific and relation-specific operations. We provide mathematical proofs to demonstrate the ability of TCompoundE to encode various relation patterns. Experimental results show that our proposed model significantly outperforms existing temporal knowledge graph embedding models. Our code is available at https://github.com/nk-ruiying/TCompoundE.

Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this task. This paper advances beyond conventional approaches by introducing more expressive quaternion representations for TKGC within hypercomplex space. Unlike existing quaternion-based methods, our study focuses on capturing time-sensitive relations rather than time-aware entities. Specifically, we model time-sensitive relations through time-aware rotation and periodic time translation, effectively capturing complex temporal variability. Furthermore, we theoretically demonstrate our method's capability to model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns. Comprehensive experiments on public datasets validate that our proposed approach achieves state-of-the-art performance in the field of TKGC.