Hyper-relational knowledge graphs (HKGs) enrich knowledge graphs by extending a triplet to a hyper-relational fact, where a set of qualifiers adds auxiliary information to a triplet. While many HKG representation learning methods have been proposed, they often fail to effectively utilize the HKG’s structure. This paper demonstrates that thoroughly leveraging the structure of an HKG is crucial for reasoning on HKGs, and a purely structure-based representation learning method can achieve state-of-the-art performance on various link prediction tasks. We propose MAYPL, which learns to initialize representation vectors based on the structure of an HKG and employs an attentive neural message passing consisting of fact-level message computation and entity-centric and relation-centric aggregations, thereby computing the representations based solely on the structure. Due to its structure-driven learning, MAYPL can conduct inductive inferences on new entities and relations. MAYPL outperforms 40 knowledge graph completion methods in 10 datasets, compared with different baseline methods on different datasets to be tested from diverse perspectives.

Inductive knowledge graph completion aims to predict missing triplets in an incomplete knowledge graph that differs from the one observed during training. While subgraph reasoning models have demonstrated empirical success in this task, their theoretical properties, such as stability and generalization capability, remain unexplored. In this work, we present the first theoretical analysis of the relationship between the stability and the generalization capability for subgraph reasoning models. Specifically, we define stability as the degree of consistency in a subgraph reasoning model’s outputs in response to differences in input subgraphs and introduce the Relational Tree Mover’s Distance as a metric to quantify the differences between the subgraphs. We then show that the generalization capability of subgraph reasoning models, defined as the discrepancy between the performance on training data and test data, is proportional to their stability. Furthermore, we empirically analyze the impact of stability on generalization capability using real-world datasets, validating our theoretical findings.

While a number of knowledge graph representation learning (KGRL) methods have been proposed over the past decade, very few theoretical analyses have been conducted on them. In this paper, we present the first PAC-Bayesian generalization bounds for KGRL methods. To analyze a broad class of KGRL models, we propose a generic framework named ReED (Relation-aware Encoder-Decoder), which consists of a relation-aware message passing encoder and a triplet classification decoder. Our ReED framework can express at least 15 different existing KGRL models, including not only graph neural network-based models such as R-GCN and CompGCN but also shallow-architecture models such as RotatE and ANALOGY. Our generalization bounds for the ReED framework provide theoretical grounds for the commonly used tricks in KGRL, e.g., parameter-sharing and weight normalization schemes, and guide desirable design choices for practical KGRL methods. We empirically show that the critical factors in our generalization bounds can explain actual generalization errors on three real-world knowledge graphs.

Inductive knowledge graph completion has been considered as the task of predicting missing triplets between new entities that are not observed during training. While most inductive knowledge graph completion methods assume that all entities can be new, they do not allow new relations to appear at inference time. This restriction prohibits the existing methods from appropriately handling real-world knowledge graphs where new entities accompany new relations. In this paper, we propose an INductive knowledge GRAph eMbedding method, InGram, that can generate embeddings of new relations as well as new entities at inference time. Given a knowledge graph, we define a relation graph as a weighted graph consisting of relations and the affinity weights between them. Based on the relation graph and the original knowledge graph, InGram learns how to aggregate neighboring embeddings to generate relation and entity embeddings using an attention mechanism. Experimental results show that InGram outperforms 14 different state-of-the-art methods on varied inductive learning scenarios.

In a hyper-relational knowledge graph, a triplet can be associated with a set of qualifiers, where a qualifier is composed of a relation and an entity, providing auxiliary information for the triplet. While existing hyper-relational knowledge graph embedding methods assume that the entities are discrete objects, some information should be represented using numeric values, e.g., (J.R.R., was born in, 1892). Also, a triplet (J.R.R., educated at, Oxford Univ.) can be associated with a qualifier such as (start time, 1911). In this paper, we propose a unified framework named HyNT that learns representations of a hyper-relational knowledge graph containing numeric literals in either triplets or qualifiers. We define a context transformer and a prediction transformer to learn the representations based not only on the correlations between a triplet and its qualifiers but also on the numeric information. By learning compact representations of triplets and qualifiers and feeding them into the transformers, we reduce the computation cost of using transformers. Using HyNT, we can predict missing numeric values in addition to missing entities or relations in a hyper-relational knowledge graph. Experimental results show that HyNT significantly outperforms state-of-the-art methods on real-world datasets.