Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.

The Knowledge Graph-to-Text Generation task aims to convert structured knowledge graphs into coherent and human-readable natural language text. Recent efforts in this field have focused on enhancing pre-trained language models (PLMs) by incorporating graph structure information to capture the intricate structure details of knowledge graphs. However, most of these approaches tend to capture only single-granularity structure information, concentrating either on the relationships between entities within the original graph or on the relationships between words within the same entity or across different entities. This narrow focus results in a significant limitation: models that concentrate solely on entity-level structure fail to capture the nuanced semantic relationships between words, while those that focus only on word-level structure overlook the broader relationships between original entire entities. To overcome these limitations, this paper introduces the Multi-granularity Graph Structure Attention (MGSA), which is based on PLMs. The encoder of the model architecture features an entity-level structure encoding module, a word-level structure encoding module, and an aggregation module that synthesizes information from both structure. This multi-granularity structure encoding approach allows the model to simultaneously capture both entity-level and word-level structure information, providing a more comprehensive understanding of the knowledge graph's structure information, thereby significantly improving the quality of the generated text. We conducted extensive evaluations of the MGSA model using two widely recognized KG-to-Text Generation benchmark datasets, WebNLG and EventNarrative, where it consistently outperformed models that rely solely on single-granularity structure information, demonstrating the effectiveness of our approach.

Causal networks are often incomplete with missing causal links. This is due to various issues, such as missing observation data. Recent approaches to the issue of incomplete causal networks have used knowledge graph link prediction methods to find the missing links. In the causal link A causes B causes C, the influence of A to C is influenced by B which is known as a mediator. Existing approaches using knowledge graph link prediction do not consider these mediated causal links. This paper presents HyperCausalLP, an approach designed to find missing causal links within a causal network with the help of mediator links. The problem of missing links is formulated as a hyper-relational knowledge graph completion. The approach uses a knowledge graph link prediction model trained on a hyper-relational knowledge graph with the mediators. The approach is evaluated on a causal benchmark dataset, CLEVRER-Humans. Results show that the inclusion of knowledge about mediators in causal link prediction using hyper-relational knowledge graph improves the performance on an average by 5.94% mean reciprocal rank.

We consider fact-checking approaches that aim to predict the veracity of assertions in knowledge graphs. Five main categories of fact-checking approaches for knowledge graphs have been proposed in the recent literature, of which each is subject to partially overlapping limitations. In particular, current text-based approaches are limited by manual feature engineering. Path-based and rule-based approaches are limited by their exclusive use of knowledge graphs as background knowledge, and embedding-based approaches suffer from low accuracy scores on current fact-checking tasks. We propose a hybrid approach -- dubbed HybridFC -- that exploits the diversity of existing categories of fact-checking approaches within an ensemble learning setting to achieve a significantly better prediction performance. In particular, our approach outperforms the state of the art by 0.14 to 0.27 in terms of Area Under the Receiver Operating Characteristic curve on the FactBench dataset. Our code is open-source and can be found at https://github.com/dice-group/HybridFC.

Knowledge graph embedding (KGE) constitutes a foundational task, directed towards learning representations for entities and relations within knowledge graphs (KGs), with the objective of crafting representations comprehensive enough to approximate the logical and symbolic interconnections among entities. In this paper, we define a metric Z-counts to measure the difficulty of training each triple ($<$head entity, relation, tail entity$>$) in KGs with theoretical analysis. Based on this metric, we propose \textbf{CL4KGE}, an efficient \textbf{C}urriculum \textbf{L}earning based training strategy for \textbf{KGE}. This method includes a difficulty measurer and a training scheduler that aids in the training of KGE models. Our approach possesses the flexibility to act as a plugin within a wide range of KGE models, with the added advantage of adaptability to the majority of KGs in existence. The proposed method has been evaluated on popular KGE models, and the results demonstrate that it enhances the state-of-the-art methods. The use of Z-counts as a metric has enabled the identification of challenging triples in KGs, which helps in devising effective training strategies.

Knowledge graphs (KGs) have recently been used for many tools and applications, making them rich resources in structured format. However, in the real world, KGs grow due to the additions of new knowledge in the form of entities and relations, making these KGs dynamic. This chapter formally defines several types of dynamic KGs and summarizes how these KGs can be represented. Additionally, many neurosymbolic methods have been proposed for learning representations over static KGs for several tasks such as KG completion and entity alignment. This chapter further focuses on neurosymbolic methods for dynamic KGs with or without temporal information. More specifically, it provides an insight into neurosymbolic methods for dynamic (temporal or non-temporal) KG completion and entity alignment tasks. It further discusses the challenges of current approaches and provides some future directions.

Knowledge Graph Completion has been increasingly adopted as a useful method for several tasks in biomedical research, like drug repurposing or drug-target identification. To that end, a variety of datasets and Knowledge Graph Embedding models has been proposed over the years. However, little is known about the properties that render a dataset useful for a given task and, even though theoretical properties of Knowledge Graph Embedding models are well understood, their practical utility in this field remains controversial. We conduct a comprehensive investigation into the topological properties of publicly available biomedical Knowledge Graphs and establish links to the accuracy observed in real-world applications. By releasing all model predictions and a new suite of analysis tools we invite the community to build upon our work and continue improving the understanding of these crucial applications.

Recommendation systems play a crucial role in helping users filter through vast amounts of information. However, traditional recommendation algorithms often overlook the integration and utilization of multi-source information, limiting system performance. Therefore, this study proposes a novel recommendation model, Knowledge Graph Attention-assisted Network (KGAT-AX). We first incorporate the knowledge graph into the recommendation model, introducing an attention mechanism to explore higher order connectivity more explicitly. By using multilayer interactive information propagation, the model aggregates information to enhance its generalization ability. Furthermore, we integrate auxiliary information into entities through holographic embeddings, aggregating the information of adjacent entities for each entity by learning their inferential relationships. This allows for better utilization of auxiliary information associated with entities. We conducted experiments on real datasets to demonstrate the rationality and effectiveness of the KGAT-AX model. Through experimental analysis, we observed the effectiveness and potential of KGAT-AX compared to other baseline models on public datasets. KGAT-AX demonstrates better knowledge information capture and relationship learning capabilities.

Recently, there has been an increasing interest in the construction of general-domain and domain-specific causal knowledge graphs. Such knowledge graphs enable reasoning for causal analysis and event prediction, and so have a range of applications across different domains. While great progress has been made toward automated construction of causal knowledge graphs, the evaluation of such solutions has either focused on low-level tasks (e.g., cause-effect phrase extraction) or on ad hoc evaluation data and small manual evaluations. In this Resource Track paper, we present a corpus, task, and evaluation framework for causal knowledge graph construction. Our corpus consists of Wikipedia articles for a collection of event-related concepts in Wikidata. The task is to extract causal relations between event concepts from the corpus. The evaluation is performed in part using existing causal relations in Wikidata to measure recall, and in part using Large Language Models to avoid the need for manual or crowd-sourced evaluation. We evaluate a pipeline for causal knowledge graph construction that relies on neural models for question answering and concept linking, and show how the corpus and the evaluation framework allow us to effectively find the right model for each task. The corpus and the evaluation framework are publicly available.

Temporal knowledge graph (TKG) reasoning predicts future events based on historical data, but it's challenging due to the complex semantic and hierarchical information involved. Existing Euclidean models excel at capturing semantics but struggle with hierarchy. Conversely, hyperbolic models manage hierarchical features well but fail to represent complex semantics due to limitations in shallow models' parameters and the absence of proper normalization in deep models relying on the L2 norm. Current solutions, as curvature transformations, are insufficient to address these issues. In this work, a novel hybrid geometric space approach that leverages the strengths of both Euclidean and hyperbolic models is proposed. Our approach transitions from single-space to multi-space parameter modeling, effectively capturing both semantic and hierarchical information. Initially, complex semantics are captured through a fact co-occurrence and autoregressive method with normalizations in Euclidean space. The embeddings are then transformed into Tangent space using a scaling mechanism, preserving semantic information while relearning hierarchical structures through a query-candidate separated modeling approach, which are subsequently transformed into Hyperbolic space. Finally, a hybrid inductive bias for hierarchical and semantic learning is achieved by combining hyperbolic and Euclidean scoring functions through a learnable query-specific mixing coefficient, utilizing embeddings from hyperbolic and Euclidean spaces. Experimental results on four TKG benchmarks demonstrate that our method reduces error relatively by up to 15.0% in mean reciprocal rank on YAGO compared to previous single-space models. Additionally, enriched visualization analysis validates the effectiveness of our approach, showing adaptive capabilities for datasets with varying levels of semantic and hierarchical complexity.