We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding techniques. Initially employing polynomial functions to compute embeddings, we progress to more intricate representations using neural networks with varying layer complexities. We argue that employing functions for embedding computation enhances expressiveness and allows for more degrees of freedom, enabling operations such as composition, derivatives and primitive of entities representation. Additionally, we meticulously outline the step-by-step construction of our approach and provide code for reproducibility, thereby facilitating further exploration and application in the field.

Language Models (LMs) recently incorporate mixture-of-experts layers consisting of a router and a collection of experts to scale up their parameter count given a fixed computational budget. Building on previous efforts indicating that token-expert assignments are predominantly influenced by token identities and positions, we trace routing decisions of similarity-annotated text pairs to evaluate the context sensitivity of learned token-expert assignments. We observe that routing in encoder layers mainly depends on (semantic) associations, but contextual cues provide an additional layer of refinement. Conversely, routing in decoder layers is more variable and markedly less sensitive to context.

Traditional query answering over knowledge graphs -- or broadly over relational data -- is one of the most fundamental problems in data management. Motivated by the incompleteness of modern knowledge graphs, a new setup for query answering has emerged, where the goal is to predict answers that do not necessarily appear in the knowledge graph, but are present in its completion. In this work, we propose AnyCQ, a graph neural network model that can classify answers to any conjunctive query on any knowledge graph, following training. At the core of our framework lies a graph neural network model trained using a reinforcement learning objective to answer Boolean queries. Our approach and problem setup differ from existing query answering studies in multiple dimensions. First, we focus on the problem of query answer classification: given a query and a set of possible answers, classify these proposals as true or false relative to the complete knowledge graph. Second, we study the problem of query answer retrieval: given a query, retrieve an answer to the query relative to the complete knowledge graph or decide that no correct solutions exist. Trained on simple, small instances, AnyCQ can generalize to large queries of arbitrary structure, reliably classifying and retrieving answers to samples where existing approaches fail, which is empirically validated on new and challenging benchmarks. Furthermore, we demonstrate that our AnyCQ models effectively transfer to out-of-distribution knowledge graphs, when equipped with a relevant link predictor, highlighting their potential to serve as a general engine for query answering.

Knowledge graph reasoning plays a vital role in various applications and has garnered considerable attention. Recently, path-based methods have achieved impressive performance. However, they may face limitations stemming from constraints in message-passing neural networks, such as missing paths and information over-squashing. In this paper, we revisit the application of transformers for knowledge graph reasoning to address the constraints faced by path-based methods and propose a novel method KnowFormer.KnowFormer utilizes a transformer architecture to perform reasoning on knowledge graphs from the message-passing perspective, rather than reasoning by textual information like previous pretrained language model based methods. Specifically, we define the attention computation based on the query prototype of knowledge graph reasoning, facilitating convenient construction and efficient optimization. To incorporate structural information into the self-attention mechanism, we introduce structure-aware modules to calculate query, key, and value respectively. Additionally, we present an efficient attention computation method for better scalability. Experimental results demonstrate the superior performance of KnowFormer compared to prominent baseline methods on both transductive and inductive benchmarks.

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.