Theorem 1. Suppose that ˆ X In DB models, the commonly used p is either 1 or 2. When p = 2, DURA takes the form as the one in Equation (8) in the main text. If p = 1, we cannot expand the squared score function of the associated DB models as in Equation (4). Therefore, we choose p = 2 . 2 Table 2: Hyperparameters found by grid search. Suppose that k is the number of triplets known to be true in the knowledge graph, n is the embedding dimension of entities. That is to say, the computational complexity of weighted DURA is the same as the weighted squared Frobenius norm regularizer.

However, their performance usually suffers from the overfitting problem seriously.

Figure 1: CLIP fails to accurately capture some fine-grained semantic information.

To show Proposition 1, we need the following defition and lemma. Suppose that K is a proper cone. A sector-cone is always axially symmetric. Therefore, when C is convex, it is axially symmetric. Therefore, a sector-cone is always axially symmetric.

The supplementary material is structured as follows: Section A.1 gives the proof and analysis of Theorem 3.1; Section A.2 introduces the datasets and their statistics in detail; Section A.3 introduces the baselines utilized in experiments; Section A.4 discusses the experimental setup of baseline models as well as MetaTKGR; Section A.5 reports detailed experiment performance with statistical test results; A.1 Statements, Proof and Analysis of Theorem 3.1 Thus, we can improve the generalization ability of our meta-learner over time by the following update step by step, A.2 Datasets Figure 1: Number of entities over time. New entities continuously emerge on three public TKGs. Integrated Crisis Early Warning System (ICEWS18) is the collection of coded interactions between 3 socio-political actors which are extracted from news articles. Y AGO). Figure 1 shows the amount of new entities appearing over time. Figure 2 shows the corresponding distributions.

Since Knowledge Graphs are often incomplete, link prediction methods are adopted for predicting missing facts. Scalable embedding based solutions are mostly adopted for this purpose, however, they lack comprehensibility, which may be crucial in several domains. Explanation methods tackle this issue by identifying supporting knowledge explaining the predicted facts. Regretfully, evaluating/comparing quantitatively the resulting explanations is challenging as there is no standard evaluation protocol and overall benchmarking resource. We fill this important gap by proposing GRainsaCK, a reusable software resource that fully streamlines all the tasks involved in benchmarking explanations, i.e., from model training to evaluation of explanations along the same evaluation protocol. Moreover, GRainsaCK furthers modularity/extensibility by implementing the main components as functions that can be easily replaced. Finally, fostering its reuse, we provide extensive documentation including a tutorial.

Pretraining a language model (LM) on text has been shown to help various downstream NLP tasks. Recent works show that a knowledge graph (KG) can complement text data, offering structured background knowledge that provides a useful scaffold for reasoning. However, these works are not pretrained to learn a deep fusion of the two modalities at scale, limiting the potential to acquire fully joint representations of text and KG. Here we propose DRAGON (Deep Bidirectional Language-Knowledge Graph Pretraining), a self-supervised approach to pretraining a deeply joint language-knowledge foundation model from text and KG at scale. Specifically, our model takes pairs of text segments and relevant KG subgraphs as input and bidirectionally fuses information from both modalities.

Multimodal knowledge graphs (MMKGs) enrich traditional knowledge graphs (KGs) by incorporating diverse modalities such as images and text. multimodal knowledge graph completion (MMKGC) seeks to exploit these heterogeneous signals to infer missing facts, thereby mitigating the intrinsic incompleteness of MMKGs. Existing MMKGC methods typically leverage only the information contained in the MMKGs under the closed-world assumption and adopt discriminative training objectives, which limits their reasoning capacity during completion. Recent large language models (LLMs), empowered by massive parameter scales and pretraining on vast corpora, have demonstrated strong reasoning abilities across various tasks. However, their potential in MMKGC remains largely unexplored. To bridge this gap, we propose HERGC, a flexible Heterogeneous Experts Representation and Generative Completion framework for MMKGs. HERGC first deploys a Heterogeneous Experts Representation Retriever that enriches and fuses multimodal information and retrieves a compact candidate set for each incomplete triple. It then uses a Generative LLM Predictor, implemented via either in-context learning or lightweight fine-tuning, to accurately identify the correct answer from these candidates. Extensive experiments on three standard MMKG benchmarks demonstrate HERGC's effectiveness and robustness, achieving superior performance over existing methods.

Embedding methods have become popular due to their scalability on link prediction and/or triple classification tasks on Knowledge Graphs. Embedding models are trained relying on both positive and negative samples of triples. However, in the absence of negative assertions, these must be usually artificially generated using various negative sampling strategies, ranging from random corruption to more sophisticated techniques which have an impact on the overall performance. Most of the popular libraries for knowledge graph embedding, support only basic such strategies and lack advanced solutions. To address this gap, we deliver an extension for the popular KGE framework PyKEEN that integrates a suite of several advanced negative samplers (including both static and dynamic corruption strategies), within a consistent modular architecture, to generate meaningful negative samples, while remaining compatible with existing PyKEEN -based workflows and pipelines. The developed extension not only enhances PyKEEN itself but also allows for easier and comprehensive development of embedding methods and/or for their customization. As a proof of concept, we present a comprehensive empirical study of the developed extensions and their impact on the performance (link prediction tasks) of different embedding methods, which also provides useful insights for the design of more effective strategies.

Recently, Hyper-relational Knowledge Graphs (HKGs) have been proposed as an extension of traditional Knowledge Graphs (KGs) to better represent real-world facts with additional qualifiers. As a result, researchers have attempted to adapt classical Knowledge Graph Embedding (KGE) models for HKGs by designing extra qualifier processing modules. However, it remains unclear whether the superior performance of Hyper-relational KGE (HKGE) models arises from their base KGE model or the specially designed extension module. Hence, in this paper, we data-wise convert HKGs to KG format using three decomposition methods and then evaluate the performance of several classical KGE models on HKGs. Our results show that some KGE models achieve performance comparable to that of HKGE models. Upon further analysis, we find that the decomposition methods alter the original HKG topology and fail to fully preserve HKG information. Moreover, we observe that current HKGE models are either insufficient in capturing the graph's long-range dependency or struggle to integrate main-triple and qualifier information due to the information compression issue. To further justify our findings and offer a potential direction for future HKGE research, we propose the FormerGNN framework. This framework employs a qualifier integrator to preserve the original HKG topology, and a GNN-based graph encoder to capture the graph's long-range dependencies, followed by an improved approach for integrating main-triple and qualifier information to mitigate compression issues. Our experimental results demonstrate that FormerGNN outperforms existing HKGE models.