However,itseffectonknowledgegraph completion task remains unknown. We further compare the performance of ConE with one that does not use cone restricted rotation for modeling hierarchical relations, which we name asRotC. ConE w/o rotation is the model that applies restricted rotation in the whole embedding space for hierarchical relations. Due to larger number ofdimensions used persubspace, weuseoverlapping subspace strategytoassign relation-specific subspaces. One of the main benefits of learning embeddings in hyperbolic space is that it can model well even in low embedding dimensionalities.

Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning.

Here we provide theoretical and empirical results to support that ConE's design choice makes sense, i.e., both rotation transformation and restricted transformation play a crucial role to the expressiveness of the model. A.1 Proof for transformations A.1.1 Proof for rotation transformation We will show that the rotation transformation in Eq. 10 can model all relation patterns that can be modeled by its Euclidean counterpart RotatE [7]. Three most common relation patterns are discussed in [7], including symmetry pattern, inverse pattern and composition pattern. Let T denote the set of all true triples. We formally define the three relation patterns as follows.

Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within sequential data, and develop a candidate computational model of how humans detect and understand such structural repeats. Based on a weighted deduction system, our model infers the minimal generative process of a given sequence in the form of a Template program, a formalism that enriches the context-free grammar with repetition combinators. Such representation efficiently encodes the repetition of sub-computations in a recursive manner. As a proof of concept, we demonstrate the expressiveness of our model on short sequences from music and action planning. The proposed model offers broader insights into the mental representations and cognitive mechanisms underlying human pattern recognition.

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to embedding methods. In particular, the geometric distortions that might occur in the representational space have been overlooked in the literature. This work studies the problem of high-dimensional multiplex graph embedding from a geometric perspective. We find that the node representations reside on highly curved manifolds, thus rendering their exploitation more challenging for downstream tasks. Moreover, our study reveals that increasing the number of graph dimensions can cause further distortions to the highly curved manifolds. To address this problem, we propose a novel multiplex graph embedding method that harnesses hierarchical dimension embedding and Hyperbolic Graph Neural Networks. The proposed approach hierarchically extracts hyperbolic node representations that reside on Riemannian manifolds while gradually learning fewer and more expressive latent dimensions of the multiplex graph. Experimental results on real-world high-dimensional multiplex graphs show that the synergy between hierarchical and hyperbolic embeddings incurs much fewer geometric distortions and brings notable improvements over state-of-the-art approaches on downstream tasks.

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.

Topic taxonomy discovery aims at uncovering topics of different abstraction levels and constructing hierarchical relations between them. Unfortunately, most of prior work can hardly model semantic scopes of words and topics by holding the Euclidean embedding space assumption. What's worse, they infer asymmetric hierarchical relations by symmetric distances between topic embeddings. As a result, existing methods suffer from problems of low-quality topics at high abstraction levels and inaccurate hierarchical relations. To alleviate these problems, this paper develops a Box embedding-based Topic Model (BoxTM) that maps words and topics into the box embedding space, where the asymmetric metric is defined to properly infer hierarchical relations among topics. Additionally, our BoxTM explicitly infers upper-level topics based on correlation between specific topics through recursive clustering on topic boxes. Finally, extensive experiments validate high-quality of the topic taxonomy learned by BoxTM.

As large language models (LLMs) are widely deployed, targeted editing of their knowledge has become a critical challenge. Recently, advancements in model editing techniques, such as Rank-One Model Editing (ROME), have paved the way for updating LLMs with new knowledge. However, the efficacy of these methods varies across different types of knowledge. This study investigates the capability of knowledge editing methods to incorporate new knowledge with varying degrees of "perplexingness", a term we use to describe the initial difficulty LLMs have in understanding new concepts. We begin by quantifying the "perplexingness" of target knowledge using pre-edit conditional probabilities, and assess the efficacy of edits through post-edit conditional probabilities. Utilizing the widely-used CounterFact dataset, we find significant negative correlations between the "perplexingness" of the new knowledge and the edit efficacy across all 12 scenarios. To dive deeper into this phenomenon, we introduce a novel dataset, HierarchyData, consisting of 99 hyponym-hypernym pairs across diverse categories. Our analysis reveal that more abstract concepts (hypernyms) tend to be more perplexing than their specific counterparts (hyponyms). Further exploration into the influence of knowledge hierarchy on editing outcomes indicates that knowledge positioned at higher hierarchical levels is more challenging to modify in some scenarios. Our research highlights a previously overlooked aspect of LLM editing: the variable efficacy of editing methods in handling perplexing knowledge. By revealing how hierarchical relationships can influence editing outcomes, our findings offer new insights into the challenges of updating LLMs and pave the way for more nuanced approaches to model editing in the future.

Open-world entity segmentation, as an emerging computer vision task, aims at segmenting entities in images without being restricted by pre-defined classes, offering impressive generalization capabilities on unseen images and concepts. Despite its promise, existing entity segmentation methods like Segment Anything Model (SAM) rely heavily on costly expert annotators. This work presents Self-supervised Open-world Hierarchical Entity Segmentation (SOHES), a novel approach that eliminates the need for human annotations. SOHES operates in three phases: self-exploration, self-instruction, and self-correction. Given a pre-trained self-supervised representation, we produce abundant high-quality pseudo-labels through visual feature clustering. Then, we train a segmentation model on the pseudo-labels, and rectify the noises in pseudo-labels via a teacher-student mutual-learning procedure. Beyond segmenting entities, SOHES also captures their constituent parts, providing a hierarchical understanding of visual entities. Using raw images as the sole training data, our method achieves unprecedented performance in self-supervised open-world segmentation, marking a significant milestone towards high-quality open-world entity segmentation in the absence of human-annotated masks. Project page: https://SOHES.github.io.