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The emergence of virtual staining technology provides a rapid and efficient alternative for researchers in tissue pathology. It enables the utilization of unlabeled microscopic samples to generate virtual replicas of chemically stained histological slices, or facilitate the transformation of one staining type into another. The remarkable performance of generative networks, such as CycleGAN, offers an unsupervised learning approach for virtual coloring, overcoming the limitations of high-quality paired data required in supervised learning. Nevertheless, large-scale color transformation necessitates processing large field-of-view images in patches, often resulting in significant boundary inconsistency and artifacts. Additionally, the transformation between different colorized modalities typically needs further efforts to modify loss functions and tune hyperparameters for independent training of networks. In this study, we introduce a general virtual staining framework that is adaptable to various conditions. We propose a loss function based on the value mapping constraint to ensure the accuracy of virtual coloring between different pathological modalities, termed the Value Mapping Generative Adversarial Network (VM-GAN). Meanwhile, we present a confidence-based tiling method to address the challenge of boundary inconsistency arising from patch-wise processing. Experimental results on diverse data with varying staining protocols demonstrate that our method achieves superior quantitative indicators and improved visual perception.

Preference learning is a widely adopted post-training technique that aligns large language models (LLMs) to human preferences and improves specific downstream task capabilities. In this work we systematically investigate how specific attributes of preference datasets affect the alignment and downstream performance of LLMs in instruction-following tasks. We use a novel synthetic data generation pipeline to generate 48,000 unique instruction-following prompts with combinations of 23 verifiable constraints that enable fine-grained and automated quality assessments of model responses. With our synthetic prompts, we use two preference dataset curation methods - rejection sampling (RS) and Monte Carlo Tree Search (MCTS) - to obtain pairs of (chosen, rejected) responses. Then, we perform experiments investigating the effects of (1) the presence of shared prefixes between the chosen and rejected responses, (2) the contrast and quality of the chosen, rejected responses and (3) the complexity of the training prompts. Our experiments reveal that shared prefixes in preference pairs, as generated by MCTS, provide marginal but consistent improvements and greater stability across challenging training configurations. High-contrast preference pairs generally outperform low-contrast pairs; however, combining both often yields the best performance by balancing diversity and learning efficiency. Additionally, training on prompts of moderate difficulty leads to better generalization across tasks, even for more complex evaluation scenarios, compared to overly challenging prompts. Our findings provide actionable insights into optimizing preference data curation for instruction-following tasks, offering a scalable and effective framework for enhancing LLM training and alignment., Comment: 23 pages

Predicting answers to queries over knowledge graphs is called a complex reasoning task because answering a query requires subdividing it into subqueries. Existing query embedding methods use this decomposition to compute the embedding of a query as the combination of the embedding of the subqueries. This requirement limits the answerable queries to queries having a single free variable and being decomposable, which are called tree-form queries and correspond to the $\mathcal{SROI}^-$ description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the $\mathcal{ALCOIR}$ description logic, propose a query embedding method for them, called DAGE, and a new benchmark to evaluate query embeddings on them. Given the computational graph of a DAG query, DAGE combines the possibly multiple paths between two nodes into a single path with a trainable operator that represents the intersection of relations and learns DAG-DL from tautologies. We show that it is possible to implement DAGE on top of existing query embedding methods, and we empirically measure the improvement of our method over the results of vanilla methods evaluated in tree-form queries that approximate the DAG queries of our proposed benchmark.

Despite the remarkable success of deep neural networks (DNNs) in computer vision, they fail to remain high-performing when facing distribution shifts between training and testing data. In this paper, we propose Knowledge-Guided Visual representation learning (KGV), a distribution-based learning approach leveraging multi-modal prior knowledge, to improve generalization under distribution shift. We use prior knowledge from two distinct modalities: 1) a knowledge graph (KG) with hierarchical and association relationships; and 2) generated synthetic images of visual elements semantically represented in the KG. The respective embeddings are generated from the given modalities in a common latent space, i.e., visual embeddings from original and synthetic images as well as knowledge graph embeddings (KGEs). These embeddings are aligned via a novel variant of translation-based KGE methods, where the node and relation embeddings of the KG are modeled as Gaussian distributions and translations respectively. We claim that incorporating multi-model prior knowledge enables more regularized learning of image representations. Thus, the models are able to better generalize across different data distributions. We evaluate KGV on different image classification tasks with major or minor distribution shifts, namely road sign classification across datasets from Germany, China, and Russia, image classification with the mini-ImageNet dataset and its variants, as well as the DVM-CAR dataset. The results demonstrate that KGV consistently exhibits higher accuracy and data efficiency than the baselines across all experiments.

Complex query answering (CQA) on knowledge graphs (KGs) is gaining momentum as a challenging reasoning task. In this paper, we show that the current benchmarks for CQA are not really complex, and the way they are built distorts our perception of progress in this field. For example, we find that in these benchmarks, most queries (up to 98% for some query types) can be reduced to simpler problems, e.g., link prediction, where only one link needs to be predicted. The performance of state-of-the-art CQA models drops significantly when such models are evaluated on queries that cannot be reduced to easier types. Thus, we propose a set of more challenging benchmarks, composed of queries that require models to reason over multiple hops and better reflect the construction of real-world KGs. In a systematic empirical investigation, the new benchmarks show that current methods leave much to be desired from current CQA methods.

Silicon modulators have garnered considerable attention owing to their potential applications in high-density integration and high-speed modulation. However, they are increasingly challenged by the limited 3 dB bandwidth as the demand for modulation speed in optical communications continues to rise, impeding their ability to compete with modulators made of thin-film lithium niobate. This bandwidth limitation arises because of the parasitic resistance and capacitance in the PN junction of the silicon modulators. This study demonstrates the first silicon modulator exceeding 110 GHz without any resonant structure using a tunable time-frequency equalization technique. This substantial breakthrough enables on-off keying modulation at a rate of 140 Gbaud without digital signal processing. These accomplishments represent the highest bandwidth and maximum baud rate achieved without digital signal processing in an all-silicon modulator, reaching the testing limitations of the experimental system. This opens the possibility of attaining modulation rates of up to 200 or even 300 Gbaud by adopting design strategies such as slow light and technologies such as digital signal processing. This advancement extends the speed capabilities of silicon modulators to the level of thin-film lithium niobate modulators, thereby promoting their application in the broader array of fields, such as linear-drive pluggable transceivers.

Large language models (LLMs) have demonstrated remarkable performance on various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for embedding tokens in LLMs. In this study, we first investigate the non-Euclidean characteristics of LLMs. Our findings reveal that token frequency follows a power-law distribution, with high-frequency tokens clustering near the origin and low-frequency tokens positioned farther away. Additionally, token embeddings exhibit a high degree of hyperbolicity, indicating a latent tree-like structure in the embedding space. Building on the observation, we propose to efficiently fine-tune LLMs in hyperbolic space to better exploit the underlying complex structures. However, we found that this fine-tuning in hyperbolic space cannot be achieved with naive application of exponential and logarithmic maps, when the embedding and weight matrices both reside in Euclidean space. To address this technique issue, we introduce a new method called hyperbolic low-rank efficient fine-tuning, HypLoRA, that performs low-rank adaptation directly on the hyperbolic manifold, avoiding the cancellation effect caused by the exponential and logarithmic maps, thus preserving the hyperbolic modeling capabilities. Through extensive experiments, we demonstrate that HypLoRA significantly enhances the performance of LLMs on reasoning tasks, particularly for complex reasoning problems. In particular, HypLoRA improves the performance in the complex AQuA dataset by up to 13.0%, showcasing its effectiveness in handling complex reasoning challenges, Comment: The preliminary work was accepted for the ICML 2024 LLM Cognition Workshop, and this version includes new investigations, analyses, experiments, and results

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., Comment: Doctoral Dissertation, 177 pages

The important challenge of keeping knowledge in Large Language Models (LLMs) up-to-date has led to the development of various methods for incorporating new facts. However, existing methods for such knowledge editing still face difficulties with multi-hop questions that require accurate fact identification and sequential logical reasoning, particularly among numerous fact updates. To tackle these challenges, this paper introduces Graph Memory-based Editing for Large Language Models (GMeLLo), a straightforward and effective method that merges the explicit knowledge representation of Knowledge Graphs (KGs) with the linguistic flexibility of LLMs. Beyond merely leveraging LLMs for question answering, GMeLLo employs these models to convert free-form language into structured queries and fact triples, facilitating seamless interaction with KGs for rapid updates and precise multi-hop reasoning. Our results show that GMeLLo significantly surpasses current state-of-the-art (SOTA) knowledge editing methods in the multi-hop question answering benchmark, MQuAKE, especially in scenarios with extensive knowledge edits.

LiNbO3 (LN) is renowned for its exceptional ferroelectric properties, particularly its notable linear electro-optical (EO) effect, which is highly advantageous for various applications such as high-speed communication, optical computation, and quantum information processing. Compared to its ferroelectric properties, the magnetism of LN is not attractive enough due to its weak ferromagnetic nature. Theoretical studies suggest that LN may exhibit a novel magnetoelectric coupling via ferroelectrically-induced ferromagnetism. However, this mechanism has not yet been experimentally validated in any materials, presenting significant challenges for research. In this study, we provide the first experimental evidence supporting the mechanism of ferroelectrically-induced ferromagnetism in LN, including observations of the Dzyaloshinskii-Moriya interaction (DMI) and magnetoelectric coupling. Additionally, we have identified various multiferroic skyrmions, within which ferroelectric polarization signals are detectable. These signals can be influenced by the magnetic vortex structures, indicating a magnetoelectric coupling nature. Currently, they are the only multiferroic skyrmions that can keep stable at room temperature. Moreover, these magnetic textures significantly affect the ferroelectric properties, as demonstrated by an enhancement of the linear electro-optic effect of LN by over 200%. Given the novel magnetoelectric coupling mechanism, the potential of multiferroic skyrmions in spintronics and advanced data storage, and the extensive use of LN EO modulators, our research has significant implications for condensed matter physics, multiferroic materials, and optoelectronics.

Knowledge graph embeddings (KGE) apply machine learning methods on knowledge graphs (KGs) to provide non-classical reasoning capabilities based on similarities and analogies. The learned KG embeddings are typically used to answer queries by ranking all potential answers, but rankings often lack a meaningful probabilistic interpretation - lower-ranked answers do not necessarily have a lower probability of being true. This limitation makes it difficult to quantify uncertainty of model's predictions, posing challenges for the application of KGE methods in high-stakes domains like medicine. We address this issue by applying the theory of conformal prediction that allows generating answer sets, which contain the correct answer with probabilistic guarantees. We explain how conformal prediction can be used to generate such answer sets for link prediction tasks. Our empirical evaluation on four benchmark datasets using six representative KGE methods validates that the generated answer sets satisfy the probabilistic guarantees given by the theory of conformal prediction. We also demonstrate that the generated answer sets often have a sensible size and that the size adapts well with respect to the difficulty of the query., Comment: Accepted as a main conference paper at NAACL 2025

Knowledge graph embedding (KGE) models are often used to predict missing links for knowledge graphs (KGs). However, multiple KG embeddings can perform almost equally well for link prediction yet give conflicting predictions for unseen queries. This phenomenon is termed \textit{predictive multiplicity} in the literature. It poses substantial risks for KGE-based applications in high-stake domains but has been overlooked in KGE research. We define predictive multiplicity in link prediction, introduce evaluation metrics and measure predictive multiplicity for representative KGE methods on commonly used benchmark datasets. Our empirical study reveals significant predictive multiplicity in link prediction, with $8\%$ to $39\%$ testing queries exhibiting conflicting predictions. We address this issue by leveraging voting methods from social choice theory, significantly mitigating conflicts by $66\%$ to $78\%$ in our experiments., Comment: Accepted as EMNLP'24 Finding

Graph neural networks (GNNs) have achieved significant success in various applications. Most GNNs learn the node features with information aggregation of its neighbors and feature transformation in each layer. However, the node features become indistinguishable after many layers, leading to performance deterioration: a significant limitation known as over-smoothing. Past work adopted various techniques for addressing this issue, such as normalization and skip-connection of layer-wise output. After the study, we found that the information aggregations in existing work are all contracted aggregations, with the intrinsic property that features will inevitably converge to the same single point after many layers. To this end, we propose the aggregation over compacted manifolds method (ACM) that replaces the existing information aggregation with aggregation over compact manifolds, a special type of manifold, which avoids contracted aggregations. In this work, we theoretically analyze contracted aggregation and its properties. We also provide an extensive empirical evaluation that shows ACM can effectively alleviate over-smoothing and outperforms the state-of-the-art. The code can be found in https://github.com/DongzhuoranZhou/ACM.git., Comment: This paper has been accepted by PAKDD 2024 as an oral presentation

Statistical information is ubiquitous but drawing valid conclusions from it is prohibitively hard. We explain how knowledge graph embeddings can be used to approximate probabilistic inference efficiently using the example of Statistical EL (SEL), a statistical extension of the lightweight Description Logic EL. We provide proofs for runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach., Comment: under review

Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of $SROI^-$ description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a $SROI^-$ description logic concept. Every $SROI^-$ concept is embedded as a cone in complex vector space, and each $SROI^-$ relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn $SROI^-$ axioms, and defines an algebra whose operations correspond one to one to $SROI^-$ description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering., Comment: Accepted by ECAI 2024

Lithium Niobate (LN) is a ferroelectric material with exceptional electrical characteristics, including high piezoelectricity, high Pockels effect, etc. These properties make it a promising platform for numerous fields such as high-speed communication, optical computation, and quantum information processing. Besides these, the introduction of magnetic structures to LN holds significant potential to achieve magnetoelectric coupling, which can be applied in magnetic memory and data-processing devices with high efficiency. Here, for the first time, we observe a special topological magnetic structure called magnetic skyrmion in LN (SK-LN) by the combination of magnetic field annealing and rapid annealing processes . Compared to the magnetic skyrmions reported in magnetic systems, SK-LN exhibit exceptionally high stability. Additionally, the center of the magnetic vortex exhibits spontaneous ferroelectric polarization, indicating its multiferroic characteristic. With the excitation of these multiferroic skyrmions, the modulation efficiency of the electro-optical (EO) modulator fabricated on thin film lithium niobate on insulator (LNOI) wafer was found to be enhanced from 1.98 V*cm to 0.63 V*cm. It is considered that the multiferroic skyrmions significantly enhance the Pockels coefficient of LN to 101 pm/V, nearly three times the result (32pm/V) reported previously.

Recently, MBConv blocks, initially designed for efficiency in resource-limited settings and later adapted for cutting-edge image classification performances, have demonstrated significant potential in image classification tasks. Despite their success, their application in semantic segmentation has remained relatively unexplored. This paper introduces a novel adaptation of MBConv blocks specifically tailored for semantic segmentation. Our modification stems from the insight that semantic segmentation requires the extraction of more detailed spatial information than image classification. We argue that to effectively perform multi-scale semantic segmentation, each branch of a U-Net architecture, regardless of its resolution, should possess equivalent segmentation capabilities. By implementing these changes, our approach achieves impressive mean Intersection over Union (IoU) scores of 84.5% and 84.0% on the Cityscapes test and validation datasets, respectively, demonstrating the efficacy of our proposed modifications in enhancing semantic segmentation performance.

Reasoning with knowledge graphs (KGs) has primarily focused on triple-shaped facts. Recent advancements have been explored to enhance the semantics of these facts by incorporating more potent representations, such as hyper-relational facts. However, these approaches are limited to \emph{atomic facts}, which describe a single piece of information. This paper extends beyond \emph{atomic facts} and delves into \emph{nested facts}, represented by quoted triples where subjects and objects are triples themselves (e.g., ((\emph{BarackObama}, \emph{holds\_position}, \emph{President}), \emph{succeed\_by}, (\emph{DonaldTrump}, \emph{holds\_position}, \emph{President}))). These nested facts enable the expression of complex semantics like \emph{situations} over time and \emph{logical patterns} over entities and relations. In response, we introduce NestE, a novel KG embedding approach that captures the semantics of both atomic and nested factual knowledge. NestE represents each atomic fact as a $1\times3$ matrix, and each nested relation is modeled as a $3\times3$ matrix that rotates the $1\times3$ atomic fact matrix through matrix multiplication. Each element of the matrix is represented as a complex number in the generalized 4D hypercomplex space, including (spherical) quaternions, hyperbolic quaternions, and split-quaternions. Through thorough analysis, we demonstrate the embedding's efficacy in capturing diverse logical patterns over nested facts, surpassing the confines of first-order logic-like expressions. Our experimental results showcase NestE's significant performance gains over current baselines in triple prediction and conditional link prediction. The code and pre-trained models are open available at https://github.com/xiongbo010/NestE., Comment: The 38th Annual AAAI Conference on Artificial Intelligence (AAAI'24)

Modeling evolving knowledge over temporal knowledge graphs (TKGs) has become a heated topic. Various methods have been proposed to forecast links on TKGs. Most of them are embedding-based, where hidden representations are learned to represent knowledge graph (KG) entities and relations based on the observed graph contexts. Although these methods show strong performance on traditional TKG forecasting (TKGF) benchmarks, they face a strong challenge in modeling the unseen zero-shot relations that have no prior graph context. In this paper, we try to mitigate this problem as follows. We first input the text descriptions of KG relations into large language models (LLMs) for generating relation representations, and then introduce them into embedding-based TKGF methods. LLM-empowered representations can capture the semantic information in the relation descriptions. This makes the relations, whether seen or unseen, with similar semantic meanings stay close in the embedding space, enabling TKGF models to recognize zero-shot relations even without any observed graph context. Experimental results show that our approach helps TKGF models to achieve much better performance in forecasting the facts with previously unseen relations, while still maintaining their ability in link forecasting regarding seen relations., Comment: Accepted to NAACL 2024 main conference

We study the buildup of antiferromagnetic (AF) correlation in the dynamically tuned Ising models which are realized by the Rydberg atomic system. In short-time scale, we apply Magnus expansion (ME) to derive the high-order analytic expression of the connected correlation functions and compare it with exactly numerical results for the different lattice geometries, e.g., 1D chain, $2 \times n$ lattice, and $n \times n$ lattice. It is shown that the high-order expansion is required to describe accurately the buildup of AF correlation in the quench dynamics. Moreover, through a 2D square lattice, we find that the magnitude of AF correlation for the same Manhattan distance is proportional to the number of the shortest paths in a sufficiently long time until long and distinct paths are involved significantly with the buildup of the correlation. Finally, we propose an applicable experimental setup to realize our findings., Comment: 8 pages of RevTex4-2, 7 figures

Computed Tomography (CT) with its remarkable capability for three-dimensional imaging from multiple projections, enjoys a broad range of applications in clinical diagnosis, scientific observation, and industrial detection. Neural Adaptive Tomography (NeAT) is a recently proposed 3D rendering method based on neural radiance field for CT, and it demonstrates superior performance compared to traditional methods. However, it still faces challenges when dealing with the substantial perturbations and pose shifts encountered in CT scanning processes. Here, we propose a neural rendering method for CT reconstruction, named Iterative Neural Adaptive Tomography (INeAT), which incorporates iterative posture optimization to effectively counteract the influence of posture perturbations in data, particularly in cases involving significant posture variations. Through the implementation of a posture feedback optimization strategy, INeAT iteratively refines the posture corresponding to the input images based on the reconstructed 3D volume. We demonstrate that INeAT achieves artifact-suppressed and resolution-enhanced reconstruction in scenarios with significant pose disturbances. Furthermore, we show that our INeAT maintains comparable reconstruction performance to stable-state acquisitions even using data from unstable-state acquisitions, which significantly reduces the time required for CT scanning and relaxes the stringent requirements on imaging hardware systems, underscoring its immense potential for applications in short-time and low-cost CT technology.

Light-field fluorescence microscopy (LFM) is a powerful elegant compact method for long-term high-speed imaging of complex biological systems, such as neuron activities and rapid movements of organelles. LFM experiments typically generate terabytes image data and require a huge number of storage space. Some lossy compression algorithms have been proposed recently with good compression performance. However, since the specimen usually only tolerates low power density illumination for long-term imaging with low phototoxicity, the image signal-to-noise ratio (SNR) is relative-ly low, which will cause the loss of some efficient position or intensity information by using such lossy compression al-gorithms. Here, we propose a phase-space continuity enhanced bzip2 (PC-bzip2) lossless compression method for LFM data as a high efficiency and open-source tool, which combines GPU-based fast entropy judgement and multi-core-CPU-based high-speed lossless compression. Our proposed method achieves almost 10% compression ratio improvement while keeping the capability of high-speed compression, compared with original bzip2. We evaluated our method on fluorescence beads data and fluorescence staining cells data with different SNRs. Moreover, by introducing the temporal continuity, our method shows the superior compression ratio on time series data of zebrafish blood vessels.

Logical rules are essential for uncovering the logical connections between relations, which could improve reasoning performance and provide interpretable results on knowledge graphs (KGs). Although there have been many efforts to mine meaningful logical rules over KGs, existing methods suffer from computationally intensive searches over the rule space and a lack of scalability for large-scale KGs. Besides, they often ignore the semantics of relations which is crucial for uncovering logical connections. Recently, large language models (LLMs) have shown impressive performance in the field of natural language processing and various applications, owing to their emergent ability and generalizability. In this paper, we propose a novel framework, ChatRule, unleashing the power of large language models for mining logical rules over knowledge graphs. Specifically, the framework is initiated with an LLM-based rule generator, leveraging both the semantic and structural information of KGs to prompt LLMs to generate logical rules. To refine the generated rules, a rule ranking module estimates the rule quality by incorporating facts from existing KGs. Last, the ranked rules can be used to conduct reasoning over KGs. ChatRule is evaluated on four large-scale KGs, w.r.t. different rule quality metrics and downstream tasks, showing the effectiveness and scalability of our method., Comment: 11 pages, 4 figures

Temporal characteristics are prominently evident in a substantial volume of knowledge, which underscores the pivotal role of Temporal Knowledge Graphs (TKGs) in both academia and industry. However, TKGs often suffer from incompleteness for three main reasons: the continuous emergence of new knowledge, the weakness of the algorithm for extracting structured information from unstructured data, and the lack of information in the source dataset. Thus, the task of Temporal Knowledge Graph Completion (TKGC) has attracted increasing attention, aiming to predict missing items based on the available information. In this paper, we provide a comprehensive review of TKGC methods and their details. Specifically, this paper mainly consists of three components, namely, 1)Background, which covers the preliminaries of TKGC methods, loss functions required for training, as well as the dataset and evaluation protocol; 2)Interpolation, that estimates and predicts the missing elements or set of elements through the relevant available information. It further categorizes related TKGC methods based on how to process temporal information; 3)Extrapolation, which typically focuses on continuous TKGs and predicts future events, and then classifies all extrapolation methods based on the algorithms they utilize. We further pinpoint the challenges and discuss future research directions of TKGC.

The combination of multi-component Bose-Einstein condensates (BECs) and phase imprinting techniques provides an ideal platform for exploring nonlinear dynamics and investigating the quantum transport properties of superfluids. In this paper, we study abundant density structures and corresponding dynamics of phase-separated binary Bose-Einstein condensates with phase-imprinted single vortex or vortex dipole. By adjusting the ratio between the interspecies and intraspecies interactions, and the locations of the phase singularities, the typical density profiles such as ball-shell structures, crescent-gibbous structures, Matryoshka-like structures, sector-sector structures and sandwich-type structures appear, and the phase diagrams are obtained. The dynamics of these structures exhibit diverse properties, including the penetration of vortex dipoles, emergence of half-vortex dipoles, co-rotation of sectors, and oscillation between sectors. The pinning effects induced by a potential defect are also discussed, which is useful for controlling and manipulating individual quantum states.

Link prediction on knowledge graphs (KGs) has been extensively studied on binary relational KGs, wherein each fact is represented by a triple. A significant amount of important knowledge, however, is represented by hyper-relational facts where each fact is composed of a primal triple and a set of qualifiers comprising a key-value pair that allows for expressing more complicated semantics. Although some recent works have proposed to embed hyper-relational KGs, these methods fail to capture essential inference patterns of hyper-relational facts such as qualifier monotonicity, qualifier implication, and qualifier mutual exclusion, limiting their generalization capability. To unlock this, we present \emph{ShrinkE}, a geometric hyper-relational KG embedding method aiming to explicitly model these patterns. ShrinkE models the primal triple as a spatial-functional transformation from the head into a relation-specific box. Each qualifier ``shrinks'' the box to narrow down the possible answer set and, thus, realizes qualifier monotonicity. The spatial relationships between the qualifier boxes allow for modeling core inference patterns of qualifiers such as implication and mutual exclusion. Experimental results demonstrate ShrinkE's superiority on three benchmarks of hyper-relational KGs., Comment: To appear in ACL 2023