相关论文: Generalization Error Bound for Hyperbolic Ordinal …

Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation…

Hyperbolic representations have shown remarkable efficacy in modeling inherent hierarchies and complexities within data structures. Hyperbolic neural networks have been commonly applied for learning such representations from data, but they…

Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…

Temporal heterogeneous information network (temporal HIN) embedding, aiming to represent various types of nodes of different timestamps into low dimensional spaces while preserving structural and semantic information, is of vital importance…

We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…

Recently, tight-binding models on hyperbolic lattices (discretized AdS space) have gained significant attention, leading to hyperbolic band theory and non-Abelian Bloch states. In this paper, we investigate these quantum systems from the…

Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit…

Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…

Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN…

Bayesian optimization (BO) is one of the most powerful strategies to solve computationally expensive-to-evaluate blackbox optimization problems. However, BO methods are conventionally used for optimization problems of small dimension…

The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also…

Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic…

Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their…

Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered…

Large language models (LLMs) have revolutionized natural language processing, yet their practical utility is often limited by persistent issues of hallucinations and outdated parametric knowledge. Although post-training model editing offers…

Let $\rho$ be a maximal representation of a uniform lattice $\Gamma\subset{\rm SU}(n,1)$, $n\geq 2$, in a classical Lie group of Hermitian type $H$. We prove that necessarily $H={\rm SU}(p,q)$ with $p\geq qn$ and there exists a holomorphic…

Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

This paper focuses on the problem of unsupervised alignment of hierarchical data such as ontologies or lexical databases. This is a problem that appears across areas, from natural language processing to bioinformatics, and is typically…