Related papers: Hyperbolic Delaunay Geometric Alignment

Hypergraph Neural Networks (HyGNNs) have demonstrated remarkable success in modeling higher-order relationships among entities. However, their performance often degrades on heterophilic hypergraphs, where nodes connected by the same…

In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free…

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling…

Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…

We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…

Digraph Representation Learning (DRL) aims to learn representations for directed homogeneous graphs (digraphs). Prior work in DRL is largely constrained (e.g., limited to directed acyclic graphs), or has poor generalizability across tasks…

Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However such approaches, similar to other surface based brain morphology analysis methods, usually…

Deep learning in hyperbolic space is quickly gaining traction in the fields of machine learning, multimedia, and computer vision. Deep networks commonly operate in Euclidean space, implicitly assuming that data lies on regular grids. Recent…

In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph…

Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is…

Existing unsupervised deep product quantization methods primarily aim for the increased similarity between different views of the identical image, whereas the delicate multi-level semantic similarities preserved between images are…

Grain boundaries (GBs) can critically influence the microstructural evolution and various materials properties. However, a fundamental understanding of GBs in high-entropy alloys (HEAs) is lacking because of the complex couplings of the…

Hyperbolic neural networks can effectively capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them…

Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This…

Many real-world graphs involve different types of nodes and relations between nodes, being heterogeneous by nature. The representation learning of heterogeneous graphs (HGs) embeds the rich structure and semantics of such graphs into a…

From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an…

The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…

Hierarchical data arise in countless domains, from biological taxonomies and organizational charts to legal codes and knowledge graphs. Residual Quantization (RQ) is widely used to generate discrete, multitoken representations for such data…

While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals.…

Deep learning approaches deliver state-of-the-art performance in recognition of spatiotemporal human motion data. However, one of the main challenges in these recognition tasks is limited available training data. Insufficient training data…