Related papers: Cartan Networks: Group theoretical Hyperbolic Deep…

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…

Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…

We relate three classes of nonpositively curved metric spaces: hierarchically hyperbolic spaces, coarsely injective spaces, and strongly shortcut spaces. We show that every hierarchically hyperbolic space admits a new metric that is…

In heterogeneous graphs, we can observe complex structures such as tree-like or hierarchical structures. Recently, the hyperbolic space has been widely adopted in many studies to effectively learn these complex structures. Although these…

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper,…

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…

Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…

We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one…

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…

Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data structures prevalent in real-world datasets. Notably, residual connections, which facilitate the direct flow of information across layers, have been…

This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…

To leverage the complex structures within heterogeneous graphs, recent studies on heterogeneous graph embedding use a hyperbolic space, characterized by a constant negative curvature and exponentially increasing space, which aligns with the…

Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric…