Related papers: Numerical Aspects of Hyperbolic Geometry

Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…

This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the…

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…

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…

Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…

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…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hyperbolic space has recently gained rapid traction for learning…

Consider the Poincare disc model for hyperbolic geometry. In this paper, a convenient computational formula is developed along with an aesthetic geometric interpretation. Two proofs, one geometric and one analytical, of each result are…

Representation of 2D frame less visual space as neural manifold and its modelling in the frame work of information geometry is presented. Origin of hyperbolic nature of the visual space is investigated using evidences from neuroscience.…

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…

This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…