Related papers: Navigating Higher Dimensional Spaces using Hyperbo…
A method to visualize polytopes in a four dimensional euclidian space $(x,y,z,w)$ is proposed. A polytope is sliced by multiple hyperplanes that are parallel each other and separated by uniform intervals. Since the hyperplanes are…
Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…
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…
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
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…
3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
With the prevalence of online social media, users' social connections have been widely studied and utilized to enhance the performance of recommender systems. In this paper, we explore the use of hyperbolic geometry for social…
Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset,…
Recent advances in multimodal models have demonstrated impressive capabilities in object recognition and scene understanding. However, these models often struggle with precise spatial localization - a critical capability for real-world…
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…
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…
A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data…
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…
In the present work we intend to introduce a system based on VR (Virtual Reality) for examining analytical-geometric structures that occur in the study of mathematics and physics concepts in the last high school classes. In our opinion, an…
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases…
Hierarchical Topic Models (HTMs) are useful for discovering topic hierarchies in a collection of documents. However, traditional HTMs often produce hierarchies where lowerlevel topics are unrelated and not specific enough to their…
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…
Mediated by today's visual displays, information space allows users to discover, access and interact with a wide range of digital and physical information. The information presented in this space may be digital, physical or a blend of both,…
This is an expository article on visual metrics on boundaries of hyperbolic metric spaces. We discuss the construction of visual metrics, quasisymmetries and their invariants, Hausdorff and conformal dimension, and constructions and…