Related papers: Navigating Higher Dimensional Spaces using Hyperbo…

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…

Graph based representation is widely used in visual tracking field by finding correct correspondences between target parts in consecutive frames. However, most graph based trackers consider pairwise geometric relations between local parts.…

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…

Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…

How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways of introducing non-Euclidean geometry to…

Hyperbolic space can naturally embed hierarchies that often exist in real-world data and semantics. While high-dimensional hyperbolic embeddings lead to better representations, most hyperbolic models utilize low-dimensional embeddings, due…

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

Astronomical researchers often think of analysis and visualization as separate tasks. In the case of high-dimensional data sets, though, interactive exploratory data visualization can give far more insight than an approach where data…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…

The quest for deeper understanding of biological systems has driven the acquisition of increasingly larger multidimensional image datasets. Inspecting and manipulating data of this complexity is very challenging in traditional visualization…

Virtual Reality enables the exploration of large information spaces. In physically constrained spaces such as airplanes or buses, controller-based or mid-air interaction in mobile Virtual Reality can be challenging. Instead, the input space…

Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…

As digital worlds become ubiquitous via video games, simulations, virtual and augmented reality, people with disabilities who cannot access those worlds are becoming increasingly disenfranchised. More often than not the design of these…

Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…