Related papers: Hyperbolic Delaunay Geometric Alignment
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
We introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space. We show mathematically that hydra satisfies a certain optimality guarantee: It minimizes…
Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…
Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces.…
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure.…
Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix…
Hypernetwork is a useful way to depict multiple connections between nodes, making it an ideal tool for representing complex relationships in network science. In recent years, there has been a marked increase in studies on hypernetworks,…
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…
We consider the task of representation learning for unsupervised segmentation of 3D voxel-grid biomedical images. We show that models that capture implicit hierarchical relationships between subvolumes are better suited for this task. To…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
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…
Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…
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…
Hyperbolic representation learning has been widely used to extract implicit hierarchies within data, and recently it has found its way to the open-world classification task of Generalized Category Discovery (GCD). However, prior hyperbolic…
This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius…
Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex…
Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…
Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…
Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image…