Related papers: Representation Tradeoffs for Hyperbolic Embeddings

Hyperbolic metamaterials are strongly anisotropic artificial composite materials at a subwavelength scale and can greatly widen the engineering feasibilities for manipulation of wave propagation. However, limited by the empirical structure…

Hyperbolic Neural Networks (HNNs), operating in hyperbolic space, have been widely applied in recent years, motivated by the existence of an optimal embedding in hyperbolic space that can preserve data hierarchical relationships (termed…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…

Image-text representation learning forms a cornerstone in vision-language models, where pairs of images and textual descriptions are contrastively aligned in a shared embedding space. Since visual and textual concepts are naturally…

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…

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…

In existing models and embedding methods of networked systems, node features describing their qualities are usually overlooked in favor of focusing solely on node connectivity. This study introduces $FiD$-Mercator, a model-based ultra-low…

The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…

Embeddings serve as condensed vector representations for real-world entities, finding applications in Natural Language Processing (NLP), Computer Vision, and Data Management across diverse downstream tasks. Here, we introduce novel…

A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.

Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…

We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the Popularity$\times$Similarity…

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely…

Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings…