Related papers: Hyperbolic Manifold Regression
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
Taxonomic classification in biodiversity research involves organizing biological specimens into structured hierarchies based on evidence, which can come from multiple modalities such as images and genetic information. We investigate whether…
Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of…
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…
Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…
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,…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…
Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…
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…
For image segmentation, the current standard is to perform pixel-level optimization and inference in Euclidean output embedding spaces through linear hyperplanes. In this work, we show that hyperbolic manifolds provide a valuable…
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…
Many real-world networks exhibit hierarchical, tree-like structure and heavy-tailed degree distributions, phenomena not readily captured by standard statistical models for network data. Extensions of the popular continuous latent space…
Hyperbolic space is becoming a popular choice for representing data due to the hierarchical structure - whether implicit or explicit - of many real-world datasets. Along with it comes a need for algorithms capable of solving fundamental…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
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…
Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and…
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…
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…