Related papers: A group-theoretic framework for machine learning i…

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…

The exponential volume growth of hyperbolic geometry can embed the hierarchical relationships between states in reinforcement learning (RL) with far less distortion than Euclidean space. However, hyperbolic deep RL faces severe optimization…

Hyperbolic space is increasingly used for hierarchical, tree-like, and network-structured data, but likelihood-based density modeling on hyperbolic space remains relatively limited. This paper develops finite mixture modeling with isotropic…

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with…

Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…

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…

Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric…

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…

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is…

Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…

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…

The symmedian point of a triangle enjoys several geometric and optimality properties, which also serve to define it. We develop a new dynamical coordinatization of the symmedian, which naturally generalizes to other ideal hyperbolic…

Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…

The purpose of this review is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the solution representation of the solution. A general theory is difficult. We discuss…

Hierarchical reinforcement learning deals with the problem of breaking down large tasks into meaningful sub-tasks. Autonomous discovery of these sub-tasks has remained a challenging problem. We propose a novel method of learning sub-tasks…

Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

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…

The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…