Related papers: A Geometry-Aware Algorithm to Learn Hierarchical E…

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…

For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric…

In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

The main objective of Knowledge Graph (KG) embeddings is to learn low-dimensional representations of entities and relations, enabling the prediction of missing facts. A significant challenge in achieving better KG embeddings lies in…

A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically…

Recent work has demonstrated that embeddings of tree-like graphs in hyperbolic space surpass their Euclidean counterparts in performance by a large margin. Inspired by these results and scale-free structure in the word co-occurrence graph,…

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,…

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,…

Learning unbiased node representations for imbalanced samples in the graph has become a more remarkable and important topic. For the graph, a significant challenge is that the topological properties of the nodes (e.g., locations, roles) are…

In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual…

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…

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…

Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This…

Visual geolocalization, the task of predicting where an image was taken, remains challenging due to global scale, visual ambiguity, and the inherently hierarchical structure of geography. Existing paradigms rely on either large-scale…

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…

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…

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…

Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data. In this paper, we explore a new method…

Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully.…