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Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…

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,…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like \textit{HGCAE},…

Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…

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…

The recent reconstruction of the Drosophila brain provides a neural network of unprecedented size and level of details. In this work, we study the geometrical properties of this system by applying network embedding techniques to the graph…

Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides…

Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…

Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…

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…

HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the…

Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly…

Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for…

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…

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,…

The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like…

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…

Hyperbolic space is a natural setting for mining and visualizing data with hierarchical structure. In order to compute a hyperbolic embedding from comparison or similarity information, one has to solve a hyperbolic distance geometry…

Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation…