Related papers: Klein Model for Hyperbolic Neural Networks
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
We propose a data structure in $d$-dimensional hyperbolic space that can be considered a natural counterpart to quadtrees in Euclidean spaces. Based on this data structure we propose a so-called L-order for hyperbolic point sets, which is…
We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…
Bitcoin transaction networks are large scale socio- technical systems in which activities are represented through multi-hop interaction patterns. Graph Neural Networks(GNNs) have become a widely adopted tool for analyzing such systems,…
We consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's non-interacting limit. We map this system to a…
We show that a neural network, trained on the entanglement spectra of a nearest neighbor Heisenberg chain in a random transverse magnetic field, can be used to efficiently study the ergodic/many-body localized properties of a number of…
Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers…
Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design…
This paper investigates the self-similar solutions of the Einstein-axion-dilaton configuration from type IIB string theory and the global SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the scale transformation is…
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…
Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones…
While hyperbolic GNNs show promise for hierarchical data, they often have limited discriminative power compared to Euclidean counterparts or the WL test, due to non-injective aggregation. To address this expressivity gap, we propose the…
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to…
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…
Learning task-specific representations of persistence diagrams is an important problem in topological data analysis and machine learning. However, current state of the art methods are restricted in terms of their expressivity as they are…
The article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
We describe in this paper a geometric construction in the projective p-adic plane that gives, together with a suitable notion of p-adic convexity, some open subsets of P 2 .Q p / naturally endowed with a "Hilbert" distance and a transitive…
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 neural networks have emerged as a powerful tool for modeling hierarchical data across diverse modalities. Recent studies show that token distributions in foundation models exhibit scale-free properties, suggesting that hyperbolic…