Related papers: Klein Model for Hyperbolic Neural Networks

We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

Recently hyperbolic geometry has proven to be effective in building embeddings that encode hierarchical and entailment information. This makes it particularly suited to modelling the complex asymmetrical relationships between Chinese…

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…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with…

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…

Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce…

It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…

While machine learning (ML) has found multiple applications in photonics, traditional "black box" ML models typically require prohibitively large training data sets. Generation of such data, as well as the training processes themselves,…

Scalable and symmetry-consistent force-field models are essential for extending quantum-accurate simulations to large spatiotemporal scales. While descriptor-based neural networks can incorporate lattice symmetries through carefully…

Many AI-related tasks involve the interactions of data in multiple modalities. It has been a new trend to merge multi-modal information into knowledge graph(KG), resulting in multi-modal knowledge graphs (MMKG). However, MMKGs usually…

Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

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…

Convolutional Neural Networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation…

Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but employ reservoirs whose Euclidean geometry is mismatched to…

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…