Related papers: Hyperbolic Busemann Neural Networks
We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new…
The emergence of Deep Convolutional Neural Networks (DCNNs) has been a pervasive tool for accomplishing widespread applications in computer vision. Despite its potential capability to capture intricate patterns inside the data, the…
Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries…
Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different…
Graph-structured data provide a comprehensive description of complex systems, encompassing not only the interactions among nodes but also the intrinsic features that characterize these nodes. These features play a fundamental role in the…
Clustering is a fundamental unsupervised learning task for uncovering patterns in data. While Gaussian Blurring Mean Shift (GBMS) has proven effective for identifying arbitrarily shaped clusters in Euclidean space, it struggles with…
A collection of $U \: (\in \mathbb{N})$ data vectors is called a $U$-tuple, and the association strength among the vectors of a tuple is termed as the \emph{hyperlink weight}, that is assumed to be symmetric with respect to permutation of…
Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a…
Graph convolutional networks (GCNs) have received considerable research attention recently. Most GCNs learn the node representations in Euclidean geometry, but that could have a high distortion in the case of embedding graphs with…
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,…
Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher-order…
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…
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…
In the paper we introduce a novel bipolar morphological neuron and bipolar morphological layer models. The models use only such operations as addition, subtraction and maximum inside the neuron and exponent and logarithm as activation…
Large Language Models (LLMs) have attracted significant attention in recommender systems for their excellent world knowledge capabilities. However, existing methods that rely on Euclidean space struggle to capture the rich hierarchical…
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…
Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative…
Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the…
Universal approximation theorems show that neural networks can approximate any continuous function; however, the number of parameters may grow exponentially with the ambient dimension, so these results do not fully explain the practical…
Taxonomies are valuable resources for many applications, but the limited coverage due to the expensive manual curation process hinders their general applicability. Prior works attempt to automatically expand existing taxonomies to improve…