Related papers: AdS-GNN -- a Conformally Equivariant Graph Neural …
Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and…
Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs,…
In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically…
We propose the use of group convolutional neural network architectures (GCNNs) equivariant to the 2D Euclidean group, $E(2)$, for the task of galaxy morphology classification by utilizing symmetries of the data present in galaxy images as…
Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…
Graph Similarity Computation (GSC) is a fundamental graph related task where Graph Edit Distance (GED) serves as a prevalent metric. GED is determined by an optimal alignment between a pair of graphs that partitions each into aligned…
Convolutional Neural Networks (CNNs) can play a key role in Medical Image Analysis under large-scale annotated datasets. However, preparing such massive dataset is demanding. In this context, Generative Adversarial Networks (GANs) can…
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high…
Graph Neural Networks (GNNs) have achieved impressive performance in collaborative filtering. However, GNNs tend to yield inferior performance when the distributions of training and test data are not aligned well. Also, training GNNs…
This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy…
Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…
One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…
Predicting edge weights on graphs has various applications, from transportation systems to social networks. This paper describes a Graph Neural Network (GNN) approach for edge weight prediction with guaranteed coverage. We leverage…
We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We…