Related papers: Improving Expressive Power of Spectral Graph Neura…
This paper introduces a structured, adaptive-length deep representation called Neural Eigenmap. Unlike prior spectral methods such as Laplacian Eigenmap that operate in a nonparametric manner, Neural Eigenmap leverages NeuralEF to…
We introduce Spectral NSR, a fully spectral neuro-symbolic reasoning framework that embeds logical rules as spectral templates and performs inference directly in the graph spectral domain. By leveraging graph signal processing (GSP) and…
Recent studies suggest that artificial neural networks (ANNs) that match the spectral properties of the mammalian visual cortex -- namely, the $\sim 1/n$ eigenspectrum of the covariance matrix of neural activities -- achieve higher object…
This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace-Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We then define spectral filters…
Graph Neural Networks (GNNs), known as spectral graph filters, find a wide range of applications in web networks. To bypass eigendecomposition, polynomial graph filters are proposed to approximate graph filters by leveraging various…
The study of Graph Neural Networks has received considerable interest in the past few years. By extending deep learning to graph-structured data, GNNs can solve a diverse set of tasks in fields including social science, chemistry, and…
While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making…
While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…
We propose and study Hierarchical Ego Graph Neural Networks (HEGNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for isomorphism…
Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman…
Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power…
The eigenvalues of the normalized Laplacian matrix of a network plays an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…
Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Graph representation learning has now become the de facto standard when handling graph-structured data, with the framework of message-passing graph neural networks (MPNN) being the most prevailing algorithmic tool. Despite its popularity,…
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of…
Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning research. In this paper, we replace the output activation function of DNNs, typically the…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive…