Related papers: Shift-invariant spaces on finite undirected graphs

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…

We consider infinite graph-directed iterated function systems (GIFSs) whose contraction mappings are nonconformal. As our main result, we formulate asymptotic perturbations from conformal GIFSs to nonconformal GIFSs, and give the asymptotic…

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…

A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…

Graph Neural Networks (GNNs) have recently been explored as surrogate models for numerical simulations. While their applications in computational fluid dynamics have been investigated, little attention has been given to structural problems,…

We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded…

The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…

Graph similarity measurement, which computes the distance/similarity between two graphs, arises in various graph-related tasks. Recent learning-based methods lack interpretability, as they directly transform interaction information between…

Stacked intelligent surfaces (SIS) are a promising technology for next-generation wireless systems, offering an opportunity to enhance communication performance with low power consumption. Typically, an SIS is modelled as a surface that…

Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through…

We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…

Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from…

Infrared and visible image fusion aims to extract complementary features to synthesize a single fused image. Many methods employ convolutional neural networks (CNNs) to extract local features due to its translation invariance and locality.…

Invariant learning demonstrates substantial potential for enhancing the generalization of graph neural networks (GNNs) with out-of-distribution (OOD) data. It aims to recognize stable features in graph data for classification, based on the…

This paper investigates the geometrical structures of invariant graphs of skew product systems of the form $F : \Theta \times I \to \Theta \times I , (\theta,y)\mapsto (S\theta,f_\theta(y))$ driven by a hyperbolic base map $S : \Theta \to…

This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…

Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center (SI/Z), we develop a notion of periodization on the group Fourier transform side, and use this notion to…

Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically-driven fluid flows. These barriers were called…

Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…