Related papers: Global and Local Uncertainty Principles for Signal…

The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent…

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…

Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based…

Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in…

Within the Heisenberg's uncertainty principle it is explicitly discussed the impact of these inequalities on the theory of integrated photonics at sub-wavelength regime. More especially, the uncertainty of the effective index values in…

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…

We consider a problem of localizing a path-signal that evolves over time on a graph. A path-signal can be viewed as the trajectory of a moving agent on a graph in several consecutive time points. Combining dynamic programming and graph…

Spatiotemporal prediction plays a critical role in numerous real-world applications such as urban planning, transportation optimization, disaster response, and pandemic control. In recent years, researchers have made significant progress by…

The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg…

In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…

In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications…

Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…

Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for…

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…