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Foundation models are pretrained on large-scale corpora to learn generalizable patterns across domains and tasks -- such as contours, textures, and edges in images, or tokens and sentences in text. In contrast, discovering such generalities…

Exhibiting a deep connection between purely geometric problems and real algebra, the complexity class $\exists \mathbb{R}$ plays a crucial role in the study of geometric problems. Sometimes $\exists \mathbb{R}$ is referred to as the 'real…

The \emph{generalized sorting problem} is a restricted version of standard comparison sorting where we wish to sort $n$ elements but only a subset of pairs are allowed to be compared. Formally, there is some known graph $G = (V, E)$ on the…

It is by now a well known fact in the graph learning community that the presence of bottlenecks severely limits the ability of graph neural networks to propagate information over long distances. What so far has not been appreciated is that,…

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…

We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A* search and heuristics derived…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

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…

The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…

Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…

Graph Neural Networks (GNNs) are proposed without considering the agnostic distribution shifts between training and testing graphs, inducing the degeneration of the generalization ability of GNNs on Out-Of-Distribution (OOD) settings. The…

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their…

Graph neural networks (GNNs) have achieved great success in many graph learning tasks. The main aspect powering existing GNNs is the multi-layer network architecture to learn the nonlinear graph representations for the specific learning…

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…

Communication networks are important infrastructures in contemporary society. There are still many challenges that are not fully solved and new solutions are proposed continuously in this active research area. In recent years, to model the…

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…

Finding dense subgraphs of a large network is a fundamental problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications over the last five decades. However, most existing…

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

Let $G$ be a graph in which each vertex initially has weight 1. In each step, the weight from a vertex $u$ to a neighbouring vertex $v$ can be moved, provided that the weight on $v$ is at least as large as the weight on $u$. The total…