Related papers: On Upper Bounding Shannon Capacity of Graph Throug…
Graph Neural Networks (GNNs) show promising results for graph tasks. However, existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. The cardinal impetus underlying…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
The theory of graph limits represents large graphs by analytic objects called graphons. Graph limits determined by finitely many graph densities, which are represented by finitely forcible graphons, arise in various scenarios, particularly…
The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…
We study quantum versions of the Shannon capacity of graphs and non-commutative graphs. We introduce the asymptotic spectrum of graphs with respect to quantum and entanglement-assisted homomorphisms, and we introduce the asymptotic spectrum…
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of…
We compute Shannon capacity of nonlinear channels with regenerative elements. Conditions are found under which capacity of such nonlinear channels is higher than the Shannon capacity of the classical linear additive white Gaussian noise…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are…
Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability,…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…