Related papers: Warning Propagation on random graphs

Random unitary circuits have become a model system to investigate information scrambling in quantum systems. In the literature, mostly random circuits with Haar-distributed gate operations have been considered. In this work, we investigate…

Label propagation has proven to be a fast method for detecting communities in complex networks. Recent work has also improved the accuracy and stability of the basic algorithm, however, a general approach is still an open issue. We propose…

We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time…

Graph Convolution Network (GCN) has been widely applied in recommender systems for its representation learning capability on user and item embeddings. However, GCN is vulnerable to noisy and incomplete graphs, which are common in real…

Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…

Graph Neural Networks (GNNs) have seen significant advances in recent years, yet their application to multigraphs, where parallel edges exist between the same pair of nodes, remains under-explored. Standard GNNs, designed for simple graphs,…

Graph neural networks (GNNs) provide important prospective insights in applications such as social behavior analysis and financial risk analysis based on their powerful learning capabilities on graph data. Nevertheless, GNNs' predictive…

Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation…

Experimental validation of chemical processes is slow and costly, limiting exploration in materials discovery. Machine learning can prioritize promising candidates, but existing data in patents and literature is heterogeneous and difficult…

The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer…

We propose to learn a kernel-based message operator which takes as input all expectation propagation (EP) incoming messages to a factor node and produces an outgoing message. In ordinary EP, computing an outgoing message involves estimating…

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

Constructing appropriate representations of molecules lies at the core of numerous tasks such as material science, chemistry and drug designs. Recent researches abstract molecules as attributed graphs and employ graph neural networks (GNN)…

Graph Neural Network (GNN) resembles the diffusion process, leading to the over-smoothing of learned representations when stacking many layers. Hence, the reverse process of message passing can produce the distinguishable node…

Graph spanners are sparse subgraphs which approximately preserve all pairwise shortest-path distances in an input graph. The notion of approximation can be additive, multiplicative, or both, and many variants of this problem have been…

Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…