Related papers: Message passing on networks with loops
Message passing equations yield a sharp percolation transition in finite graphs, as an artifact of the locally treelike approximation. For an arbitrary finite, connected, undirected graph we construct an infinite tree having the same local…
Given its computational efficiency and versatility, belief propagation is the most prominent message passing method in several applications. In order to diminish the damaging effect of loops on its accuracy, the first explicit version of…
Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this…
The message passing framework is the foundation of the immense success enjoyed by graph neural networks (GNNs) in recent years. In spite of its elegance, there exist many problems it provably cannot solve over given input graphs. This has…
Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
The paper presents a solution to the problem of universal representation of graphs exemplifying communication network topologies with the help of neural networks. The proposed approach is based on message-passing neural networks (MPNN). The…
In this paper we initiate an approach that deals with the problem of calculating average properties of messages traveling on networks, by employing concepts and methods that are used for the study of the many-body problem in the field of…
Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…
The trust in the predictions of Graph Neural Networks is limited by their opaque reasoning process. Prior methods have tried to explain graph networks via concept-based explanations extracted from the latent representations obtained after…
Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes…
Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to…
Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…
One model of message delivery in a computer network is based on labelling each edge by a subset of a (reasonably small) universal set, and then encoding a path as the union of the labels of its edges. Earlier work suggested using random…
Message passing is a fundamental procedure for graph neural networks in the field of graph representation learning. Based on the homophily assumption, the current message passing always aggregates features of connected nodes, such as the…
Message-passing (MP) is a powerful tool for finding an approximate solution in optimization. We generalize it to nonlinear product-sum form, and numerically show the fast convergence for the minimum feedback vertex set and the minimum…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. This is also known as convex/convergent…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…