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Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple…

Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We…

Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…

This paper studies the problem of learning message propagation strategies for graph neural networks (GNNs). One of the challenges for graph neural networks is that of defining the propagation strategy. For instance, the choices of…

The radio wave propagation channel is central to the performance of wireless communication systems. In this paper, we introduce a novel machine learning-empowered methodology for wireless channel modeling. The key ingredients include a…

We study the behavior of the belief-propagation (BP) algorithm affected by erroneous data exchange in a wireless sensor network (WSN). The WSN conducts a distributed binary hypothesis test where the joint statistical behavior of the sensor…

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…

Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…

Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and…

Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…

Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class…

Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…

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…

Bayesian inference offers a principled account of information processing in natural agents. However, it remains an open question how neural mechanisms perform their abstract operations. We investigate a hypothesis where a distributed form…

Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide…

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics.…

Spreading models capture key dynamics on networks, such as cascading failures in economic systems, (mis)information diffusion, and pathogen transmission. Here, we focus on design intervention problems -- for example, designing optimal…

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…