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Graph Neural Networks (GNNs) are the subject of intense focus by the machine learning community for problems involving relational reasoning. GNNs can be broadly divided into spatial and spectral approaches. Spatial approaches use a form of…

Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…

Even though the TCP/IP architecture has served the Internet quite satisfactorily during its more than forty years of lifespan, there are doubts about whether this host-centric paradigm is well suited for the communication patterns of modern…

Imaging through scattering is an important, yet challenging problem. Tremendous progress has been made by exploiting the deterministic input-output "transmission matrix" for a fixed medium. However, this "one-to-one" mapping is highly…

A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…

The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…

Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix…

The group testing problem asks for efficient pooling schemes and algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected samples while conducting the least…

The Message-Passing Approach (MPA) is the state-of-the-art technique to obtain quasi-analytical predictions for percolation on real complex networks. Besides being intuitive and straightforward, it has the advantage of being mathematically…

Label propagation is a heuristic method initially proposed for community detection in networks, while the method can be adopted also for other types of network clustering and partitioning. Among all the approaches and techniques described…

The advancement of deep convolutional neural networks (DCNNs) has driven significant improvement in the accuracy of recognition systems for many computer vision tasks. However, their practical applications are often restricted in…

Interpretability techniques in NLP have mainly focused on understanding individual predictions using attention visualization or gradient-based saliency maps over tokens. We propose using k nearest neighbor (kNN) representations to identify…

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…

The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…

In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A neural network architecture suitable for detection task is firstly introduced…

Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is…

To infer multilayer deep representations of high-dimensional discrete and nonnegative real vectors, we propose an augmentable gamma belief network (GBN) that factorizes each of its hidden layers into the product of a sparse connection…

Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…

Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations (belief-propagation and TAP equations) in the best understood such machine, namely…