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It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…

Constraint programming is a general and exact method based on constraint propagation and backtracking search. We provide a function decomposing a constraint network into a ternary constraint network (TCN) with a reduced number of operators.…

We consider spectrally-efficient communication over a Rayleigh N-block-fading channel with a K- sparse L-length discrete-time impulse response (for 0<K<L<N), where neither the transmitter nor receiver know the channel's coefficients nor its…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

Classification is one of the most important problems in machine learning. To address label scarcity, semi-supervised learning (SSL) has been intensively studied over the past two decades, which mainly leverages data affinity modeled by…

Graph neural networks (GNNs) have recently received significant attention. Learning node-wise message propagation in GNNs aims to set personalized propagation steps for different nodes in the graph. Despite the success, existing methods…

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and…

We consider the problem of packing node-disjoint directed paths in a directed graph. We consider a variant of this problem where each path starts within a fixed subset of root nodes, subject to a given bound on the length of paths. This…

Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…

Recently, the method that learns networks layer by layer has attracted increasing interest for its ease of analysis. For the method, the main challenge lies in deriving an optimization target for each layer by inversely propagating the…

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…

An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…

Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice…

The algorithms based on message passing neural networks (MPNNs) on graphs have recently achieved great success for various graph applications. However, studies find that these methods always propagate the information to very limited…

In this paper, we innovately use graph neural networks (GNNs) to learn a message-passing solution for the inference task of massive multiple multiple-input multiple-output (MIMO) detection in wireless communication. We adopt a graphical…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

The mechanism of message passing in graph neural networks (GNNs) is still mysterious. Apart from convolutional neural networks, no theoretical origin for GNNs has been proposed. To our surprise, message passing can be best understood in…

Graph Neural Networks (GNNs) have achieved tremendous success in graph representation learning. Unfortunately, current GNNs usually rely on loading the entire attributed graph into network for processing. This implicit assumption may not be…

Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on…