Related papers: Gauging tensor networks with belief propagation

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…

We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two…

The Lattice Gauge Theory Hilbert space is divided into gauge-invariant sectors selected by the background charges. Such a projector can be directly embedded in a tensor network ansatz for gauge-invariant states as originally discussed in…

Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…

Graph neural networks (GNNs) have exhibited exceptional efficacy in a diverse array of applications. However, the sheer size of large-scale graphs presents a significant challenge to real-time inference with GNNs. Although existing Scalable…

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…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

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…

We propose a fast real-time state estimator based on the belief propagation algorithm for the power system state estimation. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and…

This paper proposes a novel, algorithm-independent approach to optimizing belief network inference. rather than designing optimizations on an algorithm by algorithm basis, we argue that one should use an unoptimized algorithm to generate a…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…

Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…

Recent work by Zymnis et al. proposes an efficient primal-dual interior-point method, using a truncated Newton method, for solving the network utility maximization (NUM) problem. This method has shown superior performance relative to the…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…

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…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks.…