Related papers: Loop Series Expansions for Tensor Networks

In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief…

Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a…

We propose a tensor generalized approximate message passing (TeG-AMP) algorithm for low-rank tensor inference, which can be used to solve tensor completion and decomposition problems. We derive TeG-AMP algorithm as an approximation of the…

Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art…

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…

We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

In this paper, relaxed belief propagation (RBP) based detectors are proposed for multiple-input multiple-out (MIMO) system. The factor graph is leveraged to represent the MIMO channels, and based on which our algorithms are developed.…

How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels…

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…

Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a…

Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random…

It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum…

We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an $N \times M$ square-lattice PEPs network, for arbitrary $M$, of bond dimension $2$…

In this note we study an iterative belief propagation (IBP) algorithm and demonstrate it's ability to solve sparse combinatorial optimization problems. Similar to simulated annealing (SA), our IBP algorithm attempts to sample from the…

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…

Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap,…

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case…

The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…