Related papers: Gauging tensor networks with belief propagation

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…

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…

Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…

We extend Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariates, that take…

We study the belief propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global…

As belief networks are used to model increasingly complex situations, the need to automatically construct them from large databases will become paramount. This paper concentrates on solving a part of the belief network induction problem:…

In this paper, we propose an alternative for routing based packet forwarding, which uses network coding to increase transmission efficiency, in terms of both compression and error resilience. This non-adaptive encoding is called quantized…

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…

Compared to sequential learning models, graph-based neural networks exhibit some excellent properties, such as ability capturing global information. In this paper, we investigate graph-based neural networks for text classification problem.…

We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…

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 present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…

We present a novel distributed Gauss-Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially…

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…

We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in…

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…

In Bayesian networks, exact belief propagation is achieved through message passing algorithms. These algorithms (ex: inward and outward) provide only a recursive definition of the corresponding messages. In contrast, when working on hidden…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…